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SEMI-ANNUAL STATUS REPORT #9 
TOTHENATIONAL AERONAUTICS AND SPACE ADMINISTKATION 



CRUSTAL DYNAMICS PROJECT 



NASA GRANT NAG 5-814 

"The Interpietation of Crustal Dynamics Data in Terms of Plate 

Motions and Regional Deformation Near Plate Boundanes 

for the period 
22 September 1990 - 21 March 1991 



Principal Investigator: 



Prof. Sean C. Solomon . 

Department of Earth, Atmosphenc, 

and Planetary Sciences 
Massachusetts Institute 

of Technology 
Cambridge, MA 02139 



24 June 1991 



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TABLE OF CONTENTS 

Page 



SUMMARY 

APPENDKl: GPS m«sur.men« of s^ain acaamJabon across U« In,p«i.l Valley. 4 
Califomia: 1986-1989 

APPENDIX 2: GPS measi^mems of defonrnto associaBd wifl. fte 1987 58 

SupostitiooHms earthquake: Evidence for conjugate faulcing 

APPENDlX31..eralvahaaonin„ppern^tle,en,perat««andcomp<»i6onbe^ 148 
^^IL ridges infer^d fton, shear-wave propagation, geoid. and ba.h,™e.ry 

APPENDIX4- ,ou,tinversionofshearw.vetravel.in»residuals,geoid..nddepth 151 
"^ !^lgU«Mid-AtlanticRidgeforlo„g-wavelengthvaria.K>ns.nupper 

mantle temperature and composition 



TT,isis.Se™-ABnu,l status Rep<«o«««.«hoonduc«d between 22 Sep^nber 1990 
»„i 21 Maich 1991 under NASA Gran. NAG 5-814. .n,iU«l Th. Interpreudon of Crustal 
D,™™=sD«a,.TennscfP..«Modcns«v, Region. DefonnadonncarPl^eBound^" 

™s gran, supports ^ research of one Investigator (S. C. Solomon), one Resea^h Staff (R. 
ReUingcr). and two Ph. D. sn^nts (A. F. Sheehan a^l C. J. WoUe, on behalf of the NASA 

Oeodynamics and Crustal Dynamics Programs. 

•n„ focus of theresearch has been in t«,b.o^a«as during themostrecent^-month 

period- (,)thenaturea,^dynamicsoftimeH5ependen.defonnationandstressalo„gma,or 

seismic ^ and (2) the na»e of long-waveiength oceanic geoid anomalies in tenns of 
h„eralvaria.io„sinuppermantlctemper«ureandcompositio„.-n.epri„cip^fmdingsofour 

,«.3„h to date a« described in d,. accompanying appendices, m first two and the fourth are 

p^,sofpapers,ecendysubmi..edforpublicatic„.a.«i*eU.i^i^«heabstrac.ofa,ecenay 

completed Ph.D. thesis supported by this project. 



APPENDIX 1 



GPS measurements of strain accumulation across the Imperial Valley, 

California: 1986-1989 



by S. Larsen and R. Reilinger 



Submitted to yourna/o/GwpMcfl' Research, 1991 



GPS Measurements of Strain Accumulation 
Across the Imperial VaUey, CaUfornia: 
1086-1080 

Abstract 

GPS data collected in southern California from 1986 to 1989 indicate 
considerable strain accumulation across the Imperial Valley. Displacements 
are computed at 29 stations in and near the valley from 1986 to 1988. and at 
11 sites from 1988 to 1989. The earlier measurements indicate 5.9 ± 1.0 
cm/yr right-lateral differential velocity across the valley, although the data 
are heavily influenced by the 1987 Superstition Hills earthquake sequence. 
Some measurements, especially the east-west trending displacements, are 
suspect for large errors. The 1988-1989 GPS displacements are best modeled 
by 5.2 ± 0.9 cm/yr of plate-boundary deformation, but rates calculated from 
conventional geodetic measurements (3.4-4.3 cm/yr) flt the data nearly as 
well. There is evidence from GPS and VLBI observations that the present slip 
rate along the southern San Andreas fault is smaller than the long-term 
geologic estimate, suggesting a lower earthquake potential than is currently 
assumed. The Imperial Valley GPS sites form part of a larger network of 183 
stations spanning an entire cross-section of southern California and northern 
Mexico. Once data from a recent 1990 campaign are fully analyzed and 
integrated with the previous measurements, the strain distribution across the 
San Andreas, San Jacinto, and Elsinore faults will be well established. 



pnr-cr.D'^^'JG PAfiF. BLAMK NOV f'lM'^D 



-206- 



6.1 Introduction 



The Global Positioning System (GPS) is rapidly becoming one of the most 
important tools to study tectonic deformation. Signals from earth-orbiting 
NAVSTAR satellites (NAV.gation Satellite Time And Ranging) are inverted 
to obtain S-dimensional coordinates of geodetic monuments with high 
precision. For crustal deformation studies, the relative position (or baseline) 
between stations is often measured. Under optimal conditions, the typical 
accuracy for a 50 km baseline is about 1 cm in the horizontal and 3 cm in the 
vertical [e.g., Davts ct ai, IQSQJ. The accuracy is significantly degraded from 
pcx^r observing conditions. GPS measurements are used to monitor secular 
deformation such as that associated with plate motion, or to record rapid 
strain fluctuations such as those due to seismic and volcanic activity. 

A prime location for GPS studies is the Imperial Valley of southern-most 
California (Figure 5.1). The valley is one of the most tectonically active 
regions in the state and has been the site of several large earthquakes. In 
fact, GPS monitoring was initiated in 1986 with resurveys in 1988 and 1989. 
GPS station displacements from 1986 to 1988 have been discussed by Larsen 
et ai (1990). These measurements illustrate the effect of the 1987 Superstition 
Hills earthquake sequence, as well as nonseismic displacement components 
attributed to interplate deformation. In the present study we incorporate the 
1989 GPS observations. Station displacements from 1986-1988 and 1988-1989 
are computed and these movements are related to the relative motion between 
the North American and Pacific plates. 

5.2 Seismicity and Tectonics 



-208- 



Figure 5.1: Major faults and seismicity from 1932 to 1990 (Caltech 
Catalog) in the Imperial Valley. Large earthquakes are shown as stars. 
The Brawley Seismic Zone is the region of anomalously high activity 
between the Imperial and San Andreas faults. Major earthquakes include 
the 1940 and 1979 events along the Imperial fault, the 1954 and 1968 
events along the San Jacinto fault, and the 1987 Superstition Hills 
earthquake sequence along the Superstition Hills and Elmore Ranch 



faults* 



-257- 




-288- 



The Imperial Valley (Figure 5.1) is a complex transition zone between 
crustai spreading in the Gulf of California and right-lateral transform motion 
along the San Andreas fault [Lomnitz et ai, 1970; Elders tt ai, 1972). The 
valley is 4-5 million years old and has been filled by up to 5 km of late 
Cenozoic sediments [Fuis et ai, 1982). The structural axis of the valley and 
its major fault systems trend to the northwest, roughly parallel to the 
Pacific-North American plate motion. A significant fraction of the relative 
plate displacement may be accommodated across the valley. 

The Imperial Valley is one of the most seismically active regions of 
California with much of the activity occurring along the Imperial fault and in 
the Brawley Seismic Zone [Johnson and Hill, 1982). Several large earthquakes 
have occurred in and near the Imperial Valley since 1940. The Imperial fault 
ruptured with a Ms 7.1 event in 1940 and a M, 6.6 event in 1979 [C^. 5. G. 5., 
1982). Segments of the San Jacinto fault system broke with a M, 6.2 
earthquake in 1954 (Clark segment) and the 1968 M. 6.5 Borrego Mountain 
event (Coyote Creek segment). The most GPS relevant episode of seismic 
activity occurred recently along the Superstition Hills segment of the San 
Jacinto fault system (e.g., Magtstrale tt ai, 1989). On November 24, 1987, a 
large (Ms 6.2) earthquake occurred along a northeast trending sebmic 
lineament, and was followed 12 hours by a larger event (Ms 6.6) along the 
Superstition Hills fault. 

Conventional geodetic measurements indicate significant displacements 
across the Imperial Valley, inferred to represent interplate deformation. 
Triangulation data averaged from 1941 to 1986 suggest 4.3 cm/yr plate- 
boundary movement oriented N40-W [Snay and Drew, 1988). The observed 



-250- 



deformation is time dependent, with rates of 6.1, 2.1, and 4.5 cm/yr for the 
intervals 1941-1954, 1954-1967, and 1967-1979, respectively. The high 
velocity for the earliest period supports the hypothesis of northwestward 
strain migration following the 1940 earthquake [Thatcher, 1979; Reilingcr, 
1984]. Furthermore, the computed station displacements indicate that north 
of the Imperial fault interplate deformation is distributed over a zone at least 
50 km wide whereas to the south interplate deformation is concentrated 
within a 20 km wide band centered along the Imperial fault. Trilateration 
measurements made by the U.S. Geological Survey from 1972 to 1987 
[Prcscott et ai, 1987a; Prescott et ai, 1987b] indicate 3.45 cm/yr differential 
displacement oriented roughly N40-W between stations on opposite sides of 
the valley. Unlike the increased rate following the 1940 earthquake, these 
measurements reveal no significant change in station velocity after the 1979 
event [Savage cl ai, 1986]. 

New global plate models (NUVEL-1) [DcMets et a/., 1987; DeMets et ai, 
1990] predict the Pacific-North American relative velocity at Imperial Valley 
coordinate (longitude IIS.S'W, latitude 33.0 'N) averaged over the last 
several million years to be 4.7 cm/yr oriented N39.6-W. VLBI observations 
during the 1980's suggest a similar present-day rate (e.g., Clark et a/., 1987; 
Kroger et ai, 1987]. A significant fraction of this motion may be distributed 
along faults in and near the Imperial Valley. 

5.3 GPS Observations 

The data presented here were obtained in a series of GPS field campaigns 
in 1986, 1988, and 1989. Here we provide summaries regarding the collection 



-270- 



and processing of the 1986 and 1988 surveys, discussed in more detail by 
Lar8tn tt ai [l990j, and present a more detailed account of the most recent 
campaign. In all, a total of 32 Imperial Valley stations have been occupied 
more than once between 1986 and 1989 (Table 5.1). 

The National Geodetic Survey (NGS) began GPS observations in southern 
California with a 54 station network in 1986; 42 stations are located in or 
near the Imperial Valley (Figure 5.2). TI-4100 GPS receivers were used for all 
data collection. Each of the 20 days of observation are processed 
independently utilizing the GPS22 software developed at the NGS, with 
satellite orbit parameters provided by the NSWC (Naval Surface Weapons 
Center). The day to day solutions are integrated into one set of station 
coordinates with the geodetic adjustment program DYNAP (DYNamic 
Adjustment Program) [Drew and Snay, 1989). Due to insufficient coverage 
and poor data quality during the 1986 survey, uncertainties are suggested to 
be approximately 1 ppm (parts per million) [Ntugtbauer, 1988). 

During late February and eariy March, 1988, university GPS crews 
(UNAVCO) occupied 19 sites in the Imperial Valley, including 15 marks 
observed in 1986 (Figure 5.2). The following month, the NGS returned to the 
Imperial Valley and reoccupied 21 previously established monuments. TI- 
4100 receivers were used for all measurements. Data from both surveys are 
processed independently with the Bernese GPS software package from the 
University of Bern in Switzerland. For each campaign, the data are combined 
into one multiday solution. Satellite orbits are improved with the aid of 
fiducial observations from Mojave (California), Westford (Massachusetts), and 
Richmond (Florida), made as part of the Cooperative International GPS 



-271- 



Table 5.1 Reoccupied Sutions (1986-1989) 



Station Name 



Abbr. 



Occupation Longitude Latitude Elevation 
1986 1988 1989 ! [sJ 



Acute 1934 

Alamo 

Black Butte NCMN 1982 

Brawiey 2 rm 5 

Calcadco 1954 

Calipatria 2 

Coach 

College 1967 

El Centro 2 1959 

Frink 1934 

GLO Comew 1934 

Hamar 2 1967 

Holt 1924 

Holtville (Alt) 1934 

Imp 1934 

Imperial 1934 

Junction 

Kane 1939 

L 589 1967 

Mack 2 1967 bm reset 

MeUo 3 1967 

Monument Peak NCMN 1983 

Ocotillo NCMN 1982 

Ocotillo 1935 

O&et 217 

Oflaet 224 

Offset 227 

Orient 1939 

Pinyon Flat 

Sandy Beach 

T 1226 

Tamarisk 3 1967 



ACUT 

ALAM 

BLAC 

BRAW 

CALE 

CALI 

COAC 

COLL 

ELEC 

FEIN 

GLOC 

HAMA 

HOLT 

HLTV 

IMP! 

IMPE 

JUNC 

KANE 

L589 

MACK 

MELL 

MONU 

OCOT 

OCTI 

0217 

0224 

0227 

OKIE 

PINY 

SANl 

T122 

TAMA 



•115.6093 

-115.6111 

-115.7198 

-115.5434 

-115.5064 

-115.5088 

-115.4070 

-115.5024 

-115.5622 

-115.6470 

-115.2465 

-115.5007 

-115.3963 

-115.3821 

-115.5698 

-115.5788 

-115.0619 

-115.8237 

-115.7611 

•115.1441 

-115.4653 

-116.4228 

-115.7962 

-116.0017 

-115.3131 

-115.7055 

-115.8173 

-115.4064 

-116.4588 

-115.8344 

-114.8050 

-115.4783 



33.0300 

33.1964 

33.6638 

32.9773 

32.6645 

33.1690 

33.1962 

32.8269 

32.7846 

33.3603 

32.8396 

33.0375 

32.7814 

32.8084 

32.8982 

32.8439 

32.7092 

33.0614 

32.9506 

32.7288 

32.7961 

32.8918 

32.7901 

32.7338 

32.6782 

32.6493 

32.6414 

32.9168 

33.6093 

33.1929 

32.8583 

32.8829 



-80.91 
-72.91 
490.01 
-66.78 
-34.07 
-89.03 
-8.40 
-54.63 
-45.76 
-85.39 
-15.46 
-79.80 
-36.79 
-38.77 
-59.27 
-51.85 
8.35 
10.05 
13.62 
1.20 
-47.00 
1839.41 
-36.43 
111.33 
-17.16 
50.00 
70.64 
-61.36 
1235.88 
•99.92 
141.19 
-68.19 



-272- 



Figure 6.2: GPS stations surveyed in 1986 and 1988. The 1986 
campaign was conducted by the National Geodetic Survey and included 
42 stations in and near the Imperial Valley. The 1988 observations 
consisted of two campaigns, the first by university groups in 
February/March and the second by the National Geodetic Survey in 
March/April. A total of 32 stations were occupied in 1988, of which 29 
were repeat measurements from 1986. Stations mentioned in text are 
indicated. 



-278- 



34 



33.5 



33 




32.5 



GPS 1986 

(June) 

Km 40 

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ocn A 



^' ' ■ ■ ' 



-^^ ^ 

- - - - ^^^ ^ 



^taMMl^^^Mrf^^^MM^^^^I^AiiH>*^«* 



■ I . / ■ 



33.5 - 




32.5 



-117 



-274- 



Network (CIGNET) [Chin, 1987). Since orbit improvement techniques are 
used, the (horizontal) precision for each survey is about ^ 0.03 ppm (sub- 
centimeter) [e.g., Davis tt al., 1989; Dong and Bock, 1989]. The Cartesian 
coordinate differences from the university and NGS surveys are adjusted by 
least squares to obtain station positions for 1988. 

During March, 1989, university groups occupied 28 geodetic marks in the 
vicinity of the Imperial Valley, 19 of which were previously surveyed in 1986 
or 1988 (Table 5.2, Figure 5.3). Several new marks were established north of 
the Salton Sea in the Coachella Valley. While most data were collected with 
TI-4100 GPS instruments, this campaign differed from previous surveys in 
that Trlmble-4000SD receivers were used at some sites. The field experiment 
was conducted at a time of anomalously high solar flare activity which 
created large ionospheric disturbances [Jackson tt al, 1989). The ionosphere 
creates a frequency dependent delay for the GPS multi-signal structure, 
composed of two carrier phase transmissions at 1575.42 MHz (Ll) and 1227.60 
MHz (L2) [e.g., King tt ai, 1985). For dual frequency observations (Ll and 
L2) the ionospheric contribution (error) is removed by an appropriate 
combination of the two phase observables. However, if only single frequency 
measurements are available (either intentionally or due to poor observing 
conditions), the positioning accuracy on all but the shortest baselines will be 
seriously degraded. The 1989 phase observations contain a disproportionate 
number of cycle slips and data gaps, presumably due to the poor ionospheric 
conditions. The TI-4100 instruments generally collected both the Ll and L2 
phase signals, so the ionospheric effect could be eliminated. The Trimble 
4000SD receivers, however, experienced significant difficulty maintaining 



-276- 



Table 5.2 Imperial Valley GPS Occupation History (1989) 



Day 








Stations 








65 


OCOT 


PINY' 


MONU 


BLAC 


ROBO 


EXTR' 


COAC 


66 


OCOT 


PINY' 


MONU 


BLAC 


ROBO 


extk' 


COAC 


67 


OCOT 


PINY' 


MONU 


BLAC 




YARN 


SANl' 


68 


OCOT 


THAN' 


FRIN 




COCH 


YARN 


SANl' 


69 


OCOT 


THAN' 


FRIN 


DUN? 


COCH 


GSLOC' 


YORO' 


70 


OCOT 


THAN' 


ALAM 


DUN? 


ROBO 


GLOC 


YORO' 


72 


OCOT 


KANE 


ALAM 


L589 


TAMA» 


GLOC 




73 


OCOT 


KANE 


0217' 


L58g 


TAMA' 




ACUT' 


74 


OCOT 


BORD 


0217' 


ORE 




SIPH 


ACUT' 


75 


OCOT 


BORD' 


CAU 


ORE 


TAMA' 


SIPH 




78 


OCOT 


JUNC 


COLL' 


HAMA' 


TAMA' 


SIPH 


SANl 


77 




JUNC 


COLL 


ORE' 


TAMA' 


GLOC 


SANl 



Day is Julian day of year 
^ Trimble 4000SD 



.27ft- 



Figure 5.3: Imperial Valley GPS stations surveyed in 1989. TI-4100 
GPS receivers (triangles) were used at most sites. Trimble 4000sd 
receivers (open circles) were also used. Thirty sites were occupied; 10 for 
the first time. Due to very poor ionospheric conditions, data collected 
with the Trimble 4000SD receivers are not discussed here. 



-277- 



05 

CO ^ 

CO S 

O 



Q 
CO 

o 
o 

o 



gg 



^ / 



< 
o 

< 

5 



< 

< 

< 




in 



4 


* / 


o 




; • 


\ ~ 


o 


\ 




-278- 



phase-lock on the L2 frequency (it is found that newer Trimble models, 
specifically the 4000SDT, are not as susceptible to solar activity). In fact, 
between 30-60 percent of the L2 data (Trimble 4000SD) was lost. It is 
unlikely that the centimeter level accuracy required for this study could be 
achieved solely with the Ll frequency. Therefore, data collected with Trimble 
4000SD instruments are not considered, although we are currently working on 
schemes to utilize these measurements through ionospheric modeling 
constrained by the dual frequency TI-4100 data. Continental fiducial phase 
observations from the CIGNET tracking sites were either nonexistent or of 
extremely poor quality, presumably due to the unfortunate ionospheric 
conditions. We were therefore not able to apply orbit imp,x,vement 
techniques so a multiday solution is obtained with the Bernese software 
utilizing the broadcast orbits. Positioning errors from the broadcast 
ephemerides are believed to be 0.1-1.0 ppm. 

5.4 GPS Displacements 

GPS vector displacements for the intervals 1986-1988 and 1988-1989 are 
shown in Figures 5.4 and 5.5, respectively. All measurements are made 
relative to station OCT!. Formal estimates of GPS uncertainty almost 
always underestimate variances derived from repeatability studies. We 
attempt to define more realistic errors by multiplying the structure of the 
formal covariance matrix calculated with the GPS solution by an estimated 
variance factor, which scales as the average baseline length. For the 1986- 
1988 displacements, we assume a variance factor so that the average baseline 
error is 5 cm, or 1 ppm for a 50 km baseline. The large uncertainty is due to 



-27«. 

the poor quality of the 1986 data- For the 1988-1989 displacements, the 
average baseline error is assumed 2 cm, or 0.4 ppm for a 50 km baseline. The 
largest component of uncertainty is attributed to the broadcast orbits used 
for the 1989 solution. Larscn tt ai [1990] found 1-3 cm discrepancies between 
broadcast and improved-orbit solutions in a similar sized network spanning 
the Santa Barbara channel. This approach, albeit somewhat ad hoc, allows 
for self consistent relative errors and it illustrates the much larger 
uncertainties in the east-west direction (~ 4 times larger than the north-south 
uncertainties). This distortion is primarily due to the north-south ground 
track of the satellite orbits, which significantly improves solution constraint 
along this orientation. 

Displacements for the 1986-1988 interval (Figure 5.4) are complicated by 
the 1987 Superstition Hills earthquake sequence, as well as large measurement 
uncertainties. Effects of the earthquake sequence are clearly demonstrated in 
the GPS vectors; displacements at KAME and L589 approach 0.5 meters. 
Estimates of fault rupture suggest 10 stations near the seismic rupture zone 
moved at least 5 cm [Larsen tt a/., 1990]. The displacements are consistent 
with right-lateral slip along the Superstition Hills fault and left-lateral slip 
along the Elmore Ranch fault. Still, there is a considerable component of 
southeast trending movement which can not be explained as seismic 
deformation or measurement uncertainty. The relative displacement between 
stations on opposite sides of the valley averages 5-6 cm/yr. We take this 
motion to represent continuous strain accumulation due to plate motion. 

The 1988-1989 station displacements clearly demonstrate the right-lateral 
southeast trending movement across the GPS network. Stations furthest to 



-280- 



Figure 5.4: GPS station dispiacements for the interval 1986-1088 (1.8 
years). All measurements are made relative to station OCTI. Errors are 
determined by multiplying the formal uncertainties from the GPS 
solution by a variance factor so that the average baseline error scales as 1 
ppm. The east-west uncertainties are about 4 times larger then the 
north-south. Seismically induced displacements from the 1987 
Superstition Hills earthquake sequence are most apparent at stations 
KAT^ and L589. The large non-seismic displacements are assumed to 
represent relative motion between the Pacific and North American plates, 
which is concentrated across the valley. 



•281- 




-282- 



Figure 5.5: GPS station displacements for the interval 1988-1989 (1.0 
years). All measurements are made relative to station OCTI. Errore are 
determined by multiplying the formal uncertainties from the GPS 
solution by a variance factor so that the average baseline error scales as 
0.5 ppm. Stations to the northeast moved about 6 cm southwest relative 
to stations on the other side of the valley. 



>28S- 




-284- 



the northeast are displaced approximately 5 cm to the southeast relative to 
sites on the other side of the valley, although some of the observed motion 
(e.g., BLAC) may be distortion from the larger east-west uncertainties. In 
addition, Figure 5.5 demonstrates how easily GPS can monitor tectonic 
deformation even over time scales as short as 1 year. 

The 1986-1988 and 1088-1989 displa«m«>ts ar. d«ompos«l into thdr 
aorth-south and east-w« components, comaponding to the dir«=tion, of 
minimum and maximum error, respeetiveiy (Figure 5.6 and 5.7). Each 
component is plotted as the distance from OCTI on a crass section trending 
N50-E. perpendicular to the predicted plate motion orientation (N40-W) 
{Figure 5.8). Simple dislocation theory |e.g., Ma««nha and SmyUc, 1871) is 
used to remove the eflect of the 1987 SupeH,tition HIls earthquaite «^.„ce 
from the observed 1086-1988 displacement field, following fault models 
suggested by i.r«n .< a/. 11900) (approximately 109 cm right-lateral slip on 
the Supe,,tition Hills fault and 45 cm left-lateral slip on the Elmore Ranch 
fault). 

Decomposing the vector displacements into g«,graphic component, tends 
to separate the uncertainties which are magnified along the longitudinal 
direction. The north-south movement, dearly exhibit right-lateral 
displacement for both intervab; Nation, to the northeast display ««th,rly 
o&ets relative to site, on the other side of the valley. The magnitude of the 
displacement is roughly proportional to the time interval spann«i by the 
m.«,urements, suggesting continuous strain accumulation. Station, which 
display the largest scatter in Figure 5.6 are for the most part tho« sites where 
the applied seismic correction i, greater than 4 cm (open circles). This may 



.285- 



indicate additional fault complexity not accounted for by the dislocation 
model used to remove the effects of the 1987 earthquake. 

The east-west movements for the 1986-1988 interval exhibit large scatter 
with no discernible trend across the valley. This is invariant of the seismic 
correction, so the scatter is not explained simply as unmodeled effects from 
the Superstition HiUs earthquakes. Presumably, the large deviations are due 
to fairly significant east-west oriented errors from the 1986 survey. This may 
explain the anomalous vector displacements observed in Figure 5.4, especially 
noticeable for those sites near the border east of the Imperial fault. On the 
other hand, the 1988-1989 displacements clearly show large east directed 
movements for stations furthest to the northeast, consistent with southeast 
trending deformation across the valley. 

5.5 Dbcussion 

Deformation across valley 

The 1986-1988 measurements are concentrated along the Imperial fault 
(Figure 5.4). The nonseismic displacements reveal a sharp boundary 15-20 
km wide between deformation on either side of the valley (Figure 5.6). This 
suggests that in the southern half of the Imperial Valley strain is being 
accommodated exclusively along the Imperial fault. The 1988-1989 
measurements are distributed more uniformly throughout the region (Figure 
5.5), and indicate a broader strain-transition zone (Figure 5.7). This implies 
that deformation may be occurring along several structures to the north, 
including the San Andreas, San Jacinto, and Elsinore faults. The same 



-ass- 



Figure 5.6: The north-south and east-west dkplacement components for 
the 1986-1988 interval. All distances are relative to OCTI on a cross 
section trending NSO'E, perpendicular to the plate motion (see Figure 
5.8). The effect of the 1987 Superstition Hills earthquake sequence is 
removed. Open circles indicate stations where the seismic correction is 
greater than 4 cm. The north-south offset between stations on opposite 
sides of the valley is 8.1 cm. The large scatter for the east^west 
components are presumably due to errors in the 1986 survey. The 
average uncertainty for each displacement component is shown. 



-287- 






B 

m 



u 



CO 
I 

c 
o 
2 



20 



sw 



North: 1986-198B 



8.1 cm 



•20 

20 I ' — r — ' — 

East: 1966-1988 



-20 



SJ I 

-4 — k- 



SA 



50 
Distance (km) 



NE 



v_ j^_' ^ 



100 



-288- 



Figure 5.7: The north-south and east-west displacement components for 
the 1988-1989 interval. All distances are relative to OCTI on a cross 
section trending N50 * E, perpendicular to the plate motion direction. The 
data are best-fit by 5.2 cm/yr displacement across the valley (solid line), 
although a rate of 3.4 cm/yr fit the data nearly as well (dashed line). 
The average uncertainty for each displacement component is shown. 



-280- 



6 



B 

u 

CO 




-10 " ' 



50 

Distance (km) 



100 



-2flO- 



Figure 5.8: Shear plane (10 km depth) used to model the 1988-1980 
displacements (shaded band); cross section used in Figures 5.6 and 5.7; 
and stations surveyed at least twice between 1986 and 1989. 
Considerable strain is observed across the GPS network, which is 
attributed to plate-boundary deformation between the North American 
and Pacific plates. 



•291- 



34 



33.5 



33 



32.5 



-117 



I I I I I I I I I I I I I I I I 

Plate Motion 
1986-1969 

Km 40 




-116 



\ . 



I ■ / .1 



-115 



-202- 



pattern is observed in the conventional geodetic measurements, which indicate 
concentrated strain in a narrow 20 km wide zone about the Imperial fault, 
and diffuse deformation of at least 50 km wide to the north [Snay and Drew^ 
1988; Prtscott tt al, 1987b]. 

The 1986-1988 displacements (Figure 5.4) have been modeled by Laratn tt 
aL [1990). The station movements are consistent with right-lateral slip along 
the Superstition Hills fault and left-lateral ofiset along the Elmore ranch fault. 
The nonseismic residuals indicate remaining deformation across the valley, 
evidenced by the 8.1 ± 1.3 cm ofbet in the north-south displacement 
component (Figure 5.6). The differential movement is calculated by linearly 
fitting those data furthest to the southwest and northeast. The data errors 
are increased by 0.33 times the estimated seismic displacements, giving less 
weight to those stations most affected by the 1987 earthquakes. The east- 
west components are not used due of the large data scatter. The observed 
movement is taken to represent plate-boundary deformation due to the 
relative motion between the North American and Pacific plates. The 
calculated north-south differential displacement averaged over the 1.8 year 
observation interval, is equivalent to 5.9 ± 1.0 cm/yr right-lateral movement 
oriented N40 ' W, assuming a uniform velocity field parallel to the direction of 
plate motion. Conventional geodetic data are consistent with the assumed 
orientation [Prtscott tt aL, 1987a; Snay tt a/., 1988). 

The differential movement across the Imperial Valley is clearly visible in 
the 1988-1989 displacements (Figxire 5.5 and 5.7), and is observed in both the 
north-south and east-west components. The movement is smaller than the 
earlier interval because of the shorter observation period (1.0 years). 



■2S3- 



However, the most recent measurements are not influenced by seismic activity 
and contMn smaller experimental error. Since the 1988-1989 station 
displacements are more uniformly distributed across the valley, it is difficult 
to constrain an absolute differential offiset. Instead, the measurements are 
modeled assuming a semi-infinite right-lateral shear plane at depth 
representing the Pacific-North American plate margin (Figure 5.8). The plane 
is oriented N40*W about coordinates 32.796 'N, 115.454 'W, almost 
congruent with the Imperial fault and the axis of the valley. The upper depth 
is constrained at 10 km and uniform slip is assumed over the entire shear 
boundary. Snay and Drew (1988] incorporate a similar model to explain 
triangulation observations from 1941 to 1986, but allow additional slip along 
the Imperial fault necessitated by the detailed station coverage in this region. 
More complex models assuming distributed offeet along the Imperial, San 
Andreas, San Jacinto, and Elsinore faults, and within the Brawley Seismic 
Zone have been used to explain other geodetic measurements in the valley 
(e.g., Savage et c/., 1979]. The measurements presented here are not of 
sufficient resolution or accuracy (due to the short time coverage) to warrant 
such det^l. The 1988-1989 GPS displacement vectors are best constrained by 
5.2 ± 0.9 cm/yr plate-boundary deformation. The best-fit solution to the 
observed GPS movements is shown in Figure 5.7. Additional solutions are 
obt^ned by varying the depth to the upper boundary of the shear plane from 
5 to 15 km. The calculated displacement rates range from 4.4 (5 km) to 6.0 
cm/yr (15 km), while the minimum residual solution is obtained at 10 km 
depth (5.2 cm/yr). 

Because the 1988-1989 displacements are not affected by seismic 



•204- 



deformation, we speculate this interval yields a more reliable GPS estimate of 
strain across the Imperial Valley. The GPS rates, as well as those derived 
through conventional geodetic techniques, are listed in Table 5.3. These are 
compared with the predicted relative velocity between the Pacific and North 
American plates (NUVEL-1), and rates derived from VLBI measurements 
between stations along the western coast of California and the stable North 
American continent. The 1988-1989 GPS rate k comparable to the plate 
velocity estimates, while the earlier GPS interval is somewhat higher. This 
suggests that ail plate motion is concentrated across the valley, with little or 
no deformation west of the Elsinore fault. Conventional measurements taken 
over the last 50 years indicate significantly smaller rates (3.4-4.3 cm/yr), and 
thus require additional slip on faults not spanned by the networks to satisfy 
the plate velocity. GPS and trilateration (EDM) provide comparable 
accuracies, and both are considerably more precise than triangulation 
(although GPS yields 3-dimensional positions whereas the conventional 
methods do not). Since the EDM observations span a 15 year period 
compared to the 3 year GPS coverage, the trilateration rate should more 
accurately reflect the deformation across the valley, which suggests the GPS 
measurements over-estimate the true displacement. In fact, a 3.4 cm/yr 
deformation rate fits the 1988-1989 observations nearly as well (Figure 5.7). 
An alternate explanation is accelerated deformation between 1986 and 1980. 
The triangulation data indicate highly time-dependent displacements. 
Between 1941 and 1954 the calculated rate is significantly greater than the 
average between 1941 and 1986, although this is attributed to post-seismic 
effects following the 1940 Imperial Valley earthquake. No increased rate is 
observed following the 1979 earthquake [Savage ct ai, 1986). There is 



■205- 



Table 5.3 Displacement Rates 



Method 


Region 


Interval 


Rate 
(cm/yr) 


Reference 


GPS 


Imperial Valley 


lS8&-ig88 
1088-1980 


4.8 
5.2 


This Study 


Triangulation 


Imperial Valley 


1941-1986 
1941-1954 
1954-1967 
1967-1986 


4.3 

6.1 
2.1 
4.5 


Snai and Drew [1988] 


Trilateration 


Imperial Valley 


1972-1987 


3.4 


Preacott et al. [1987b] 


Plate Model 


Plate boundary 


~ 3 m.y. 


4.7 


DeMcU tt al. [1990] 


VLBI 


Continental 


1979-1987 


4.8-5.1 


Clark tt al. [1987] 
Kroner et al. [1987] 



-29fi- 



marginal evidence for a regional strain fluctuation (increase) during 1978 and 
1979 throughout southern California, but the nature of this apparent 
deformation is uncertain [Savage tt ai, 1981; Savagt tt ai, 1986). Given the 
large uncertainties for the GPS estimates (~ 1 cm), it is not possible with the 
available data to distinguish if there has been increased deformation over the 
last several years. 

Imperial and southern San Andreas fault earthquake potential 

The earthquake recurrence interval along the Imperial fault is estimated 
using the geodeticaliy determined strain rates. The 1940 Imperial Valley 
earthquake ruptured the entire length of the Imperial fault. Approximately 
3.0 and 4.5 m slip (coseismic plus postseismic) are estimated for the northern 
and southern segments of the fault, respectively [Rcilingcr, 1984]. Surface 
ofisets were as great as 6 m south of the border with displacements tapering 
off rapidly to the north [Trifunac and Brunc, 1970; Sharp, 1982). Surface 
rupture was confined to the fault north of the border during the 1979 
earthquake. Geodetic and strong ground motion modeling suggest an average 
slip of about 1 m along the 1979 rupture plane, with patches of higher 
displacement (asperities) [e.g., HartzcU and Hcaton, 1983; Archuleta, 1984; 
Reilinger and Larstn, 1986) 

Triangulation measurements along the Imperial fault and north of the 
U.S.-Mexico border indicate concentrated deformation in a narrow 20 km wide 
zone. At an observed strain rate of 4-5 cm/yr and per event ruptures between 
1 and 3 m, a 20-75 year earthquake recurrence interval is calculated for the 
northern Imperial fault. This assumes total strain release during seismic 



-28T- 



episodes. The estimated recurrence rate is comparable to the 32 year 
earthquake repeat time suggested by Sykes and Nishtnko (1984] and the ~ 50 
year interval predicted by Andtrson and Bodin (1987). 

Conventional geodetic data north of the Imperial fault indicate 
distributed deformation over a fairly wide region (> 50 km wide) [Snay and 
Drew, 1988]. Presumably the strain that occurs almost exclusively along the 
Imperial fault in the south is transferred by some mechanism to the San 
Andreas, San Jacinto, and Elsinore faults. The slip distribution across each 
fault segment is important from an earthquake hazard standpoint. 

Three Imperial Valley GPS sites have well determined VLBI solutions 
(Very Long Baseline Interferometry) from observations since 1979 [Clark et ai, 
1987; Sauber et ai, 1989; Ma ti a/., 1989). Relative velocities of BIAC-PINY 
and BLAC-MONU for the GPS and VLBI analyses are listed in Table 5.4 and 
illustrated in Figure 5.9. The VLBI velocities vary depending on the 
continental or global nature of each solution and the extent of data 
availability. Only the north-south GPS displacements are considered because 
of the large east-west errors inherent in the 1986 survey. The fault parallel 
velocities are right-lateral assuming relative motions are oriented N40*W. 
The calculated effect from the 1987 Superstition Hills earthquake sequence is 
removed from the GPS data. The VLBI measurements indicate 1.5 to 2.1 
cm/yr fault-parallel (right-lateral) displacement across the San Andreas fault 
(BLAG-PINY) and 3.0 to 3.5 cm/yr across the valley (BLAC-MONU). The 
GPS measurements suggest 1.4 cm/yr displacement across the fault and 3.2 
cm/yr across the valley (Table 5.3 rates are different since they represent 
averages over the entire network). While the BLAC-MONU velocities roughly 



-2S8- 



Table 5.4 Displacement Rates Across San Andreas Fault 



Baseline 


Method 


Interval 


North 


East 


Fault Parallel 








(cm/yr) 
1.8 


(cm/yr) 
-1.1 


(cm/yr) 


BLAC-PINY 


VLBI' 


1982-1987 


2.1 




VLBI2 


1979-1988 


1.5 


-1.0 


1.8 




VLBI3 


1982-1988 


1.2 


-O.e 


1.5 




GPS 


1986-1988 


1.1 




1.4 


BLAC-MO^^J 


VLBI' 


1982-1987 


2.3 


-2.7 


3.2 




VLBI2 


1979-1988 


2.5 


-2.5 


3.5 




VLBI3 


1982-1988 


2.4 


-1.8 


3.0 




GPS 


1986-1989 


2.5 




3.2 


I Clark et al. [1987 
:Ma 1988] 
^ Sauber [1989 











■2fiB- 



agree with the conventional geodetic measurements (3.4-4.3 cm/yr), the fault- 
crossing displacements are somewhat surprising as they are lower than 
geologic evidence. The long-term geomorphological slip rate along the 
southern San Andreas fault over the last 10,000-30,000 years is estimated 
between 2.3 and 3.5 cm/yr [KeUcr et ai, 1982; Weldon and Sith, 19851, with 
2.5 cm/yr a commonly accepted average [e.g., Sieh and WiUiams, 1990]. The 
geologic slip rate and radiocarbon dating of Holocene offsets along the fault 
suggest a recurrence interval of about 300 years with the last major event in 
1680 [Sieh, 1986]. This logic leads to the conclusion that the potential for a 
major earthquake along the southern San Andreas is high. However, the 
geodetic evidence reported here indicates a smaller strain accumulation rate 
during the last decade, suggesting decreased earthquake potential assuming 
these measurements are indicative of the last few hundred years. This will be 
observed either as a longer recurrence interval or less slip per event. The 
geodetic data are supported by geologic trenching studies which suggest a 
decreasing southern San Andreas slip rate during the past 1000 years Sieh 
(1986). If this is true, the San Jacinto fault should play a more active role in 
regional tectonics. In fact, the shear strain along the fault determined from 
EDM observations between 1973 and 1984 is nearly the same as that for 
networks which lie on the San Andreas fault Savage et ai (1986). The two 
fault systems may alternately assume dominant roles in absorbing plate 
motions, as is suggested by variable Quaternary slip rates along the San 
Jacinto fault [Sharp, 1981). 

Future analyses 

The 1986, 1988, and 1989 Imperial Valley GPS observations are not 



-300- 



Figure 5.9: VLBI (solid arrows) and GPS (dashed arrows) velocities at 
stations PINY and MONU relative to station BLAG (Table 5.4). The 
GPS vectors contain large uncertainty in the east-west direction. The 
fault-parallel geodetic velocities across the San Andreas fault are less than 
geologic estimates. 



-301< 




-302- 



sufficiently resolved to accurately map details of the strain distribution in this 
portion of southern California. This is due to poor data quality from the 
1986 measurements, complications due to the 1987 Superstition Hills 
earthquake sequence, the inability to incorporate L2 phase data from several 
sites during 1989, and the short interval spanned by the observations (1 year 
of nonseismic displacement). However, additional GPS data have been 
collected in southern California in March/April 1988 and again in 
February/March 1990 (Figure 5.10). The 1988 measurements were made in 
conjunction with the Riverside County (California) Flood Control District 
and the Riverside County Survey Department. In a network of 62 stations 
spanning an entire cross section of southern California, a maximum of 8 TI- 
4100 GPS receivers were deployed each day over the two week survey. The 
daily observation period was about 4.5 hours. Although the instruments 
collected data every 3 seconds, during the download from receiver to floppy 
disk only every 10th measurement was recorded (30 second epochs). 
Unfortunately, the receivers were not synchronized and the recorded time-tags 
were randomly distributed at 30-second intervals. These data have been 
subsequently processed with the Bernese software. The day to day baseline 
repeatability on the 18 lines with multiple observations is 1.1 cm, suggesting 
that the receiver time-tag ofisets are not a serious source of solution error 
considering the 3 to 5 cm tectonic movements expected in southern California, 

During 1990, a high precision GPS network was established along a 400 km 
segment of the Pacific-North American plate-boundary from the Gulf of 
California in northern Mexico to just south of the junction of the San 
Andreas and San Jacinto faults (- 34 'N) [ReiUnger tt ai, 1990J. Twenty- 



•SOS- 



three receivers were used for approximately two weeks including the TI-4100, 
Trimble 4000SD, and Trimble 4000SDT models. A total of 134 stations were 
occupied during the campaign. Data collection at 103 sites lasted 6 to 7 hours 
each day, while the daily observation interval at 31 stations was 3 to 4 hours 
(half-sessions). The following month (April 1990), 3 additional monuments 
near Upland, California, were established and surveyed by the Riverside 
County Flood Control District in support of university research associated 
with the February 28 (1990) M^ 5.5 Upland earthquake. The 1990 
observations are in the process of being analyzed, although obtaining geodetic 
coordinates for the entire survey will be time consuming due to the enormity 
of the data set and the uncertainty in correlating GPS measurements from 
different receivers. 

The 1986-1990 GPS occupation summary for the Imperial Valley, 
Rivereide County, and Baja California is listed in Table 5.5. A total of 183 
stations have been occupied at least once (Figure 5.10), and of these 85 have 
been occupied at least twice with most dating back to 1986 or 1988. The 
station coverage does not include kinematic GPS measurements made on 
relatively short transects (few kilometer) crossing the southern San Andreas 
fault [K. Hudnut, personal communication, 1990]. In addition to the dense 
distribution within the Imperial Valley and Baja California, the established 
network north of the Salton Sea provides station coverage extending from the 
Califomia-Arizona border to near the Pacific Ocean. This network will be 
used to constrain the slip distribution along the major fault systems in 
southern California. When combined with geologic data of fault activity, the 
strain estimates will better define the earthquake potential in this region. The 



-304- 



Figure 5.10: GPS stations occupied from 1986 to 1990 in Riverside 
County, the Imperial Valley, and northern Baja California. Triangl 
inside circles indicate stations with multiple occupations. The network 
composed of 183 stations, of which 85 have repeated observations. 



ies 
is 



-306- 



■ I ' ' 



I I I I I I 



n 




«I 


C 




§ 


o 




a 03 


aoi 




§•2 


t:2 




.2 «* 

5f 


0) 1 




m o 


03 CO 




£ o 


rOCO 




^£ 


003 


\ 


« • 


m 


\ 


^ 


• ^ /•-- 


O 







1 I I I I J I I 

/ 




-300- 



Table 5.5 GPS C&mp&i^ Summ&ry 



Year 


Stations 


Region 


Organisation 


1986 


42 


Imperial Valley 


NGS 


1988 


15 


Imperial Valley 


UNAVCO 


1988 


62 


Riverside County 


RCFC/HUSD 


1988 


21 


Imperial Valley 


NGS 


1989 


28 


Imperial Valley 


UNAVCO 


1990 


134 


Imperial Valley /Riverside County 


UNAVCO/RCFC/RCSD/NGS 



NGS - National Geodetic Survey 
UNAVCO - University Navstar Consortium 
RCFC - Riverside County Flood Control 
RCSD - Riverside County Survey District 



-307- 



best GPS estimate of secular strain to date is provided by the 11 displacement 
vectors obtain from the 1988 and 1989 surveys. Once the 1990 data are fully 
analyzed, the increased station density (85 stations) and longer measurement 
interval (at least 2 years) will yield an order of magnitude increase in 
deformation extent and resolution. It should be possible to assess the present- 
day strain accumulation rates on the major fault systems in southern 
California to within a few millimeters per year. The network also provides 
good coverage along the southern San Andreas fault, which will be used to 
constrain fault rupture parameters in the likely event of a large earthquake 
within the next several decades [Larsen, 1990]. 

5.6 Conclusions 

GPS measurements from southern California indicate 5.9 ± 1.0 and 5.2 ± 
0.9 cm/yr right-lateral southeast trending displacement across the Imperial 
Valley for the intervals 1986-1988 and 1988-1989, respectively. These rates 
are significantly larger than those obtained from conventional geodetic surveys 
(3.4-4.3 cm/yr), suggesting the GPS observations may overestimate the true 
deformation. The earlier measurements contain relatively large errors, and 
are influenced by the 1987 Superstition Hills earthquake sequence. The 1988- 
1989 data are modeled nearly as well by 3.4 cm/yr of valley crossing 
movement. Regardless, a significant secular deformation component is clearly 
observed in the GPS displacements, which is attributed to the relative 
movement between the Pacific and North American plates. There is evidence 
from VLBI and GPS measurements that the strain accumulation rate along 
the southern-most San Andreas fault is smaller than the calculated long-term 



-308- 



geoiogic estimate. This indicates a lower earthquake potential for this 
segment of the fault than is presently assumed, and suggests that the San 
Jacinto system plays a more dominant role for relieving the strwn 
accumulation in this region. The measurements discussed here are part of a 
larger 183 station GPS network which spans an entire cross section of 
southern California. A total of 134 stations were observed during a recent 
1900 campaign; many of these sites were previously occupied in 1986 and/or 
1988. An order of magnitude increase in resolution and detail regarding the 
strain accumulation rates along the San Andreas, San Jacinto, and Elsinore 
faults is expected once the 1990 GPS data are integrated with the previous 
surveys. 



.300- 



Acknowledgements 



This research is a collaborative effort conducted jointly with Robert 
Reilinger at MIT. Helen Neugebauer and Bill Strange provided coordinate 
solutions from the 1986 NGS GPS survey. This research could not have 
taken place without the invaluable field support provided by many people. I 
thank my advisor Hiroo Kanamori for his support. This work is supported 
by U.S. Geological Survey contracts 14-08-0001-61679 (MIT) and 14-08-001- 
61354 (Caltech), and by NASA grant NAG-5-814 (MIT). 



-310- 



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southern California, GeoL Soc. Am. Bull., 96, 793-812, 1985. 

U. S. G. S., The Imperial Valley, California, earthquake of October 15, 1979, 
U.S. Geoi Surv. Prof. Pap., 1254, 451 p., 1982. 



FRECEDiriG PAGE BLAMK NOT FJLMED ^^ 



APPENDIX 2 



GPS measurements of deformation associated with the 1987 Superstition Hills 
earthquake: Evidence for conjugate faulting 



by S. Larsen, R. ReUingCT. H. Neugebauer, and W. Strange 



Submitted to Journal of Geophysical. Research, 1991 



GPS Measurements of Deformation Associated with 

the 1087 Superstition Hills Earthquake: 

Evidence for Conjugate Faulting 

Abstract 

Large station displacements observed from Imperial Valley GPS 
campaigns are attributed to the November 24, 1987 Superstition Hills 
earthquake sequence. Thirty sites from a 42 station GPS network established 
in 1986 have been reoccupied during 1988 and/or 1990. Displacements at 
three sites within 3 kilometers of the surface rupture approach 0.5 m. Eight 
additional stations within 20 km of the seismic zone are displaced at least 10 
cm. This is the first occurrence of a large earthquake (Ms 6.6) within a 
preexisting GPS network. Best-fitting uniform slip models of rectangular 
dislocations in an elastic half-space indicate 130 cm right-lateral displacement 
along the northwest trending Superstition Hills fault and 30 cm left-lateral 
oflset along the conjugate northeast trending Elmore Ranch fault. The 
geodetic moments are 9.4 x 10^ dyne-cm and 2.3 x 10^^ dyne-cm for the 
Superstition Hills and Elmore Ranch faults, respectively. Distributed slip 
solutions using Singular Value Decomposition suggest near uniform 
displacement along the Elmore Ranch fault and concentrated slip to the 
northwest and southeast along the Superstition Hills fault. A significant 
component of non-seismic secular displacement is observed across the Imperial 
Valley, which is attributed to interseismic plate-boundary elastic deformation. 



PRECEDING PAGE BLAMK NOT FILMED 

-165- 
4.1 Introduction 

The Global Positioning System (GPS) is rapidly becoming one of the most 
important tools to study tectonic deformation. By recording signals from 
earth orbiting satellites it is possible to determine 3-dimensional coordinates 
of geodetic monuments with high accuracy. With repeated observations the 
station displacement or deformation between surveys is measured. GPS can 
be used to monitor secular deformation such as that associated with plate 
motion, or to record rapid strain fluctuations such as those due to seismic and 
volcanic activity. In its final configuration scheduled for the mid 1990's, 18 
satellites will be deployed in 6 orbital planes (with 3 additional satellites used 
as active spares). When GPS becomes fully operational it will be possible to 
continuously determine 3-dimensional positions anywhere on or near the 
earth. The available satellite constellation existing for the last several years, 
was optimized for North America making geodetic studies in California 
practical. The observation window in which enough satellites have been 
visible to obtain the high accuracies necessary to measure tectonic motion has 
been about 6 to 8 hours each day. 

On November 24, 1987, two large earthquakes separated by 12 hours 
occurred in the northwest portion of the Imperial Valley region of southern 
California. The firet event was located on a northeast trending seismic 
lineament and was followed 12 hours later by rupture along the northwest 
trending Superatition hills fault. What makes this earthquake sequence so 
significant from a GPS standpoint, is that it occurred spatially and 
temporally within a preexisting GPS network. This network was established 
in the Imperial Valley in 1986, with partial resurveys in 1988 and 1990. 



-ISO- 



Fifteen stations are located within 20 km of the rupture zone; three stations 
are within 3 km. This is the firet occurrence of a large earthquake within a 
preexisting GPS network. 

We compute GPS displace: n the Imperial Valley between 1986 and 

1990. Observed movements of nea 0.5 metere are attributed to the 
Superstition Hills earthquake sequence. The earthquake-induced 
displacements are inverted to estimate seismic slip and the corresponding 
geodetic moment along the rupture planes. In addition, there b a large 
component of deformation which can not be explained by the seismic 
disturbance; we assume this to be a manifestation of continuous strain 
accumulation across the Imperial Valley due to the relative motion of the 
Pacific and North American plates. 

4.2 Imperial VaUey Seismicity and Tectonics 

The Imperial Valley region of southern California is a complex transition 
zone between crustal spreading in the Gulf of California and right-lateral 
transform motion along the San Andreas fault (Figure 4.1) [Lomnitz et al., 
1970; Elders ct ai, 1972). The valley is 4-5 million years old and has beeJ 
filled by up to 5 km of late Cenozoic sediments [Fuis et al., 1982). The major 
fault syrtems and structural grain of the valley trend to the northwest, 
roughly parallel to the direction of plate motion. A significant fraction of the 
North American and Pacific relative motion may be accommodated across thb 
region. 

The valley is one of the most seismically active regions of California 



-187- 
(Figure 4.1) with much of the activity occurring along the Imperial fault and 
within the Brawley Seismic Zone [Johnson and Hill, 1982). Several large 
earthquakes have occurred in and near the Imperial Valley since 1940 (Figure 
4.1). The Imperial fault ruptured with a Ms 7.1 event in 1940 and a Ml 6.6 
event in 1979 [U.S. Geol Surv., 1982). Segments of the San Jacinto fault 
system broke with a Ml 6.2 earthquake in 1954 (Clark segment) and the 1968 
Ml 6.5 Borrego Mountain event (Coyote Creek segment). The most GPS 
relevant episode of seismic activity occurred in 1987 along the Superstition 
Hills segment of the San Jacinto fault system, with a Ms 6.2 earthquake on a 
northeast trending seismic lineament followed 12 hours later by a Ms 6.6 
event on the Superstition Hills fault. 

Conventional geodetic measurements suggest considerable deformation 
across the Imperial Valley. In fact, a significant fraction of the Pacific-North 
American relative plate motion may be accommodated here. New global plate 
model estimates (NUVEL-1) [DeMete et a/., 1987; DeMets et aL, 1990) predict 
the rate of relative motion between the North American and Pacific plates (at 
Imperial Valley coordinates: 33.0 'N, 115.5 'W) is 4.7 cm/yr oriented 
N39.6*W. Triangulation measurements spanning this region have been 
modeled as 4.3 cm/yr of plate-boimdary deformation averaged between 1941 
and 1986 [Snay and Drew, 1988). Trilateration measurements made by the 
U.S.G.S. between 1972 and 1987 indicate 3.45 cm/yr relative movement 
between stations on opposite sides of the valley [Prescott et a/., 1987b). The 
orientations of the conventional geodetic displacements are approximately 
N40*W, although to some extent the direction is non-unique and depends 
upon a priori assumptions [e.g., Prescott, 1981). In addition, the conventional 



-158* 
Figure 4.1: Seismicity and major fault systems of the Imperial Valley. 
The Brawley " '<?mic Zone is the region of anomalously high activity 
between the r Imperial and southern San Andreas faults. The 

valley represents "on zone between crustal spreading in the Gulf 

of California to the ; nd right^lateral transform motion along the 

San Andreas system. 



ORIGINAL PAGE IS 
OF POOR QUALITY 



-150- 




-170- 



geodetic measurements indicate that deformation is concentrated in a narrow 
20 km wide zone along the Imperial fault, while to the north it is distributed 
over a region at least 50 km wide. Presumably, deformation is transferred 
from the Imperial fault, which acts as the primary strain release mechanism 
near the border, to distributed shear along the San Andreas, San Jacinto, and 
Elsinore faults. 

4.3 Superstition ffills Earthquake Sequence 

On November 24, 1987 (1:54 GMT), a large Ms 6.2 earthquake occurred 
along a northeast trending seismic lineament northeast of the Superstition 
Hilb fault (Figure 4.2) [Magistrate et ai, 1988]. The focal mechanism and 
aftershock sequence, which extended for 26 km to the northeast and into the 
Brawley Seismic Zone, are consistent with left-lateral strike slip motion on a 
vertical fault. Seven foreshocks were recorded in the 22 minutes prior to the 
main event, including two with Ml > 4.0. Surface rupture consisted of a 
complex pattern of left-lateral northeast-trending ofisets ranging in length 
from 1.5 to 10 km, and with maximum displacements between 3 and 13 cm 
[Budding and Sharp, 1988; Hudnut tt al., 198ea]. We refer to this northeast 
trending lineament as the Elmore Ranch fault, although more precisely this 
name refers only to the longest of the surface fractures. 

Twelve hours after the Elmore Ranch event (13;15 GMT), a Mg 6.6 
earthquake occurred along the northwest trending Superstition Hilb fault. 
The epicenter was near the intersection of the Elmore Ranch and Superetition 
Hilk faults. Strong ground motion and teleseismic data suggest the rupture- 
process for this second event was somewhat complicated, consisting of 



-171- 
multiple sub-events [Bent tt al., 1989; Frankel and Wennerberg, 1989; Hwang 
et ai, 1990; Wald tt ai, 1990J. Surface rupture extended 24 km along the 
previously mapped trace of the fault [WiUiams and MagistraU, 1989). Up to 
50 cm right-lateral displacement were measured Immediately following the 
earthquake. The aftershock pattern was concentrated slightly to the west of 
the fault and did not extend the length of the surface rupture. Magistrate et 
al. [1989] suggested the aftershock sequence was highly correlated with 
basement structure. Both the Superstition Hills and Elmore Ranch events 
triggered sympathetic surface oflEsets along the Imperial, San Andreas, and 
Coyote Creek faults [McGill et ai, 1989; Hxidnut and Clark, 1989]. 

Significant afterslip was recorded along the Superstition Hills fault 
following the second mainshock. No afterslip was measured along any of the 
surface ruptures associated with the Elmore Ranch event. In fact, all seismic 
activity essentially stopped along this segment after the initiation of the 2nd 
mainshock. 

One of the most interesting aspects of this earthquake sequence is the 
conjugate nature of faulting. That is, two surface ruptures oriented nearly 
perpendicular to each other. As discussed below, this type of fault interaction 
may be typical of Imperial Valley tectonics and may dictate the mode of 
stress/strwn transfer from one fault system to another. 

What makes the Superstition Hills earthquake sequence unique from a 
GPS perspective is that it occurred within a preexisting GPS network. 
Stations located near the seismic rupture zone were displaced neariy 0.5 
meters. These movements, as well as smaller displacements observed at 



-172- 
Figure 4.2: Seismicity and surface faulting associated witli the November 
24, 1987 Superstition HiUs earthquake sequence. A Mg 6.2 event occurred 
along a northeast trending structure (referred to here as the Elmore 
Ranch fault) and was followed by 12 hours with a Mg 6.6 event along the 
northwest trending Superstition PTills fault. The focal mechanisms, 
aftershock distribution, and surface ofiEset measurements are consbtent 
with left-lateral strike-slip motion along the Elmore Ranch fault and 
right-lateral strike-slip motion along the Superstition Hills fault. A 
significant amount of postseismic slip was observed along the surface 
trace of the Superstition Hills fault, while activity essentially ceased on 
the Elmore Ranch fault after the Mg 6.6 event. The shaded strips along 
each fault indicate the geometrical extent of the dislocations used to 
model the geodetic displacements. 



-178- 



33.2 - 




32.6 



-115.8 



-115.6 



-174- 



nearby stations can be inverted to infer properties of the rupture process. 
This b the first time GPS measurements have recorded the deformation from 
a large earthquake. 



4.4 GPS Observations 



After a brief introduction to the Global Positioning System, in thb section 
we report how the GPS data were obtained from field campaigns in 1086, 
1988, and 1990, as well as the processing methods used to obtain station 
coordinates. The GPS displacement vectors between surveys are presented 
and we discuss how measurement errors are handled for this study. More 
complete details about the Global Positioning System, including theoretical 
aspects and processing methods, are found in King et al. [1985], Wdls ct al. 
(1987), and Rocken [1988]. 

The signal structure broadcast from each GPS satellite consists of two 
carrier phase signals modulated by a navigational message as well as pseudo 
random codes. The two carrier frequencies, known as the Ll and L2 phases, 
are broadcast at 1575.42 Mhz (Ll) and 1227.60 Mhz (L2). This b equivalent 
to wavelengths of about 19 cm for the Ll and 24 cm for the L2. The 
navigational message contains the satellite coordinates (broadcast ephemeris), 
clock parameters, satellite health, and general system status. The pseudcK 
random codes are accurate time marks which allow a GPS receiver to 
determine the transmission time of the signal. When scaled by the speed of 
light, the pseudorange. or the satellite-receiver distance b computed. If 
measurements to at least 4 GPS satellites are available, and if satellite, 
coordinates are known (usually with the broadcast ephemeris), the 3- 



-175- 

dimensional receiver position as well as the satellite-receiver time offset can be 
determined. The positioning accuracy with the pseudorange is 1 to 100 m, 
depending on whether the P or C/A code is used, the receiver type, length of 
observation, and the static or kinematic behavior of the instrument. It is the 
pseudorange which will be used for civilian and military navigation. For 
highly accurate geodetic positioning, however, it is necessary to use the carrier 
phase measurements in a post-processing mode. That is, the data collected in 
the field are brought back to the office or laboratory for analysis, usually with 
a fairly robust computer software system. 

GPS Surveys — Data Collection 

The GPS data for this study were collected during 4 Imperial Valley field 
campaigns from 1986 to 1990 (Table 4.1). A total of 46 stations in or near 
the valley have been occupied at least once during this interval (Figure 4.3), 
while 30 sites have been reoccupied since 1986 (Figure 4.3, Table 4.2). TI- 
4100 GPS receivers supporting GESAR software were used during 1986 and 
1988, while Trimble 4000SDT instruments were used during the 1990 survey 
As one of the first commercially available instruments, the TI-4100 is a code 
correlating receiver which allows the simultaneous tracking of up to 4 
satellites at a time. This instrument records the Ll and L2 carrier signals, the 
P and C/A pseudo-codes, and the broadcast message. The Trimble 4000SDT 
is able to record the Ll and L2 phase components for up to 8 satellites at 
once, Bs well as the C/A code and the broadcast message 

The National Geodetic Survey (NGS) occupied 54 sites in southern 
California in May/ June 1986; 42 stations were located in or near the Imperial 



-175- 
Figure 4.3a: Imperial Valley and related GPS stations surveyed in 1986, 
1988, and/or 1990. Station names for sites indicated in the shaded box 
are given in Figure 4.3b. 



-177- 




-178- 
Figure 4.3b: Central-southern Imperial Valley and related GPS stations 

surveyed in 1986, 1988, and/or 1990. 



-170- 



CO 


CO 


CU 


QU 


a 


o 


CD 


CD 


CO 





o 


C3B 


v-l 


«^ 


4 


o 




-180- 

Table 4-1 Imperial Valley GPS Campaign Summary 



Year 


Month 


Days 


Stations 


Organization 


1986 


Ma> e 


20 


42 


NGS 


1988 


Febr larch 


9 


10 


UNAVCO 


1988 


March/April 


6 


21 


NGS 


1990 


April 


1 


3 


UNAVCO/RCFC 



NGS - National Geodetic Survey 
UNAVCO - University Navstar Consortium 
RCFC - Riverside County Flood Control 



-181- 



Tabl€ 4.2 Reoccupicd GPS Sutions 



Station Name 



Abbr. 



Occupation Longitude 

1986 1988* 1988^ 1990 



Acute 1934 

Alamo 

Black Butte NCMN 1982 

Brawley 2 rm 5 

Calexico 1954 

Coach 

College 1967 

El Centre 2 1959 

Frink 1934 

GLO Comcw 1934 

Hamar 2 1967 

Holt 1924 

HoltviUc (Alt) 1934 

Imp 1934 

Imperial 1934 

Junction 

Kane 1939 

L 589 1967 

Mack 2 1967 bm reset 

MeUo 3 1967 

Mound 1934 

OcotiUo NCMN 1982 

OcotiUo 1935 

Oflset 217 

Offset 224 

Offset 227 

Orient 1939 

Pinyon Flat 

T 1226 

Tamarisk 3 1967 



Latitude Elevation 



ACUT • 


• • 


ALAM • 


• • 


BLAC • 




BRAW • 


• 


CALE • 




COAC • 




COLL • 




ELEC • 




FRIN 




GLOC • 




HAMA • 




HOLT • 




HLTV . 




IMPI « 




IMPE « 




JUNG • 




KANE 


1 • • 


L58g i 


1 • < 


MACK 




MELL 




MOUN 




OCOT 


• • < 


OCTI 


• • 1 


0217 


• • 


0224 




0227 




ORE 


• • 


PINY 




T122 




TAMA 


• • 



•115.6093 

■115.6111 

■115.7198 

■115.5434 

■115.5064 

■115.4070 

■115.5024 

■115.5622 

■115.6470 

■115.2465 

■115.5007 

■115.3963 

■115.3821 

-115.5698 

-115.5788 

-115.0619 

-115.8237 

-115.7611 

-115.1441 

-115.4653 

■115.6998 

■115.7962 

•116.0017 

■115.3131 

-115.7055 

■115.8173 

-115.4064 

-116.4588 

■114.8050 

■115.4783 



33.0300 

33.1964 

33.6638 

32.9773 

32.6645 

33.1962 

32.8269 

32.7846 

33.3603 

32.8396 

33.0375 

32.7814 

32.8084 

32.8982 

32.8439 

32.7092 

33.0614 

32.9506 

32.7288 

32.7961 

32.9502 

32.7901 

32.7338 

32.6782 

32.6493 

32.6414 

32.9168 

33.6093 

32.8583 

32.8829 



-80.91 
-72.91 
490.01 
-66.78 
-34.07 
-8.40 
-54.63 
-45.76 
-85.39 
-15.46 
-79.80 
-36.79 
-38.77 
-59.27 
-51.85 
8.35 
10.05 
13.62 
1.20 
-47.00 
3.40 
-36.43 
111.33 
-17.16 
50.00 
70.64 
-81.36 
1235.88 
141.19 
-68.19 



' UNAVCO 
^NGS 



-182- 
Valley. Most marks were observed at least two days (Table 4.3), although 
redundant baselines were relatively uncommon (i.e., simultaneous occupation 
of the same station-station pair for two or more days). Unfortunately, the 
quality of the observations were very poor. The scheduled 4.5 hour daily 
occupations were somewhat less than the 6-8 hour sessions typical of other 
southern California campaigns. In addition, due to a variety of equipment 
and logistical problems, less than 2 hours of data were collected at several 
sites. In the observation scenario, there was less than a 2 hour period in 
which more than 3 satellites were simultaneously tracked. In fact, there was a 
scheduled 1 hour gap in Satellite 6 during the middle of the measurement 
session. The data were generally noisy and the final double difference phase 
observables may contain uncorrected cycle slips. 

In February/March 1988 university field crews (UNA.VCO) observing for 9 
days reoccupied 15 of the Imperial Valley marks, as well as establbhing 4 new 
stations along the Salton Sea. These new sites were installed at tide gauge 
monitoring facilities and will be used to constrain vertical GPS baseline 
components and for monitoring tectonic tilting in the Salton Trough. Most 
monuments were occupied for 2 days (Table 4.3) (1 was observed 3 days, 1 for 
4 days, and 2 for 1 day). The scheduled nightly observation scenario lasted 
7.5 hours, with a total of 7 satellites tracked. 

In March/April 1988 the NGS reoccupied 21 of the 1986 stations (7 of 
which were observed by the university crews a month eariier). Most sites were 
occupied only 1 day (Table 4.3). The daily observation period of 6.0 hours 
was slightly shorter than the February /March survey, although 7 satellites 
were tracked each day. 



-183- 



Tablc 4.3 Imperial Valley GPS Occupation History 



Year Day 








Stations 








1986 141 


COLL 


CALE 


L589 












142 


0217 


0216 


MELL 


E122 


HOLT 


EI,EC 


0227 




143 


COLL 


CALE 


TAMA 


HLTV 


MACK 


0224 


IMPE 


0225 


144 


OCT! 


IMPI 


F122 


OCOT 




0224 


0227 


0225 


145 


KAMA 


IMPI 


ALAM 






ACUT 


MOUN 




146 


HAMA 


CALE 


TAMA 


ORCE 




GI,OC 


C012 


BRAW 


147 


COAC 


CALI 


ALAM 


ORE 


FRIN 


BLAC 


KANE 




148 


OCT! 


MONU 


L589 


OCOT 


FRIN 


ACUT 


KANE 


BRAW 


149 


0217 


0216 


J060 


T122 


MACK 


GLOC 


MOUN 


YUMA 


150 


COAC 


MONU 


MEI.L 


T122 


HOLT 


BLAC 


C012 


YUMA 


151 


G035 


S025 


L589 


D26B 


HOLT 


ACUT 


X35A 


JUNC 


153 


G035 


S025 


J060 


D26B 






X35A 


BRAW 


161 


PINY 




SAND 


OCOT 


PEAR 


BLAC 






162 


PINY 




SAND 


OCOT 


PEAR 


BLAC 




YUMA 


163 


PINY 




SAND 


OCOT 


SANT 


BLAC 




YUMA 


164 


PINY 




JPLP 


OCOT 




BLAC 




YUMA 


167 


PINY 


MONU 


MOJA 


NIGU 


SOLE 






YUMA 


168 


PINY 


MONU 


MOJA 


NIGU 


SOLE 


OTAY 




YUMA 


169 


LAJO 


MONU 


MOJA 


BOUC 




OTAY 




YUMA 


170 


LAJO 


MONU 


MOJA 


BOUC 


CUYA 






YUMA 


1988* 55 


L589 


BLAC 


FTJS 


COAC 


SANl 








56 


ALAM 


GLOC 


OCOT 


SSPl 


SANl 








57 


ALAM 


GLOC 


OCOT 


SSPl 


ORE 








58 


L589 


GLOC 


BOBl 


COAC 


ORE 








59 


L589 


BLAC 


FTJS 


KANE 


FRIN 








60 


U89 


CALE 


TAMA 


KANE 


FRIN 








62 


0217 


CALE 


TAMA 












63 


0217 


COLL 


OCTl 












64 


HAMA 


COLL 


OCTI 












1988' 88 


PINY 


OCOT 


BRAW 


HOLT 


MEI.L 








89 


PINY 


OCOT 


IMPE 


IMP! 


0217 








90 


PINY 


OCOT 


ACUT 


HAMA 


KANE 








91 


PINY 


OCOT 


ELEC 


HLTV 


OCTl 








92 


PINY 


OCOT 


MACK 


0227 


T122 








93 


PINY 


FRIN 


JUNC 


L588 


0224 








1990 100 


BLAC 


MOUN 


BCOl 












Day a Julian day of 


year 














'UNAVCO 
















'NGS 



















-184- 
In addition to the UNAVCO and NGS campaigns, GPS observations in 
1988 were made at Mojave (California), Westford (Massachusetts), and 
Richmond (Florida). These sites are continuously monitored as part of the 
Cooperative International GPS Network (CIGNET) [Chin, 1988]. Data from 
CIGNET stations are used to improve satellite orbits in the GPS processing. 
Unfortunately, these observations are frequently of poor quality and contain 
abundant cycle slips. During the 1988 campaign, observations were not 
always available or usable at all CIGNET sites on all days (Table 4.4). 

Station MOUN (Mound), which was surveyed in 1986, was destroyed from 
the 1987 earthquake sequence. The site is located less than 1 km from the 
surface rupture of the Superstition Hills fault. Field investigation during 
early 1988 revelled that the monument and supporting concrete base had been 
completely uprooted from the ground. Destroyed monuments usually can not 
be tied to previous surveys because of the high accuracy required for crustal 
motion research. If the suspected deformation b significantly large, however, 
some information may be recovered if the monument (or a substitute) is reset 
in approximately the same location. Site inspection at MOUN clearly showed 
where the old monument had been and in early April, 1990 a rebar rod acting 
as a temporary benchmark was set at approximately the same position. We 
estimate the temporary mark was set within 0.15 m of the previous 
monument. Because of its proximity to the 1987 rupture zone, the calculated 
seismic displacement at MOUN is about 0.5 m. Therefore, reoccupation of 
thb site should retrieve a tectonic component larger than the expected 
uncertainty. 

The 1990 survey was conducted to establish the displacement of MOUN 



-185- 
relative to its 1986 position. This 'mini-campaign" (Table 4.3), which 
included stationary GPS receivers at only three sites (MOUN, BLAC, and 
BCOl) was performed interactively with kinematic GPS transects along the 
southern San Andreas fault (K. Hudnut, personal communication, 1990). 
Data were collected for only one night; a total of 9 satellites were visible 
during the scheduled 7.0 hour experiment. 

GPS Processing 

The 1986 GPS observations were processed with the GPS22 software 
developed at the National Geodetic Survey. Satellite orbital information was 
provided by the NSWC (Naval Surface Weapons Center). A tropospheric 
delay parameter was solved at each station, constrained by surface 
meteorological measurements. Ambiguities were fixed to the nearest integer. 
Each of the 20 days of observation was processed separately, and the daily 
solutions were combined to form one set of station coordinates with the 
geodetic adjustment program DYNAP (DYNamic Adjustment Program) 
[Drew and Snay, 1989), All coordinates were computed in the WGS-84 
reference frame [Defense Mapping Agency, 1987]. Due to poor data quality 
and observation constraints, the accuracy of these measurements is believed to 
be on the order of 1 ppm (parts per million) [Neugebauer, 1988]. 

Data from both 1988 campaigns were processed with the Bernese GPS 
analysis software (version 3.0), from the University of Bern in Switzerland. 
(Preliminary processing such as data translation and cycle slip fixing were 
performed with an earlier version of the software.) The Bernese GPS analysis 
package allows 3-dimensional station coordinates to be determined from the 



•ISO- 
integration of carrier phase, pseudo-range, and orbital data (e.g., Gurtner et 

ai, 1985; BeuUer et al., 1985; Rocken, 1988). In addition to measuring station 

coordinates, the double difference estimation algorithm can solve for 

adjustments to six Keplerian elements and two radiation pressure coefficients 

for each satellite, an atmospheric zenith delay parameter at each station, a 

clock error term at each site, ionospheric model coefficients, and cycle 

ambiguity terms [e.g., Rocken, 1988]. 

For each of the 1988 surveys, all data were combined into a simultaneous 
multi-day solution. Surface meteorologic data (temperature, pressure, relative 
humidity) were used to constrain a Saasmotonian atmospheric model, and 
independent tropospheric zenith delay parameters were estimated at each 
station. We experimented with Exing ambiguities but found mixed results, 
therefore, ambiguities were left unresolved in the final solutions. 

In addition to station coordinates, satellite orbital parameters were 
estimated for both solutions. GPS observations from the CIGNET tracking 
sites were used to constrain the orbits. The Bernese software is able to 
combine ephemeris information from several days into a single multi-day arc. 
It has been suggested that multi-day satellite arcs significantly improve GPS 
precision (e.g., Lichten, 1987). Typically, 6 Keplerian elements and 2 
radiation pressure coefficients are estimated for each satellite. Davis et al. 
[1989] utilized 4-day arcs (72 hours plus the length of the daily observation 
session) to analyze GPS data from North America. A 5-day satellite arc was 
used to process GPS data off the southern California coast near Santa 
Barbara {Larsen et ai, 1990). 



-187- 
There comes a point, however, when the force model describing the 
satellite orbits begins to break down. It is unlikely that the 10-day interval 
of the February /March 1988 survey (9 observation days plus one day of no 
measurements) could be modeled from a 10-day satellite arc. For purposes of 
orbit determination, therefore, this campaign is divided into multiple 3-day 
arc segments (days 55-57, 58-60, and 62-64), each defined by its own initial 
conditions. The data are still processed simultaneously, except that 
independent satellite parameters are estimated for each 3-day arc. For the 
entire campaign, 18 Keplerian orbital elements and six radiation pressure 
terms are estimated for each satellite. A similar technique is used for the 
March/April survey. The satellite orbits for this campaign are defined by two 
3-day arcs (days 88-90 and 91-93). 

Orbits are improved by holding the coordinates of at least 3 CIGNET 
stations fixed, to values well determined from VLBI and satellite laser ranging 
[Murray and King, MIT interoffice memorandum, 1988]. The GPS phase 
observables from these fiducial sites constrain the orbits, which in turn 
improve the solution accuracy of the unfixed stations estimated as free 
parameters. Notice in Table 4.4 that there are several gaps in the fiducial 
coverage. Although it would be better to have complete data, in general, this 
is not a problem since there is always at least one day in each 3-day arc 
interval where observations from 3 fiducial sites are available. 

After each 1988 campaign was processed separately, the Cartesian 
coordinate differences from the two solutions were adjusted by least squares to 
obtain one set of coordinates for that year. 



-188- 



Table 4.4 CIGNET Data Availability 1988 



Day 



55 
56 
57 
58 
59 
60 
62 
63 
64 
88 
89 
90 
91 
92 
.21. 



MOJA 



WEST RICH 



Day is Julian day of year 
• Good quality data 
□ Poor quality data 




-180- 

The 1990 "mini- campaign" was processed with the Trimvec software, 

made available from the receiver manufacturer (Trimble Navigation, 
Sunnyvale, California). Recall that the purpose of this survey was to 
establish the displacement at station MOUN, presumed large because of its 
proximity to the 1987 seismic rupture. Since this mark had been reset 
between the 1986 and 1990 occupations, the error in the displacement 
estimate will be fairly large (~ 15 cm). Therefore, high accuracy from a GPS 
perspective is not required. Only stations BLAC and MOUN were included in 
the processing since BCOl was not occupied in 1986. The orbits were given 
by the broadcast ephemeris, and surface meteorological data were used to 
constrain a tropospheric delay model. (This line was processed by K. 
Hudnut.) 

Station Displacements 1986-1088 

GPS station displacements for the interval 1986 to 1988 are shown in 
Figure 4.4. All movements are made relative to station OCTI. Only 
horizontal components are shown. The method in which errors are 
formulated and utilized is disussed below. Generally, the observed 
displacements can be decomposed into 3 components: l) seismic deformation 
due to the Superstition Hills earthquake sequence, 2) secular deformation due 
to the Pacific-North American relative plate motion, and 3) measurement 
error attributed to poor data quality from the 1986 survey, most notable in 
the east-west direction. 

The GPS displacement vectors suggest considerable deformation between 
the 1986 and 1988 campaigns, of which a significant fraction is attributed to 



Figure 4.4: Imperial Valley GPS station displacements between 1986 and 
1988. All movements are relative to station OCTI. The observed 
displacements are attributed to the 1987 earthquake sequence, secular 
plate-boundary deformation across the Imperial Valley, and measurement 
error. Movements near the 1987 rupture zone approach 0.5 m. Error 
ellipses are determined by multiplying the formal errors by a variance 
factor, determined so the average error scales as 1 ppm (parts per 
million). The uncertainty in the east-west direction is about 4 time larger 
than that in the north-south direction. The anomalous southwest 
trending apparent movements for those stations to the southeast are 
attributed to measurement error. 



-101- 




-102- 
the 1987 Superstition Hills earthquake sequence. Stations nearest the seismic 
rupture zone (KANE and L589) show movements on the order of 40 cm. In 
fact, the 13 km KANEJ-L589 baseline was shortened by 70 cm. The 
orientations of the displacements are consistent with the conjugate fault 
pattern indicated by the mapped surface ofisets (i.e., right-lateral rupture on 
the Superstition Hills fault and left-lateral rupture along the Elmore Ranch 
fault). Other stations near the active fault system appear to have been 
aflfected by the 1987 event as well. 

There is an additional component of displacement not readily expidned 
by the seismic deformation. Stations east of the Imperial fault tend to be 
moving south or southeast relative to sites on the other side of the valley. 
This secular displacement is attributed to the relative motion between the 
North American and Pacific plates. Unfortunately, it is difficult to ascertain 
the magnitude of this deformation since station coverage west of the Imperial 
fault is somewhat lacking and many of these sites have rather large 
seismically induced displacements (recall that all GPS vectors are relative to 
OCT!). However, the plate-boundary deformation does appear lo be 
considerable, which is not too surprising considering conventional geodesy 
indicates a significant fraction of relative plate motion is occurring across the 
Imperial Valley. 

Also evident in Figure 4.4 are unusual movements which do not appear to 
be tectonically related. Most notable are the southwest trending vectors (as 
opposed to southeast) for those sites near the border east of the Imperial 
fault. It appears as if the entire network has undergone a systematic 
clockwise rotation. We have investigated this possibility by assuming the 



network could be rotated (and translated) In terms of an outer coordinate 
solution by minimiring the displacement component perpendicular to the 
structural axis of the valley (N40* W) [e.g., Prtscott, 1981]. Stations KANE 
and L589 were not included in the solution. However, the applied adjustment 
did not correct for the anomalous displacements, and in fact, made the 
apparent deformation less uniform. Although these unusual movements can 
not be attributed to a simple coordinate rotation, they can be explained by 
large east-west trending systematic measurement errors in the 1986 survey. 
This is consistent with the longitudinal orientation of the computed error 
ellipses (see below) and suggests the north-south displacement components 
may be a more reliable indicator of tectonic deformation. 

Station Displacements 1086-1900 

The 1986-1990 displacement of MOUN relative to BLAC is shown in 
Figure 4.5 (dashed arrow). Although the errors are large because MOUN was 
reset between surveys, the GPS data indicate significant movement attributed 
to the Superstition Hills events (recall MOUN is less than 1 km from the 1987 
surface rupture). However, based on conventional geodesy as well as the 
1986-1988 GPS movements, a non-seismic plate-boundary displacement 
component is suspected in the measurements. We attempt to remove this 
component by estimating the MOUN-BLAC secular displacement based on 
EDM observations. This is discussed in more detail below. We remove 2 
years of the accumulated MOUN-BLAC secular movement, and then compute 
the displacement relative to station OCTL Although the measurements still 
contain 2 years of non-seismic deformation, it places the displacements into 
the same reference frame as the 1985-1988 movements. The adjtisted MOUN 



-104- 

Figure 4.5: Imperial Valley GPS station displacements between 1986 and 
1990. The displacement at MOUN relative to BLAC is shown by the 
dashed arrow. For consistency with the 1986-1988 observations the 
estimated displacement at MOUN relative to OCTI is calculated by 
subtracting the estimated secular velocity of BLAC relative to OCTI 
obtained from conventional geodetic measurements (see Figure 4.9). 
Station MOUN was reset between surveys and site inspection during 1990 
revealed a positioning error of about 15 cm. 



-105- 



ffi.2 2 



o 






in 




-105- 
displacement is shown in Figure 4.5 (solid arrow). 

Station Dbplacements 1088-1988 (February* April) 

Seven GPS sites were occupied during both 1988 campaigns (Table 4.2), 
Calculated site displacements for this 1 month interval are shown in Figure 
4,6. An adjustment (simple translation) was applied to all movements so that 
the sum of the vector displacements is zero. The magnitude of the apparent 
movements range from 0.9 to 2.9 cm, averaging 1.6 cm. It is interesting that 
the 2.9 cm displacement at KANE is to the west-southwest, more or less 
expected if left-lateral afterslip occurred along the Elmore Ranch fault. 
However, while postseismic offsets were significant along the Superstition PTills 
fault, almost all Elmore Ranch activity ceased after the initiation of the 2nd 
main event [WUliams and Magtstralc, 1989; Magistralt, 1989; Hudnut tt al, 
1989a). The observed displacements probably represent measurement error as 
opposed to real deformation. Note that the largest vector components are 
oriented in the east-west direction. Station 0217 also exhibits a fairiy large 
apparent east-west directed movement, although this is almost certainly not 
tectonically related. 

Even if the displacements shown in Figure 4.6 are entirely measurement 
error, they do illustrate two points: 1) the accuracy with GPS is easily 
sufficient to monitor tectonic motions, and 2) the anomalous displacements for 
the 1986-1988 interval (Figure 4.4) are probably due to the poor quality of the 
1986 data. Typical crustal deformation rates across major tectonic structures 
in southern California are between 1 and 5 cm/yr. At 1 to 2 cm GPS 
accuracy, such deformation would be resolvable in time scales as short as 1 



-107- 
year. Although the short baseline (~ 50 km) horizontal precisions computed 
from GPS repeatability studies are generally at the sub-centimeter level (e^g., 
Dong and Bock, 1989], these tests usually involve multiple occupations of the 
same network over a consecutive 4 to 5 day interval. Because the 7 stations 
shown in Figure 4,6 were not all observed simultaneously (Table 4.3), the 
repeatability is somewhat degraded since errors will tend to propagate 
through the solutions. However, the relatively good consistency suggested 
with the 1988 results suggest that some of the unusual movements observed 
with the 198&-1988 displacement vectors are probably due to poor data 
quality from the 1986 campaign. 

GPS Errors 

Formal estimates of GPS uncertainty almost always underestimate 
variances derived from repeatability studies. We attempt to determine more 
realistic and illustrative errors by multiplying the structure of the formal 
covariance matrix calculated with the GPS solution by an estimated variance 
factor, which scales as average baseline length. For the 1986-1988 
displacements, the primary error source is presumably due to the 1986 survey, 
where the estimated accuracies are on the order of 1 ppm. We have chosen a 
variance factor so that the average baseline error scales as 1 ppm. Since the 
1988 data were processed robustly utilizing orbit improvement techniques (not 
available with the 1986 data), we assume these errors are negligible. 
Although this method is somewhat ad hoc, it does illustrate an important 
fundamental. Notably, the error in the east-west component is about 4 times 
larger than the north-south uncertainty. This is attributed to the north- 
south ground-track of the satellite orbits. 



-108- 
Figure 4.6: Imperial Valley GPS station displacements between 

February/March 1988 and March/April 1988. The observed movements 

indicate the magnitude of errors due to the 1988 survey. The vector scale 

is twice that of Figures 4.4 and 4.5. The displacement at KANE could 

represent postseismic deformation from the 1987 earthquake sequence. 



-100- 



' 


03 
CO 
OB 


1 


-p 


<— • 






••^ 




Ǥ 


U 

CU 


1^ 


■ Sg 


< 

1 


•CJ2 




' CM 


og. 


CO 




ffi.2 







Q 


U 






^ 
V 

fc 





T^ 



o 

CVi 






in 




-200- 
Because station MOUN was reset between the 1986 and 1990 surveys, the 
largest error source is due to the difficulty in establishing the new mark at the 
previous location. From field inspection, this uncertainty is estimated at 15 
cm (in all directions) and b additive to the GPS measurement error. 

4.6 Modeling 

Theory 

Simple dislocation theory is often used to model seismically induced 
geodetic deformation. The earth is considered a homogeneous isotropic elastic 
half-space with no stress applied to the free surface. The displacement field 
ujt for a dislocation L in the medium is given by 

"''-8^^^^"'"^id^ (4.1) 

where Vu, is the discontinuity, w* are the displacement Green's functions due 
to a set of strain nuclei, and Vj are the direction cosines of the normal to the 
surface element dE [Stckctec, 1958; Chtnncry, 1961). Analytical solutions to 
this integral are rather complex, but have been simplified for special cases of 
dislocation or fault geometry [e.g., CAmncry, 1961; Savage and Hastie, 1966; 
Manstnha and Smylic, 1967). General expressions of the displacement field for 
rectangular strike and dip-slip faults of arbitrary inclination have been 
computed by Manstnha and Stnylie [1971) and Okada [1985). Arbitrary slip 
directions can be designed by the superposition of strike and dip-slip 
dislocations. 

The strain/stress within a medium is computed by diflferentiating the 
displacement field. For the displacement u^ where « b a function of the 



-201- 



geometrical coordinates X;, the components of the strain tensor E are given by 

(4.2) 



1 ^i ^ auj 



" 2 (axj axi 

In an isotropic medium the stress tensor a is given by 

a..-X55,j+2^ij (4.3) 

where 6 is the dilatation (^-Se.,). We consider the medium as a Poisson 

i-l 

solid with X-M -2.8x10'^ dyne-cm"^. 

A rectangular dislocation within an elastic half-space will create a 
spatially dependent stress tensor c throughout the volume. The force acting 
at a point along an arbitrarily oriented plane in the medium is computed by 
multiplying a by the outward normal vector to the plane (5Jj. That is, the 
traction vector T is given by 

If we assume the plane is coincident with a fault, then the forces generated on 
this secondary structure due to the initial dislocation are determined by 
calculating the traction vectors at selected points along the fault. The normal 
(o-J, strike-slip {a,), and dip-slip [c^) stresses on the fault plane are computed 
by 

a.-T-K (4.5b) 

where Kn, K,, and ^^ are the normalized vectors perpendicular to, along 
strike, and along dip to the fault plane. Analytic solutions for the dislocation 
generated stress and strain fields within a medium are given by Iwasaki and 
Sato (1970) and AUwinc [1974]. 



-202- 
Inverse Methods 



Inversion of seismically generated geodetic displacements can yield fault- 
rupture parameters, such as the slip distribution along a fault plane {e.g. 
Ward and Bamentos, 1386; Harris and Segall, 1987; SegaU and Harris, 1087; 
Snay, 1989]. We use a ir od similar to that outlined in SegaU and Harris 
[1987]. Singular Value De osition (SVD) [e.g., Lanczos, 1961; Jackson, 

1972; Menkc, 1984] and elastic dislocation theory are used to invert the 
Imperial Valley GPS measurements for seismic slip along the Superstition 
Hills and Elmore Ranch faults. 

The relationship between surface deformation and slip along a rectangular 
dislocation is defined by Equation (4.1). The rupture plane is modeled as a 
set of non-overlapping rectangular dislocations. That is, the fault plane is 
partitioned into multiple sub-eiements or sub-faults. The slip distribution 
along the seismically active fault is given as the discreate approximation of 
slip along each sub-element. The normal equations which govern surface 
displacement resulting from such slip is given by 

AW-d* (4.6) 

where the superscripts g and / refer to geodetic observation and fault slip, 

respectively. Each row of A* is determined from (4.1), and is a function of 

sub-fault geometry and geodetic position. The slip dbtribution m' is defined 

by m'-lmi.mj, ■ • • ,mj^, where m; is the slip along the ith sub-fault. The 

data vector d^ contains the geodetic observables. Each GPS station 

displacement will add 3 rows to A« and 3 elements to d^, corresponding to the 

vertical and two horizontal components. In practice, we may choose to ignore 

the less accurate vertical observation. This te especially true in strike-slip 



•203- 



environments where the predominant displacement direction is horizontal. 

Surface rupture is easily included into (4.6) by considering measurements 
of surface displacement as geodetic observation. The ofiisets are modeled as a 
priori slip information on the surface intersecting sub-faults. Equation (4.6) 
becomes 



Am' 



A8 
A' 



m' 



d8 
d" 



(4.7) 



where d,' are the discreate approximations of surface slip along the fault trace 
and A^^ = 1 if sub-fault element j corresponds to surface slip ofbet t; otherwise 
A,^=0. 

The GPS displacements shown in Figures 4.4 and 4.5 are not connected to 
an external reference but are defined relative to station OCTI. (Some geodetic 
measurements such as line-length change recorded by EDM observations are 
independent of an absolute reference.) The displacement at OCTI is assumed 
to be 0, which in fact may be true from a seismic standpoint since this site is 
far from the Superstition Hills rupture zone. However, any attempt to use 
the GPS displacements as a criteria for evaluating the effect of the earthquake 
sequence will be distorted by measurement error at OCTI and/or non-seismic 
deformation between this site and the other stations. This ambiguity is 
largely circumvented if displacement-ofifeet terms are estimated in addition to 
the fault slip parameters. Equation (4.7) is then rewritten 



Am—A 



m' 
m^ 



(4.8) 



where m^^ is the ith non-seismic component (i.e., north-south, east-west, 
vertical) uniformly added to all station displacements. 



-204- 



The Singular Value Decomposition of A is given by 

A-UXVT ^^g^ 

where U is a matrix of eigenvectors spanning the data space, V is a matrix of 
eigenvectors spanning the parameter space, and X is a diagonal matrix of 
singular values. Without loss of generality this is written 

A-UpXpVpT (4 JO) 

where p refers to the non-zero singular values. If the normal equations of 

(4.8) are normalized to have unit variance [e.g., Scgall and Harris, 1987), the 

generalized inverse of (4,8) and (4.10) is given by 

[Lanczos, 1961; Menke, 1984). In practice it is often necessary to restrict the 
volume of the parameter space by considering only the it largest singular 
values, setting all others to 0. 

The generalized solution to (4.8) for the k largest singular values is given 

by 

m-Afc-M+VoQ^ (4.12) 

where Vg are eigenvectors spanning the null space of the model and Qq is a 

vector of arbitrary coefficients. The volume of the model space not 

constrained by observation is defined by VoO^ This term is not influenced by 

the geodetic data and is thus arbitrary. Often it is the minimum-length 

solution m — A,p*d which is of interest (the coefficients of Oq are 0). However, 

some other solution criteria can be satisfied by carefully designating the 

coefficients of Qq. 

For high resolution fault models where the rupture plane is partitioned 
into numerous sub-faults, it is necessary to apply some type of smoothing 



-205- 
constraint over the dislocation surface to prevent the slip distribution from 
taking on an oscillatory pattern. Scgall and Harris (1987] showed that the 
"roughness" of fault slip could be minimized by considering smoothness as an 
a priori constraint utilized from the model null space through the coefficients 
of Oq (Equation 4.12). They considered a smoothing matrix T^ with 
coefficients determined from the discreate approximation of the Laplacian 
operator V^^d^/dx^ +d^/dy^^ where x and y are the fault distances along 
strike and dip, respectively. The boundary conditions around the lower and 
lateral edges of the dislocation are assumed to be null slip, so that the applied 
smoothing operator causes the calculated fault oflbet to tend toward zero 
along these boundarys. Because the Superstition Hills and Elmore Ranch 
faults ruptured the surface, the upper boundary is considered an 
unconstrained dislocation. The estimated fault slip is then given by 

m - (I -- VoCVoTtTtVo)- Vo^TTTlAfc-M (4.13) 

(Equation 13, [Segall and Harris, 1987J). A similar formulation for utilizing 

fault smoothness over the model null space is given by Harris and Segall 

[1987); an alternate method considering fault smoothness as quasi-data is 

provided by Snay (1989). 

For over-constrained solutions, where there are more independent data 
than parameters, if k«"p then SVD is equivalent to simple least-squares. 
This is advantageous since the solution provided by (4.12) can be utilized for 
either uniform dislocations or for detailed parameterizations where the fault 
plane is partitioned into multiple sub-elements. 

Simple dislocation theory has the advantage that the displacement and 
stress/strain fields for simple fault ruptures can be computed almost 



-205- 

instantaneously. The inverse problem of using geodetic data to calculate the 
slip distribution along a fault plane is also stnughtforward. However, we 
have assumed the earth can be modeled as a homogeneous half-space. Crustal 
layering or inhomogeneities in the earth can introduce non-existent structure 
into half-space modeb [Savage^ 1987). While low- resolution schemes such as 
the average slip over the fault plane will not be seriously affected, attempts to 
resolve detailed properties may be badly contaminated by artifacts of earth 
structure. 

Seismic Displacement 

We model rupture along the Superstition Hills and Elmore Ranch faults 
as strike-slip dislocations along vertical planes extending from the surface to 
10 km depth. Each dislocation approximately coincides with the mapped 
surface rupture and/or aftershock distribution. The geometrical parameters 
for the modeled faults are listed in Table 4.5. Initially, the Superstition Hills 
and Elmore Ranch faults are considered uniform dislocations, with no slip 
variation allowed on the rupture planes. The dislocations are then 
partitioned into multiple sub-elements and the slip distribution along the two 
faults is calculated from the discrete ofibet for each sub-fault. 

For an initial estimate of slip along the two faults, we consider only the 
displacements at KANE, MOUN, and L589; the three GPS sites nearest the 
seismic rupture zone (Figure 4.7). Because the observed movements at these 
stations are relative to OCTI, we also solve for a imiform north-south and 
east-west ofiEset in the displacements. This will remove any systematic 
distortion due to measurement error at OCTI. Both faults are regarded as 



-207- 
Table 4.5 Parameters for Modeled Dislocations 





Superstition Hills 


Elmore Ranch 


Length (km) 


25 


25 


Width (km) 


10 


10 


Strike 


N50*W 


N40*E 


Dip 


90 


90 


Depth (km) 








Latitude ( • N) 


32.9569 


33.1078 


Longitude ( ' E) 


-115.7431 


-115.7505 



Latitude and Longitude are coordinates 

at top center of dislocation 
Depth is depth to top of fault 



-208- 

Figure 4.7: The best-fit solution to Model 1 (3-station inversion). The 
solid arrows indicate the observed displacements, while the dashed arrows 
represent the computed displacement based on Model 1. The shaded 
region indicates where horizontal displacements are greater than 4 cm. 



•2og- 







in 



iq 

iri 



CO 






CO 

I 



-210- 

simple dislocations not segmented into sub-regions. The solution to this 
simple model is given in Table 4.6 (Model 1) and the observed vs. calculated 
displacements are shown in Figure 4.7, Generally, there is good agreement 
between model and observation. This is not altogether unexpected since we 
are solving for 4 parameters with 6 data. The large discrepancy at MOUN is 
presumably due to the imcertainty in relocating the 1990 reset monument at 
the 1986 position (recall the estimated error is 15 cm in each direction). The 
surface deformation pattern computed from Model I is fairly extensive; the 4 
cm horizontal displacement contour is shown in Figure 4.7. 

The north-south and east-west displacement components at each Imperial 
Valley site, plotted as a function of distance from a N40*W trending line 
through OCTI are shown in Figure 4.8. Shown are the non-seismic 
movements; that is, the seismic component computed from Model 1 is 
subtracted from the observed displacements (Figure 4.4). Stations where the 
seismic correction is greater than 4 cm (in the component plotted) are shown 
as open circles, other sites as filled circles. The displacements represent a 
cross-section of non-seismic deformation perpendicular to the plate motion 
direction. 

A fairly consistent pattern is observed in the north-south components 
(Figure 4.8). Stations to the northeast have moved south (or southeast) 
about 8.1 cm relative to sites on the other side of the valley. Stations which 
display the largest deviation are for the most part those sites where the 
applied seismic correction is greater than 4 cm (open circles). This may 
indicate additional fault complexity not accounted for by the simple 
dislocation model used to remove the effects of the 1987 earthquake. The 



-211- 



Table 4.6 Inverse Models of Seismic Slip 



Model 


Fault 


Sub-faults 


Slip 


Moment 






Strike 


Dip 


(c 


m) 
±13. 


(xlO^* dyne-cm) 


Model 1 


SH 


1 


1 


109. 


7.8 


Model 1 


ER 


1 


1 


-45. 


±19. 


3.4 


Model 2 


SH 


1 


1 


130. 


.± 8. 


9.4 


Model 2 


ER 


1 


1 


-30. 


±10. 


2.3 


Model 3a 


SH 


10 


5 






9.9 


Model 3a 


ER 


10 


5 






5.9 


Model 3b 


SH 


10 


5 






8.4 


Model 3b 


ER 


10 


5 






7.0 


Model 3c 


SH 


10 


5 






6.2 


Model 3c 


ER 


10 


5 






3.9 


Model 3d 


SH 


10 


5 






9.2 


Model 3d 


ER 


10 


5 






4.9 


SH-I 
ER- 


Superstition Hills fault 
Elmore Ranch fault 









-212- 
Figure 4.8: The north-south and east-west GPS displacement 
components for the 1986-1988 interval. All distances are computed 
relative to OCTI on a cross section trending N50 ' E, perpendicular to the 
plate motion direction. The effects of the 1987 Superstition Hills 
earthquake sequence based on Model 1 are removed. Open circles indicate 
stations where the seismic correction is greater than 4 cm (for that 
component). The 8.1 cm north-south offset between stations on opposite 
sides of the valley is equivalent to 5.9 cm/yr displacement oriented 
N40*W. The large scatter for the east-west component is presumably 
due to large measurement errors in the 1986 survev. 



-213- 









n 
•*^ 

0) 

CO 
I 

o 



20 



sw 



— I — . — 

h North: 1988-19BB 



8.1 cm 



■20 

20 I — ' — r — ' — ' 

East: 1988-1988 



-20 



SJ I 

-4 — t- 



SA 

1 



III' 



t O ,0 



50 
Distance (km) 



NE 



_ J *_ «. 



100 



-214- 
east-west oriented displacements, however, show large data scatter; no 
distinguishable pattern is readily visible across the valley. The scatter is not 
a function of the magnitude of the applied seismic correction, so presumably 
it represents the large measurement errors inherent in the east-west direction. 

We assume the 8.1 cm north-south offset (Figure 4.8) is attributed to 
plate-boundary deformation ^'^tween the North American and Pacific plates. 
Taking into account the c. e. of the suspected deformation (N40*W), 

as well as the time interval bei.v..u .ae 1986 and 1988 survev^ 3 years), 
the north-south movements are consistent with 5.9 cm/yr displacement across 
the valley. This is significantly larger than the 3.45-4.3 cm/yr rates obtained 
from conventional surveys. Although accelerated deformation between the 
GPS campaigns can not be ruled out, there is relatively poor station coverage 
in the southwest portion of the valley so it is difficult to estimate the valley 
crossing displacement precisely. TL's is even more true considering most of 
the southwestern sites suffered large seismic displacements during 1987. If 
Model 1 (Table 4.6) does t^o^ -- 'v reflect the rupture process during the 

Superstition Hills earthq the unmodeled effects will propagate 

into the non-seismic estimate. 

The fault rupture calculated from Model 1 depends heavily on shallow slip 
since the three stations used are all within close proximity to the dislocation 
planes. While the observed surface offsets indicate rupture extends to the 
surface, greater slip at depth may go undetected. Therefore, it is necessary to 
examine the displacement at stations away from the fault to ascertain the 
depth extent of faulting. 



ORiGINAL PAGE IS 
OF POOR QUALITY 



-215- 
To incorporate more GPS data into the fault-plane inversion, it is 
necessary to remove the non-seismic deformation from the displacement field. 
Perhaps the best example of secular deformation across the Imperial Valley is 
provided by U.S.G.S. trilateration measurements between 1972 and 1987 [e.g., 
Prtscott tt ai, 1987a; Prtscott ct a/., 1987b], Computed station velocities for 
the Salton Trough EDM network (Figure 4.9) are roughly parallel to the 
direction of plate motion (N40"W), although to some degree the geodetic 
orientation is dictated by the outer coordinate solution imposed to transform 
EDM line-length changes into station displacements [Prescottj 1981). The 
total differential velocity across the network is 3.45 cm/yr and is 
accommodated in a 50 km wide zone [Prcscott tt ai^ 1987b). Triangulation 
measurements suggest a larger rate between 1941-1986 (4.3 cm/yr) but these 
observations are not as accurate as the EDM measurements [Snay and DrtWy 
1988). However, along the Imperial fault where EDM sites are sparse, the 
triangulation data suggest concentrated deformation in a narrow 20 km wide 
zone. The conventional geodetic data are modeled using the following 
empirical approach. The differential velocity across the valley is taken to be 
3.45 cm/yr. Running along the axis of the valley is a transition zone(s) 
(Figure 4.9), where the strain gradient is defined by simple shear with the 
displacements oriented N40*W, The transition zone north of the Imperial 
fault is 50 km wide; to the south it is 20 km wide. The modeled station 
movements shown by the dashed arrows in Figure 4.9 fit the observed EDM 
displacements extremely well. 

The secular deformation derived from the conventional measurements is 
removed from the observed GPS displacements (Figures 4.4 and 4.5) leaving 



-216- 
Figure 4.9: Imperial Valley EDM station velocities computed between 
1972 and 1987 (solid arrows). The movements are largely attributed to 
secular deformation due to the relative motion between the North 
American and Pacific plates. The displacements are modeled (dashed 
arrows) by 3.45 cm/yr displacement across the valley, with right-lateral 
simple shear oriented N40 * W occurring in a transition zones 50 km wide 
north of the Imperial Fault and 20 km wide to the south (shaded). The 
secular deformation is subtracted from the GPS displacements shown in 
Figures 4.4 and 4.5. 



-217- 




-218- 



the seismic component (and measurement error). For Model 2 (Table 4.6) the 
uniform slip along the Superstition Hills and Elmore Ranch faults is 
recomputed using all GPS data (without the secular deformation). The 
residuals (observed minus calculated) for this model are shown in Figure 4.10. 
The largest station discrepancies between model and observation trend in the 
longitudinal direction and are especially noticeable for those sites in the 
southeast. This simply reconfirms our speculation for large east-west trending 
errors. However, the residuals at the three stations nearest the seismogenic 
zone are unusually large. The large vector at MOUN is easily explained since 
this station was reset between surveys. The residuals at L589 and KANE, 
however, are significantly larger than the average discrepancy computed for 
the other stations. Because both sites are located in close pmximity to the 
earthquake rupture zone, this suggests additional seismic slip not accounted 
for by the simple dislocation parameters used for Model 2. 

AJthough the inversion results (Table 4.6) between Model 1 and 2 are 
marginally different (less slip on the Elmore Ranch fault; more on the 
Superstition Hills fault), this is not significant considering the estimated 
uncertainties. In fact, because the near-field (Model 1) and far-field (Model 2) 
solutions are similar, this suggests that to fi«t order there is not significant 
slip dependence with depth (within a factor of 2 or 3). It is also noteworthy 
that the uncertainties improve by only ^ SO % with the additional data 
supplied with Model 2. This illustrates the necessity of measurements near 
the seismic rupture. For simple fault models, where uniform slip is 
constrained to a single dislocation plane (or two planes in the case of the 
Superstition Hills sequence), it is as important to have at least minimal 



-210- 

Station coverage within a few kilometers of the seismogenic zone as it is to 
have many sites located away from the fault(s). 

Sebmic Slip Distribution 

Uniform dislocations along the Superstition Hills and Elmore Ranch faults 
were utilized for Models 1 and 2. To estimate the seismic slip distribution, it 
is necessary to partition the rupture planes into multiple regions or sub-faults 
(Model 3). The divisions must be sufficiently dense as to provide reasonable 
slip resolution. We choose 10 sub-fault elements in the horizontal and 5 in 
the vertical, so that each fault is partitioned into 50 sub-regions. The 
dimensions of each dislocation element is 2.0 km in width (vertical) and 2.4- 
2.6 km in length (2.4 km for Superstition Hills and 2.6 km for the Elmore 
Ranch fault). The slip distribution along the two rupture planes is 
constrained to be sufficiently smooth (Equation 4.13). The GPS 
displacements are adjusted according the the estimated north-south and east- 
west offsets from Model 2. 

In addition to the GPS data, a priori surface-slip information is added to 
the solution. Surface slip along the Superstition Hills fault (Figure 4.11) 
[Williams and Magistrale, 1989] extends (nearly) the entire length of the 
modeled fault plane. The surface rupture has been incremented into 2.4 km 
segments corresponding to the horizontal dimension of each sub-fault. The 
average slip over each segment is assigned as an a priori slip estimate for the 
surface fault element which it corresponds. Surface rupture along the Elmore 
Ranch fault is confined to the southwestern segment (Figure 4.11). Recall for 
this event that the mapped surface breaks occurred along several nearly 



-220- 
Figure 4.10: The residuals (observed minus calculated) for the best-fit 
solution to Model 2, The large residual components in the east-west 
direction are suggestive of measurement error. The residual at MOUN is 
likely attributed to the reset benchmark between surveys. The unusually 
large discrepancy at L589 (and KANE) suggest additional seismic 
deformation not accounted for by the simple uniform slip 
parameterization considered for Model 2. 



-221- 



c 2 ^ te 



•CBa o 
o V S 



o 

CM 



o 

CM 



E 



\ 



I 



1X3 



t» 




id 

I 



f 



CO 



o 



L 



in 



W 
« 



iq 



-222- 
Figure 4.11: Observed surface slip along the Superstition Hills and 
Elmore Ranch faults (dashed lines). The Superstition Hills ofisets were 
measured on January 25 and 26, 1988 about 1 month before the GPS 
observations. Decaying afterslip is recorded up to nearly 1 year after the 
earthquake sequence. The Elmore Ranch measurements are the 
cumulative slip from multiple surface breaks across a 10 km wide zone, 
with no recorded postseismic ofiEset after the earthquake. The discrete 
approximation to the siirface slip used to constrain the uppermost sub- 
fault elements in Models 3a and 3b is shown by the solid lines. 



.223- 



SW 



3. 40 - 



w 20 

u 

t: 

m 



Elmore Ranch Fault 
(left-lateral) 



1 L' "* 4l 







J— 



NE 



■ ■ I 



Constrained Slip 
Observed Slip 



100 r 



6 



^ 50 

0) 
U 

ed 
CO 



Superstition Hills Fault 
(right-lateral) 



^1^ 



\ 






I 






I \ 



10 



20 



Distance Along Strike (km) 



SE 



' ' ' ' 



30 



-224- 



parallel strands (Figure 4.2). We take the cumulative surface oflfaet for all 
strands [Hudnut et ai, 1989a} averaged over 2.6 km segments along the fault, 
and apply this as a priori slip information for the surface sub-fault elements. 
Where no rupture is mapped (to the northeast), the surface intersecting fault 
partitions are assigned slip. The a priori uncertainty for each surface-slip 
estimate is assimied to be 10 cm. 

The number of independent parameters estimated through singtilu- value 
decomposition depends on the number of singular values k utilized in 
Equation (4.12). A trade-ofiF exists between solution variance and resolution 
[e.g., Menke, 1984). While large k produces highly resolved models, this is at 
the expense of increasing solution uncertainty. Correspondingly, small it 
yields low variance solutions but does not provide detailed resolution. A total 
of 100 sub-fault elements are incorporated into Model 3 (50 for each fault). If 
k - 100 then slip along each sub-fault will be determined uniquely. Because of 
limited geodetic coverage, however, it is practical to consider only the first few 
eigenvectors of the parameter space defined by the geodetic observations. 
Therefore, each solved parameter is a function of some average slip over 
multiple sub-fault elements. This is fundamental property of singular value 
decomposition when used to solve under-determined or pooriy-determined 
problems [e.g., Jackson, 1972). It is necessaiy to determine the k which 
maximizes the resolution without allowing the solution to become too 
oscillatory or unstable. 

The geodetic moment, solution instability, and model residual calculated 
for different values of k are shown in Figure 4.12. The moment is a function 
of the average slip along the fault planes, while solution instability is 



.225- 

detcrmined from the standard deviation of slip for each sub-fault element. 
An instability of (stable) indicates uniform slip along the fault planes, while 
high values indicate an oscillatory or unstable solution. The RMS indicates 
the agreement between model and observation and is calculated by 
RMS^^{o^ — c^/€r^ where 0| is the observed, q is the calculated, and a^ is 
the uncertainty assigned to the ith observation. 

With surface slip incorporated into the solution (Figure 4.12a), the first 20 
singular values are well constrained by the measured oflbet along the fault, 
and are influenced little by the geodetic observations. The surface 
measurements reflect the dislocation on the uppermost fault elements, with 
little depth resolution. This is illustrated by the solution for k — 20. The 
calculated moments are significantly less than that for Model 2, presumably 
because the surface oSiset is not representative of the larger displacement 
along the rest of the fault plane(s). Consequently, in order to estimate the 
slip distribution with depth it is necessary to consider solutions where k > 20. 
After k=«30 the solution becomes very oscillatory as is indicated by the 
increasing instability value. The RMS is significantly reduced beyond k«=20 
but only improves marginally with increasing L The solution fit for k > 20 is 
slightly better than that for Model 2. 

Also evident in Figure 4.12a are the large moment estimates for the 
Elmore Ranch fault, which are almost equal to the computed moments for the 
Superstition Hills fault. This is unexpected considering the latter event 
yielded a significantly greater surface wave magnitude, as well as a larger 
moment estimated from Model 2. It is diflBcult to distinguish slip between the 
two faults using SVD as is illustrated by Figure 4.13. The displacement 



-225- 
Figurc 4.12a: The geodetic moment, standard deviation of sub-fault slip 
(instability), and solution RMS calculated for different singular values (k). 
Shown here are solutions constrained by surface slip measurements 
(20<k<30). 



-227- 



Constrained 
Surface Slip 



SH 

ER 

Total 



-^ 2.0x10^° r 
u 
a; 

>. 1.0x10=* 



0.0x10° 



jy 



'^m^^^'^'mm 



' Model 2 
SH 



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ER 



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2000 c 



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300 r 
200 - 
100 

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a o e- 



' Model 2 



• a o o o 



I * I ■ I II jb» 



20 



25 



30 



Singular Values (k) 



-228- 



Figure 4.12b: The geodetic moment, standard deviation of sub-fault slip 

(instability), and soi ^S calculated for different singular values (k). 

Shown here are solutic onstrained by surface slip measurements 

(l<k<10). 



ORIGINAL PAGE fS 
OF P00l«t QUALITY 



■229- 



Unconstrained 
Surface Slip 



u 
I 

9) 

>. 1.0x10"" 



0.0x10° 



CO 



2000 r 



1000 



CO 







300 r 



200 



100 







SH 

ER 

Total 



* Model 2 
SH 



'Model 2 

ER 



<t=AS 



Q >^ 



' Model 2 



o o o o 



5 



10 



Singular Values (k) 



-230- 
Figurc 4.13: The horizontal slip distribution calculated independently 
for the Superstition Hills and Elmore Ranch faults based on Model 2. 
The shaded region indicates where the horizontal deformation is greater 
than 2 cm for the Superstition Hills fault and 0.5 cm for the Elmore 
Ranch fault. The scale for the Elmore Ranch event is altered to account 
for the smaller dislocation. The deformation pattern is almost identical 
between the two faults, although the displacement magnitudes are larger 
for the Superstition Hills event. This illustrates the diflBculty in using the 
GPS measurements to resolve slip between the two faults. 



-231- 



33.5 



33 



T — ' ' ' ' 1 ' ^ 

SuperstiUon HillB Faiilt 
130 cm Dislocation 



Displacement 



50 cm 




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-232- 

pattem for a 130 cm rupture on the northwest trending right-lateral 
Superstition Hills fault is compared with a 30 cm rupture on the northeast 
trending left-lateral Elmore Ranch fault. Although the magnitude is different, 
the deformation pattern between the two dislocations is almost identical. As 
a result, the larger slip estimate along the Superstition Hills fault is being 
mapped onto the Elmore Ranch fault plane producing the higher moment. 
This is all the more true considering only the first few model-space 
eigenvectors are utilized, as is necessary since Model 3 is very underdetermined 
(more model parameters than data). Therefore, only linear combinations of 
model parameters are uniquely defined. The similar moments indicated by 
Figure 4.12a suggest slip between the two faults is strongly correlated in the 
solution. 

The estimated seismic slip distribution along the Superstition Hilb and 
Elmore Ranch faults for k"«23 and k««27 are shown in Figure 4.14a. We 
refer to these solutions as Models 3a and 3b, respectively (Table 4.6). 
Although both faults are partitioned into 50 elements, the fault-rupture is not 
as resolved as the contours suggest since only the first few (non-surface) 
model-space eigenvectors are independently solved. For k="23 the solution 
suggests fairly uniform rupture along both fault planes. The dislocation may 
be slightly concentrated to the southwest along the Elmore Ranch fault. The 
apparent '*bullseye" pattern is due to the smoothness constraints requiring the 
slip to tend towards along the lateral edges and lower boundaries (the upper 
boundaries are constrained by the surface slip information). There is little 
difference in the slip distribution for k—21 through k=26. However, there is 
a noticeable change in the dislocation pattern starting with k =27. While slip 



-233- 

along the Elmore Ranch fault still appears fairly uniform, displacement along 
the Superstition Hills fault is concentrated to the northwest and to the 
southeast. This change is significant and is caused by the GPS displacement 
at one station. Recall the large residual for L589 in Model 2 (Figure 4.10). 
This discrepancy is nearly eliminated beginning with k««27. Therefore, in 
order to satisfy the observed displacement at L580, it is necessary to 
concentrate rupture at each end of the Superstition Hills fault. Of course this 
analysis assumes the observed GPS displacement at L589 is seismically 
generated, and not contaminated by unusually large measurement error. The 
dislocation null near the center of the fault roughly corresponds to the drop in 
fault offset measured at the surface (Figure 4.11). 

Independent solutions are made without constraining the upper sub-fault 
elements by measurements of surface offset (Figure 4.12b). The unconstrained 
moments are generally smaller than when surface slip is incorporated into the 
model. This is because the surface measurements are less than the average 
slip estimate along the fault plane. Without surface constraint, the geodetic 
data are satisfied to a greater degree by slip near the surface; otherwise, it is 
necessary to compensate the small shallow offisets by increased slip at greater 
depths. The seismic slip distribution estimated without surface constraint 
along the Superstition Hills and Elmore Ranch faults for k=«3 and k = 7 are 
shown in Figure 4.14b. We refer to these solutions as Models 3c and 3d, 
respectively (Table 4.6). For these unconstrained solutions the slip 
distribution is confined to shallower depths. Slip concentration at each end of 
the Superstition Hills fault is suggested for k="7, although this division is not 
as pronounced as in Model 3b. We conclude that incorporating measurements 



-234- 
Figure 4.14a: Slip distribution along the Superstition Hills and Elmore 
Ranch faults computed from Singular Value Decomposition. Each fault is 
partitioned into the 50 sub-elements indicated by the grid spacing. 
Shown here are solutions for k=23 and k=27 constrained by 
measurements of surface ofEset. 



.236- 




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-23ft- 
Figure 4.14b: Slip distribution along the Superstition Hills and Elmore 
Ranch fatilts computed from Singular Value Decomposition. Each fault is 
partitioned into the 50 sub-elements indicated by the grid spacing. 
Shown here are solutions for k =3 and k«7 unconstrained by surface slip 
measurements. 



-237- 



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-238- 

of surface ofifeet tends to change displacement magnitude by requiring slip at 
greater depths, however, it does not significantly alter estimates of slip 
distribution. 

4.6 Geophysical Implications 

Conjugate Faulting 

The most prominent feature of the Superstition Hills earthquake sequence 
is the conjugate relationship exhibited by near-simultaneous ruptures along 
right-lateral northwest and left-lateral northeast trending faults. In the 
context of the Imperial Valley, the northeast trending structures are termed 
"cross-faults" [e.g., Hudnut et ai, 1989aj. Conjugate and cross-fault seismicity 
seems to be a fairly typical phenomenon for this region (Figure 4.15), and 
may dictate the strain transfer mechanism between faults. The 1981 
Westmoriand earthquake (Ml 4.1) is a prime example of cross-fault tectonics. 
The mainshock and aftershock sequence is clearly mapped onto a northeast 
trending lineament. Other examples are associated with the Imperial fault. 
The largest aftershock (Ml 5.8) following the 1979 Imperial Valley earthquake 
(Ml 6.6) was located near the town of Brawley [Johnson and Hutton, 1982], 
The focal mechanism and following seismicity suggested left-lateral slip along 
a vertical northeast trending fault. ReiUnger and Larsen (1986] found that 
rupture along an identical conjugate structure successfully modeled geodetic 
observations within the Brawley Seismic Zone. A large (Ml 5.5) afterahock 
was also recorded near Brawley following the 1940 earthquake [Neumann, 
1942). Due to the sparslty of seismic data, neither the mechanism nor 
location are precisely determined, although we speculate this event occurred 



-230- 

along the same northeast trending feature as the large 1979 aftershock. Of 
historical interest are Imperial Valley earthquake pairs during 1915 (Ml 6.3, 
Ml 6.3) and 1927 (Ml 5.8, Ml 5.5) [Beal, 1915; Toppozada et ai, 1978]. In 
each case the 2nd shock followed the first by about 1 hour, contrasting with 
the 12 hour interval between the 1987 events. It is not known which fault(s) 
ruptured during these earthquake sequences, but conjugate fault interaction is 
highly probable. 

Rupture on the Superstition Hills fault was almost certainly triggered by 
c^e Elmore Ranch event (occurring 12 hours earlier) suggesting some 
mechanism of stress transfer between the two faults. Figure 4.16 shows the 
normal {a^) and strike-shear (05) stress components instantaneously applied 
to the Superstition Hills fault due to a 30 cm left-lateral Elmore Ranch 
dislocation (Model 2). Tension and right-lateral shear are considered positive, 
both tending to induce failure on the rupture plane. Also shown is the 
Coulomb failure stress {a^), here given by a^^<T^ + tx(T^, where /i— 0.75. 
Positive values indicate stress-loading leading toward shear failure. 

The stress regime necessary for left-lateral rupture along a northeast 
trending fault is identical to that required for right-lateral failure along a 
northwest trending fault. Hence, we can assume that the Superstition Hills 
rupture plane was at or near failxire at the time of the Elmore Ranch event. 
The initial shock generated an increase in the Coulomb failure potential along 
the Superstition Hills fault (Figure 4.16), possibly advancing it past its failure 
threshold. This is seen mostly as a combination of reduced compressive 
normal stress (earthquake inducing) countered by left-lateral shear 
(earthquake inhibiting). The increase is maximized along the northwest 



-240- 
Figure 4.16: Known and/or potential conjugate /cross-fault seismic 
episodes in the Imperial Valley since 1900. Seismic release on (left-lateral) 
northeast trending structures was observed in 1979, 1981, and 1987. 
Earthquake pairs or msunshock/aftershock sequences suggestive of 
conjugate faulting were observed in 1915, 1927, 1940. This suggests 
conjugate/cross-fault interaction is typical for the Imperial Valley, 



•241- 




-242- 



Figure 4.16: Strike-shear (right-lateral positive) and normal stress 
change (dilatation positive) induced on the Superetition Hills fault due to 
a 30 cm left-lateral Elmore Ranch dislocation (Model 2). Also shown is 
the Coulomb failure stress change, where positive values indicate an 
increased potential for rupture (earthquake inducing stress). The 
northwest third of the 1987 Superstition Hills rupture plane underwent a 
stress change tending it toward failure with the maximum change 
calculated in the epicentral region near the intersection with the Elmore 
Ranch fault. There was no rupture to the northwest where the Coulomb 
failure stress was negative (reduced earthquake potential). The 
magnitude of the stress change (in bars) is in the range of typical 
earthquake stress drops. 



-24S- 



I ° 



Superstition Hills Surface Rupture 



Elmore Ranch Fault 

NW 



Q 10 



.""1 r"/' 

'. Normal Stress 1 I 

1 \ 


77' 

1 1 
1 1 
t 1 


1 > 


\ 1 




I 



43 5 - 



Q 10 



I I I I I I I I I I I I I I I I f I I I I ■ I I I I 

\ ) I 

Shear Stress , ,' 



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-20 20 

Distance Along Strike (km) 



Earthquake Increasing Stress (bars) 




<0 



o-i 



1-2 2-6 6-10 > 10 



-244- 



boundary of the rupture plane, near the nucleation point of the second event. 
Presumably rupture began where the applied stress was greatest and then 
propagated to the southeast. Northwestward rupture is prohibited because 
the increase in compressive forces tends to inhibit shear failure along this 
segment of the fault. The magnitude of the Coulomb stress increase near the 
Superstition Hills epicentrai zone (~ 10 bars) is comparable to typical 
earthquake stress drops. 

The one to several hour delay recorded between events during observed 
and suspected conjugate episodes in the Imperial Valley is significant from an 
earthquake failure perspective. Shown in Figure 4.17 are potential scenario's 
for earthquake ruptures involving conjugate-mainshock interaction, such as 
that observed for the Superstition Hills events. We assume faults fail by an 
undefined mechanism when they are at or above some critical stress level. 
The regional strain acting over several years brings a given fault near this 
critical failure point. A stress increase is induced along part of the fault plane 
due to rupture on a conjugate structure (e.g., Figure 4.16), which may or may 
not be sufficient to push the stress state past its critical threshold. In the case 
of Earthquake 1 (Figure 4.17a), the stress change caused by the conjugate 
event is not enough to induce failure. Some form of time dependent stress 
transfer onto the fault is active and eventually the critical level is reached. 
Such a mechanism involving postseismic viscous creep along the Elmore 
Ranch fault has been suggested for the 1987 Superstition Hills sequence [Given 
and Stuart, 1988). If this scenario is valid we would equally expect failure 
modes such as that indicated by Earthquake 2. Here the instantaneous stress 
applied to the fault from the conjugate event pushes the stress state past the 



-245- 
critical level and rupture is immediate. In this case failure along the two 

perpendicular fault planes will occur simultaneously. However, this behavior 

is not observed in the Imperial Valley. Conjugate episodes characteristically 

have been separated by one to several hours. This suggests that the critical 

stress level can be exceeded without immediate failure. Therefore, some time 

dependent mechanism must be active on the fault plane, as opposed to 

additional stress transfer through the crust. We loosely refer to this as "stress 

corrosion" (Figure 4.17b) [e.g., Das and Scholz, 1981). In the case of 

Earthquakes 3 and 4, it is suggested that the critical stress level must be 

exceeded for a period of one to several hours before failure occurs. Hudnut et 

al. [1989b] proposed fluid diffusion as an alternate mechanism, whereby the 

effective normal stress was reduced (made more positive) due to pore-fluid 

infiltration into the rupture plane, thus increasing the Coulomb failure stress. 

Th'is process still involves action on the fault plane rather than stress transfer. 

Regardless of cause, the temporal and geometric relationship exhibited by the 

conjugate fault interaction is seemingly typical of Imperial Valley tectonics 

and is thus an important factor for the potential prediction of large 

earthquakes and aftershocks. 

Moment and slip distribution 

The geodetic (GPS) source parameters for the Superstition Hilb and 
Elmore Ranch earthquakes are listed in Table 4.6 and Figure 4.14. The 
seismic moment is best defined by Model 2, while the slip distribution is best 
expressed by Models 3a and 3b. Model 1 is constrained with minimal station 
coverage and Models 3c and 3d do not include the additional information 
supplied from surface slip measurements. The GPS observations are directly 



-240- 



Figure 4.17: Schematic of potential earthquake failure processes in the 
Imperial Valley, a) Earthquake failure occurs after some critical stress is 
reached, b) Earthquake failure occurs following a time dependent delay 
after critical stress is exceeded. 



-247* 



a) 


(1) 


(2) 




Time Dependent 


Immediate 




Failure 


Failure 




Stress Hours 






Transfer ^--..^^ r^^ 


A ■ 






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Critical » 

Stress 


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Earthquake 
Stress 








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^ 


^ 


^/^ 


A 




C 




w 


/ 


c 
o 










Years 


Time 





b) 



Critical 
Stress 



GQ 

CO 
0) 

CO 



(3) 

Time Dependent 
Failure 

Hours 



(4) 



Time Dependent 
Failure 

Hours 



,.„^ Stress 

^g^ Corrosion 




y//. 



173 



Years 



Time 



-248- 



proportional to the combined effect of the Elmore Ranch and Superstition 
Hills events, although we have attempted to resolve slip between each fault 
plane. The calculated parameters are a function of the coseismic ofeet, as 
well as 3-4 months of postseismic slip (plus 1.5 years of preseismic movement, 
if any). The average Elmore Ranch dislocation is about 30 cm (left-lateral) 
with fairly uniform distribution along the fault plane. In the case of the 
Superstition Hills fault, the average slip is estimated at 130 cm with 
concentrated deformation along the northwest and southeast sections of the 
fault. Because the GPS sampling frequency is so low (years), the calculated 
source parameters should contain the total coseismic moment release, which 
includes several months of postseismic slip. 

In Table 4.7 the GPS moments are compared with estimates made 
through seismic and other geodetic studies. Forward and inverse models 
using teleseismic [Dziewonski tt ai, 1989; Bent et a/., 1989; Sipkin, 1980; 
Hwang ct ai, 1990] and strong-motion recordings [Frankel and Wenntrberg, 
1989; Wald ct ai, 1990] are used to constrain source parameters, as well as 
investigate complexities of the Superstition Hills rupture process. The 
teleseismic moments agree fairly well with the GPS estimates, while the strong 
ground motion data yield significantly lower results. The high-frequency 
strong-motion measurements are dominated by energy around 1 second and 
conceivably miss a sizable portion of the long-period energy release recorded 
with the teleseismic and GPS data. Hence, the near field seismic solutions 
may underestimate the total moment release. 

Geodetic measurements from Pinyon Flat observatory are used to 
constrain planer and curved dislocation models for the Superstition Hills and 



Method 



-249- 
Table 4.7 Moment Comparison 



Moment (xlO^ dyne-cm) Reference 
SH ER Total Ratio 



GPS (Model 2) 


9.4 


2.3 


11.7 


4.1 


This Study 


Tdeseismic 


7.2 


1.4 


8.6 


5.1 


Daewotuki et al. [1988] 


Tdeseismic 


10. 


2.3 


12. 


4.3 


Sipkm (1988] 


Tdeseismic 


10.8 


2.7 


13.5 


4.0 


Bent et al. [1989] 


Tdeseismic 


8. 








Hwang et al. [1990] 


Strong Motion 


5.2 








Wali el al. [1989] 


Strong Motion 


1.8 








FrankeU and Wennerberg [1989] 


Pinyon Flat (Planar-A) 


3.7 


0.8 


4.3 


4.6 


Agnew and Wyatt [1989] 


EDM 


9.3 








Luowaki and Savage [1988] 



SH - Superstition Hills fault 
ER - Elmore Ranch fault 



-250- 



Elmore Ranch faults [Agnew and Wyatt, 1989). The data are obtained from 
long-base strsun and tilt*meters, as well as a borehole diiatometer. The best- 
fit planer models to all observations (Table 4.7) are significantly lower than 
those calculated with the GPS and teleseismic data, although a 70 % moment 
increase for the Superstition Hills fault is obtained when the str^nmeter data 
are excluded. The low moment estimate may be due to a number of factors 
[Agnew and Wyatt, 1989]: 1) measurement quality, particular with the 
strainmeter, 2) rheologic differences between Superstition PTills and Pinyon 
Flat, and 3) strainmeter-dilatometer sensitivity to the nodal deformation 
plane roughly on azimuth with the observatory. 

Geodoiite observations of the Salton Trough EDM network were made in 
early December (1987), several days after the two large earthquakes [Lisowski 
and Savage, 1988]; the last previous occupation was in January, 1987. Simple 
dislocation models with 40 cm left-lateral slip along the Elmore Ranch fault 
and 120 cm right-lateral slip along the Superstition Hills fault best-fit the 
observations. The estimated moment for the Superstition Hills event (Table 
4.7) is comparable to that obtained with the GPS displacements. 

The discrepancies in Table 4.7 are largely attributed to the alternate 
methodologies, observations, and parameters used to constrain each model. 
However, for those calculations which include moment estimates for both the 
Superstition Hills and Elmore Ranch events, the ratio between the two 
ruptures is fairly constant. This illustrates an internal consistency with each 
method. More importantly, it suggests that postseismic slip along the 
Superstition Hills faxilt is probably confined to the shallow segment of the 
rupture plane. Since seismic activity on the Elmore Ranch fault essentially 



-251- 



ceased after the 2iid main event, if postseismic slip were occurring in mass 
along a large fraction of the Superstition Hills rupture plane, the GPS 
moment ratio would be considerably larger. 

While the epicenter and aftershock sequence for the Superstition Hills 
event were concentrated along the northwestern portion of the fault, strong 
ground motion, teleseismic, and surface ofiset data suggest significant moment 
release on the southern section of the Superstition Hills fault [Wald ti a/., 
1989; Btni tt ai, 1989; Hwang tt ai, 1990; Williams and Magistrale, 1989]. 
An exception is the strong ground motion study of Frankcl and Wenntrberg 
[1989] where slip is confined to the northwest. However, their low 
Superstition Hills moment (Table 4.7) suggests this analysis may be strongly 
susceptible to the high-frequency content of the data, indicating rupture along 
the southeast segment was dictated primarily by low-frequency energy release. 
The GPS data also reveal dislocation along the southeastern segment of the 
fault, and further suggests a displacement null near the faults mid-section. 
This slip deficiency may be related to the surface ofiset drop observed along 
the center of the fault (Figure 4.10). 

Deformation across the Imperial Valley 

The 1986-1988 GPS station displacements indicate a significant 
component of deformation across the Imperial Valley not associated with the 
1987 Superstition Hilb earthquake sequence (Figures 4.4 and 4.8). This 
motion is attributed to plate-boundary deformation due to the relative 
velocity between the Pacific and North American plates. From empirical 
evidence provided by Salton Trough EDM observations between 1972 and 



-2o2 



1987, these non-seismic movements were inodeled as 3.45 cm/yr differential 
velocity across the valley. However, after removing the seismic deformation 
predicted with a preliminary model (Model 1, Table 4.6) the calculated GPS 
displacements average 5.9 cm/yr (Figure 4.8). significantly larger than that. 
obtained with the triiateration measurements over the last two decades. Thb 
GPS velocity is also larger than the 4.7 cm/yr plate motion predicted from 
global models (for Imperial Valley coordinates) [DcMets tt «/., i980l. Most 
likely the GPS rate is an overestimate, especially considering it contains large 
measurement uncertainty due to poor 1986 data quality, and is heavily 
influenced by seismic effects from the 1987 earthquake sequence. It is possible, 
however, that the 1986-1988 GPS rate could represent accelerated 
deformation. In fact, GPS observations between 1988 and 1989 indicate 5.2 ± 
0.9 cm/yr displacement across the Imperial Valley {Larstn and Reilingcr, 
19901. Accelerated deformation is not without precedence. Triangulation' 
observations suggest a rate of 6.2 cm/yr between 1941 and 1954. although 
this is attributed to postseismic deformation following the 1940 Imperial 
Valley earthquake. Increased deformation following the 1979 earthquake is 
not observed In the EDM observations [Savage ct ai, 1986). Additional GPS 
measurements are necessary in the Imperial Valley in order to ascertain the 
current deformation rate. 



4.7 Conclusions 



Station movements computed from 4 Imperial Valley GPS campaigns 
indicate large crustal displacements during the periods 1986-1988 and 1986- 
1990. Much of the deformation is attributed to the 1987 Superatition Hills 



OR[G[MAL PAGE IS 
OF POOR QUAUTY 



-253- 

earthquake sequence. Ten sites near the seismic rupture zone are displaced at 

least 10 cm, although the GPS observations contain large uncertainties due to 
poor data quality from the initial (1986) survey. This is the first occurrence 
of a large earthquake within a preexisting GPS network. 

The 1987 earthquake sequence is initially modeled as uniform offsets along 
rectangular dislocations in an elastic half-space. The best-fit model to the 
GPS observations requires 130 cm right-lateral slip along the northwest 
trending Superstition Hills fault and 30 cm left-lateral motion along the 
conjugate northeast trending Elmore Ranch fault* The slip distribution along 
each fault is investigated by partitioning the rupture planes into 50 sub- 
elements and utilizing Singular Value Decomposition to estimate the slip 
along each sub-fault. Measurements of surface offset are used to constrain the 
shallow elements of the fault plane. The estimated slip distribution along the 
Elmore Ranch fault is fairly uniform. Slip along the Superstition Hills fault 
appears to be concentrated to the northwest and the southeast with a 
displacement drop indicated near the faults midsection. There is some 
evidence that postseismic slip along the Superstition Hills fault was 
concentrated near the surface. The estimated moments are 9.4 x 10^^ dyne- 
cm and 2.3 x 10^^ djrne-cm for the Superstition Hills and Elmore Ranch 
faults, respectively, which are consistent with moments obtained from 
teleseismic data. 

In addition, the 198&-1988 GPS observations suggest non-seismic 
movements across the Imperial Valley of up to 5.9 cm/yr. These secular 
displacements are attributed to plate-boundary deformation due to the 
relative motion between the North American and Pacific plates. The observed 



-254- 
rate is probably an overestimate, however, as it is heavily influenced by 
unmodeled seismic effects and measurement error. Regardless, the observed 
seismic and secular deformations clearly emphasize the importance of future 
GPS study in the Imperial Valley, 



.265- 



Acknowiedgements 

This research was a collaborative effort conducted under the auspices of 
Robert Reilinger (MIT). The field support provided by so many people has 
proven invaluable. William Young and Gerald Dole at the Riverside County 
Flood Control District and Gerald Stayner at the Riverside County Survey 
Department provided support for the 1990 mini-campaign. I am especially 
grateful to the support provided by Hiroo Kanamori. This work is supported 
by U.S.G.S. grants 14-08-0001-61679 (MIT) and 14-08-001-61354 (Caltech), 
and by NASA contracts NAG-5-842 (Caltech) and NAG-5-814 (MIT). 



-2SS- 
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148 
PRECEDING PAGE BLAf^K NOV FSlMED 

APPENDIX 3 



Lateral variation in upper mantle temperature and composition beneath mid-ocean 
ridges inferred from shear-wave propagation, geoid, and bathymetry 



by Anne F. Sheehan 



Abstract from Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, 258 r)., 1991 



149 



ABSTRACT 



Resolution of both the extent and mechanism of lateral hetaogeneity in the upper 
mantle constrains the nature and scales of n«ntle convection. ^^T^^^TJ 
DMticular interest as they are likely to provide our closest glunpse at the patterns of 
SSiJ? SSS and convective flow in the upper mantle because of the^ young age 
S^Sr<SS^ relative to continental regions. Our objectives m this Aesis are 
HeSnektcral variations in the seismic velocity and attenuatton structure of the 
UthSSS^and^nospheie beneath the oceans, and to combine these seismotopcal 
oteSva^ns with the date and theory of geoid and bathymetry anomalies m order to test 
S^^e ^m models for seaHoor Ipieading and "lande conv^«. ^^^^ 
on detCTimning variations in mande properties on a scale of about 1000 km, comparable to 
Ae aS^ of tSupper mantie. SeisSc velocity. geoi<l and bathymetry anomah^ are 
^S^to variants in upper mande density, and we formulate inversions to conibme 
m^Stivdy these different d£ and search for a common ongm. Vanajons m m^tie 
Sty ^ be either of thermal or compositional origin and are presumably related to 
mantie convection and differentiation. 

Bv means of a large data base of digital seismograms and waveform cross-c«relation 
and s^Stfo S^ues, we have m^ured SS-S differential travel tmie residuals and 
SSffoSaSation i2 order to determine lateral variations in upper mande stru(^ 
bSSTe iSi-Atiantic Ridge and East Pacific Rise. Differential travel times of such 
Sf af Sslmd S with identical source and receiver have die advantage that r^^duals are 
fcte dotted by contributions from die upper mande n^ the siufa^ U^^^uit 
of die reflected phase (SS). Under this assumption, differential SS-S ttavel tinae residuals 
^^pSlnhe sfbounce points as a means of deUneating lateral vanations m m^tie 
SnirZTAfter removing die signature of Udiosphere age, we find evidence for long- 
wteS^^vSSTnls Srelduals along the'Mid-Adan^ 
wave en|S of tfiese variations is 1000 to 2000 km. TTie^ trayeUrne anom;^^^^^ 
ouSivcly widi along-axis variations in badiymetry and geoid height We formukte a 
SSSeSw travel time residual, geoid height, and badiymetry under die assumption 
C aS arise from variations in upper mande temperature or buUc compoation 
Inarameterized in terms of Mg#). The inversion employs geoid and topography keiriels 
wSdS^ci^dtemantie viscosity structure. Inversion for temperature pertijrbations 
S^e mSJidesVood fits to travel time and geoid data. The fit to topography^hich is 
S^SyEnSiSby unmodeled crustal diickness variations, is not as good. The inversions 
fOT terniSSau^avOT die presence of a diin low viscosity layer in die upper rnande and 
teS^^bations concentrated at depdis less tiian 300 km- Compo^tional 
vSons al^are unable to match die travel time and geoid or badiymety da^ 
SKusly. A joint inversion for temperatiire and coinposition provwfcs good fits to 
h^a fffioid and ttavel time anomaUes. Temperatiue variations are ± 50 K and 
^tSStio^vScSTare ± 0.5-3 % Mg# for models widi die temperati« variations 
SSXtributed over die uppermost 300 km and die compositional variations eidier 
Sbuted uniformly over die same interval or concentrated at shallower depdisJThe 
SSdmdesSS variations are consistent widi die chemistiy and geodiermometry of 
dredged peridotites along die Mid-Atlantic Ridge. 

ruffrffntial travel times of SS-S pairs in die east cenoal Pacific show several 
differei^ftSm A^ m>XAdiitic. m most obvious difference is diat the travel time 
^dSe^iSidy larger dian in die Adantic. even at a fixed age The ti^vel time - 
TgVr^lt^is SSn Ae Pacific, aldiough diis may be partially attributable to the fact 
S weh^e nS^pled a large range of plate ages in die eastern Pacific. In die Adantic 



150 



our results are not consistent with the presence of a simple pattern of ^^^^^^^X^P^;, 
wMle in the Pacific the data arc consistent with the presence of weak anisottopy in the upper 
m«nSe U ha/^ sueSstcd that anisotiopy may be more pronounced at fi«t spreading 
^Aai i do^SSg n^b^ in the Uthosphere (due to a rate dependence of the 
SSSi?f« oriSoUv^e crystals in the Uthosphere) and the asthenosplwre (because 
SriS^"<S Sow SS St moving plates is likely to take the form of a I^J^^ve 
SeSvSi can produce a lattice preferred orientation of olivine crystals), and o^ 
3 ^^ri^nt wiUi this suggestion There is substantial ^b^tym our^m,py 
iSasurements for the Pacific, however, due to a poor samphng of azimuthsjo mat it is 
S::^" diu^ hete^geneity rather than -futhal an^y «^i^g^^^^ 
obsaved azimuthal pattern. SampUng at a more uniform distnbution of a^™^shouia 
SteSds re^t less^unbiguous, and as more seismic stanons are deployed at new 
geographic locations our chances of resolving tins issue will improve. 

Inversion of travel time residuals, geoid, and batiiymetry data [^,^^'^'^'^'' 
indic^tfiatcomDOsitionalvariationsaloneareinadequatetomatchallofthedata 

SS^sl^^^S^ results for die north Atiantic. Temperatme van^ons ato^. 
KZ produce significant variance reduction. The "jversion «duti(»s ^i^^^^^ 
t««~^h,n. in the vicinitv of tiie Galapagos hotspot in the range 50 - 150 K. further 
S^Tn^^to^SIie die effSc^ of subduction zone stnicttire and possible crustal 
tiiickening in die eastern Cocos plate region. 

As a comolement to die study of travel times, we have measured SS-S differential 
attenuii^SeSi Atbntic region. Mapping seismic Q in die upper mantie is an 
SSiTiSl to ^sslnTmechSisms ofTtertl heterogeneity bccau^ die attenuation of 
^S^a^is sensitive to variations in temperature and ^P^^^^^ereS^ 
attenuation is positively correlated widi SS-S travel tmie ««dual. Both dif^«^ 
a^nuation andttavel time residual decrease widi increasmg seafloor age. Tht age 
SSTsS^S travel time residual can be explained entirely ^ die coohng of ^ 
S^khAoVohwe ie, contributions from die asdienosphere or from a ^^ 
SS are^t^ilhS On die assumption diat plate cooline also dominates the vanatton 
S^tiS^^Sn widi age, we derive an empirical C^J-temperature «lanon for the 
^?Sph«€ The variation of Q-^ widi temperature diat we denve is not as strongly 
SSeniS^teWature as tiiat obsei^ed in laboratory studies. Systematic lc«g- 
vSSShTlMS^ km) variations in upper mande differential attenuation are evident 
Sa Sla^^s ofdic^^ Ridge. 'Aese variations correlate approximately widi 

S-w*tekn^v^on7Tn shear wive travel time residuals and are attributed to along- 
axis differences in upper mande temperature. 



151 



APPENDIX 4 



Joint inversion of shear wave travel time residuals, geoid, and depth anomalies 
along the Mid-Atlantic Ridge for long-wavelength variations in upper mantle 

temperature and composition 



by Anne. F. Sheehan and Sean C. Solomon 



Submitted to Journal of Geophysical Research, March 1991 



PRECEDING PAGE BLANK NOT FILMEJ 2 

ABSTRACT 
Utilizing a digital data base of over 500 seistnograms and a wavefonn cross-correlation 
technique, we have measured SS-S differential travel time residuals as a means to examine the 
shear wave velocity structure in the vicinity of the Mid-Atlantic Ridge. Differential travel times 
of such phases as SS and S with identical source and receiver have the advantage ti.at residuals 
are Ukely to be dominated by contributions fiom die upper mantle near ti.e surface bounce point 
of the reflected phase (SS). Under this assumption, differential SS-S travel time residuals are 
napped at the SS bounce points as a means of delineating lateral variations in mantie structure. 
After removing ti.e signature of lithosphere age, we find evidence for long-wavelength variations 
in SS-S residuals along the ridge. The dominant wavelength of these variations is 1000 to 2000 
km. These travel time anomaUes correlate qualitatively with along-axis variations in bathymetry 
and geoid height We formulate a joint inversion of travel time residual, geoid height, and 
batiiymetry under the assumption that all arise from variations in upper manUe temperature or 
bulk composition (parameterized in terms of Mg#). THe inversion employs geoid and 
topography kernels which depend upon the mantie viscosity structure. Inversion for thermal 
perturbations alone provides good fits to travel time and geoid data. The fit to topography, 
which is likely dominated by unmodeled crustal tiiickness variations, is not as good. The 
inversions for temperature favor the presence of a thin low vi«:osity layer in die upper mantle 
and temperature perturbations concentrated at depths less tiian 300 km. Compositional variations 
alone are unable to match the travel time and geoid or bathymetry data simultaneously. A joint 
inversion for temperature and composition provides good fits to botii geoid and travel time 
anomalies. Temperature variations are ± 50 K and compositional variations are ± 0.5-3 % Mg# 
for models with the temperature variations uniformly distributed over the uppermost 300 km and 
the compositional variations either distributed uniformly over the same interval or concentrated at 
shallower depths. The magnitudes of these variations are consistent with die chemistry and 
geothermometry of dredged pcridotites along the Mid-Atiantic Ridge. 



iNTOODUCnON 



Seismic velocity and density of upper manUe material are expected to be functions of 
temperature and composition. The deUneation of long wavelength variations in these physical 
properties thus provide important constraints on mande convection, crust-mande differentiation, and 
mande chemical heterogeneity. In this study we determine lateral variations in upper mande 
temperature and composition along the Mid-Atiantic Ridge through tiie combined inversion of shear 
wave differential travel times, geoid height, and bathymetric depth anomalies. 

The advent of seismic tomography has led to a number of tiiree-dimensional maps of lateral 
variations in seismic velocity in the upper mande, and several such models of the north Adantic 
region have been developed, both as parts of global studies [e.g., Woodhouse and Dziewonski . 
1984; Nakanishi and Anderson, 1984; Tanimoto, 1990] and tiirough regional investigations of 
long-period surface waves [e.g., Honda and Tanimoto, 1987; Mocquet et a/., 1989; Mocquet and 
Romanowicz, 1990]. With surface wave methods each wave samples the average vertical variation 
in upper mande structure along its path, but because of the long wavelengths involved the inversion 
of phase or group velocity from many paths tends to smooth out lateral variations. Body wave 
travel times can provide independent information about upper mande heterogeneity at potentially 
shorter horizontal scales than surface waves can resolve, and progress has been made in the 
determination of lateral heterogeneity in the North Adantic through the use of bodi differential and 
absolute travel times of body waves [Kuo et ai, 1987; Grand, 1987, 1989]. 

The travel times used in diis study are differential times of die body wave phase pair SS-S. 
Differential travel times of shear wave pairs are weU suited to the study of upper mande 
heterogeneity [Sipikin ami yordon, 1976. mO; Stark and Forsyth, m3;Butler, \919; Kuo et ai, 
mi; Woodward and Masters, 1991] and have the advantage that source and receiver effects are 
apFoximately common to both phases and are tiius largely eliminated by differencing. Under the 
assumption that die lower mande is relatively homogeneous and that die portions of the ray patiis in 



the upper mantle are steep, the differential travel time anomaly is associated with upper mantle 
heterogeneity in a small volume centered beneath the surface bounce point of the reflected (SS) 
phase. This technique is thus well suited to the investigation of horizontal variation.\n structure, 
but the resolution of variations with depth is poor. 

Oceanic bathymetry and geoid height data are sensitive to variations in manUe density at 
depth. Such variations can be either thermal or compositional in origin and, like seismic velocity, 
are presumably related to mantle convection and differentiation. Geoid (or gravity) and topography 
have become the most commonly used tools for mapping out and constraining models of upper 
manUe convection [e.g., Anderson et ai, 1973. McKenzie and Bomn, 1976; McKenzie, 1977; 
McKenzie etaL, 1980, Parsons and Daly, 1983; Buck and Parmentier, 1986; Craig and McKenzie, 
1986]. In addition, measurement of the admittance (the spectral ratio of geoid to topography) has 
been widely utilized to estimate the depth and mode of compensation of oceanic sweUs and plateaus 
[e.g.. Watts et al, 1985, Cazenave et al., 1988; Sandwell and MacKenzie, 1989; Sheehan and 
McNutt, 1989]. Several workers [Dziewonski et ai, 1977; Nakanishi and Anderson, 1984; 
Tanimoto and Anderson, \m; Stark and Forsyth, m3; Dziewonski, l9M;KuoetaL, 1987] 
have noted correlations of geoid and travel time (or velocity structure) at a number of different 
wavelengths, although only a few [Richards and Hager, 1984; Hager and Clayton, 1989] have 
combined observational seismology with geoid anomalies in a quantitative and dynamically 

consistent manner 

In this study we present the first formal inversion of geoid, depth, and travel time anomaly 
data for lateral variations in upper mantle temperature and composition along the Mid-Atlantic 
Ridge. Given a distribution of temperature or density perturbations in the upper mantle, the 
forwaixl problem of calculating differential travel time, geoid, and depth anomalies is 
straightforward. This forward problem forms the basis for a joint linear inversion of these three 
types of observations under the assumption that all arise from parameterized long-wavelength 
variations in upper mantle temperature or composition. Results of a set of inversions carried out 



u»Jer differ, assumptions reganitag Ac depd, ex>em of lattnl heterogendn. and U« n»mle 
viscosinr Sttuctme arc compared with o<her constraints on variations in mantle temperature and 
degree of melt removal. 

MEASUREMENT OF DIFFERENTIAL TRAVEL TIMES 

The seismic data used in this study consist of long-period S and SS phases obtained from the 
Global Digital Seismic Network (GDSN) \Feterson ex al., 1976; Peterson and Hm, 1982]; the 
Network of Autonomously Reconiing Seismographs (NARS), a linear broadband array in western 
Europe [met and Vlaar, mi]; and several broadband stations from the global GEOSCOPE 
network [Romanowicz et a/.. 1984]. A list of stations used in this study is presented in Table 1. 
We use only transversely polarized (SH) seismograms (rotated from N-S and E-W components) to 
avoid interference from the SKS phase and contamination from P-SV conversions at the base of the 
crust and other near-surface discontinuities. Recent work by Gee and Jordan [ 1989] suggests that 
travel times depend on the frequency band used in the analysis. In order to maintain a self- 
consistent data set for our study, additional processing is appUed to data from the NARS and 
GEOSCOPE arrays in oider to mimic the instrument response of the longer period GDSN stations. 
This Focessing allows us to measure travel times from a set of seismograms that all have 
essentially the same frequency response. Data from the NARS and GEOSCOPE arrays are 
decimated (with a low-pass antialiasing filter) to a common samphng interval of 1 s. The data are 
further filtered using a noncausal 3-point Butterwoith filter {Rader and Gold. 1967] with a 
frequency bandpass of 0.01 - 0.20 Hz. This additional filtering greaUy improves the signal-to- 

noise ratio of the SS phase. 

A wavefom. crossK»nelation method is utilized to detemnne the differential travel time 
between the phases S and SS \Bmler. 1979; Smrk and Forsyth. 1983; Km, e, at.. 1987). Tlte 
procedure involves the constmcdon of a "synthetic" SS pulse from S and die evaluation of the 



„„,3^,ado„ function between *e,«l and synthcucwindowedSSphascsCHgure .). 11.0 
s,„U,edc SS pu.sc is crea^d fton. S in U,e foUowin, manner. The S pulse is windowed and 
a»nua«d (wid. ««„uadon paran,e.er ,-= 3 s, ,Ora.^ a.^ He^r.er, 1984; Kuoe,^.. .987, <o 
accoun. for *e additional d,ne SS ■rave.s in U,e manUe, and men a ^ phase shift (H..ber. 

^.sfonn, is appUed «, ihe a.«nua.ed S pulse u, sin,ula,e ti,e frequency-dependent phase staf. 
Which *eSSwave«ndergc«sa.anin«n,alcausticlC,.,W«-c,..'^. 19751. Tl-edifferential 

a»e is ohuined fton, d.e pealc of .he cross cor^lation between *e syndetic SS ccnsm.c«d f^ 

U.e S wave and d» real SS. Tl-e tesidual SS-S tin^s a« obtained by subtiacting .he Observed 

diffe^ntia. tin« fron, d«. predicted by the PREM Earth n,odel m^-^ <^ ^"^-^ '«»" 
and coveting for Ear* ellipticity (Dzi.w„n.*i ar^ Gilten. .976, and SS bounce point 
bathymetiy. Our convention is *at negative residuals are indicative of either ear.y SS or .ate S. 
constant window lengths of .20 s are used for ^th the S and SS phases. In general. ti>e 

^served diffetential travel times vary by as much as 1 s depending on how S and SS are 
windowed, our .^Kielling with synthetic seismo^ams indicates matemphasi^gtiteonsetof the 

SS waveform can lead to bias for bounce points in areas of oceanic sediments. "Hte effect of 
sediments a, long periods is to produce precursory arrivals from teflections at the base of the 
s^nts and late arrivals from waves which travel through the low-velocity sediments and are 
^fleeted a. thecrust-water interface. The netaffec, after convolving ti-ecrustal response wtth the 

.ong-period ODSN ins^mem response, is that the time center of the SS phase is effectively 
unchanged but ti« puhe is broadened both at the front and at the back, in our procedure the use of 

• • tt,. .nri,^ SS Dulse should yield differential travel times that are litUe 
a constant window containing the entire S»i> puise snouiu y 

affected by the presence of sediments. 



DATA 



TV nonh Atlantic is an ideal area for conducting a differentia, .rave, titne sUKiy in terms of 



fte geographic dismbution of available events and smnons at suitable distances. The range in 
source-receiver sepamdon was taken ,0 be 55- to 86- to ensure separation of S and ScS at the longer 
distances and to avoid triplication in SS at shoner distances. Tlte SS and S phases bottom ftom 
about 670 km to 2300 km depth. We peKormed a search over all earthquakes in the Harvard 
cntroidmomenttensorCCMT) catalog for the years 1977-1987 lDzi««,n.« « oi., 1981; 
D^iewonski and Woo4kouse, 1983] and over all GDSN. NARS. and GEOSCOPE digital seismic 
stations in order to find event-station pairs of the proper epicentral distance which provide SS 
bounce points in the Notti, Atlantic tegion. Epicenters were obtained firm, the Bulletin of the 
International Seismological Centte OSC) for events occurring before 1987 and fix,m the 
••PreUminary Detemdnation of Epicenters" of the U.S. National Earthquake Information Service 
(NEIS)foreven,soccu,ringin 1987. TTe fmal distribution of sources and stations used to measure 
SS-S differential travel times is shown in Figure 2. The majority of data in Utis smdy comes ftom 
™=onis of equatorial fracture «.ne earthquakes at North American and European stations, nor* and 
central AUantic events at North American stations, Central American events at European stations, 
and Mediterranean and European earthquakes at North American stations. 

TWs search yielded over 2000 event-station pairs with the proper epicentral separation. After 
winnowing the list because of station inoperation, poor signal to noise ratio for U« phases of 
interest, and interfering events, the final data se, consists of nearly 500 SS-S differential travel time 
residuals witi, bounce points in the nor* Adantic (Ftgure 3). Uncenainties are determined for each 
measurement following the procedure oudined in Appendix A. 



RESULTS 



We interpm the variations in SS-S differential travel times in lemts of lateral velocity 
variations within tire cmst and upper manUe beneati, ttte surface reflection points of the SS wave 

path Kuoe,<U. 11987) and Wooded a«l Masters [1991] tested the validity of this assumption 



by plotting absolute S and SS residuals against SS-S lesiduals. They found that S and SS-S 
residuals aie unconelated while SS and SS-S residuals aie strongly eoirelated. indicating tiaat tfie 
assumption is justified. The validity of this assumption is further supported by tiie strong 
correlation of SS-S times with surface tectonic features in the vicinity of ti.e SS bounce point The 
„,siduals are further interpreted in terms of such upper mande processes as UAospheric aging, flow- 
induced anisotropy. and along-axis heterogeneity in mantle structure. 

Lithospheric Aging 

Cooling and thickening of the lithosphere should yield a tendency toward an increase in 
seismic velocity with increasing hthospheric age. A linear regression experiment was performed to 
examine the correlation of the SS-S residuals with seafloor age. A gridded map of seafloor ages 
was constructed for the north Atlantic from the magnetic anomalies oi Klitgord and Schouten 
[1986] and ages assigned according to Kent and Gradstein [1986] and Klitgord and Schouten 
(19861. The isochrons of Sclater et al. [1981] were used in a few regions which were not covered 
by the KUtgord and Schouten [1986] data set. To obtain a representative age value for tire region 
spanning approximately one horizontal wavelength of the incident (SS) wave, an average seafloor 
age was estimated for a r x T box centered on each SS bounce point. To reduce scatter, 
rrreasurements whose bounce point depths differed by more tiran 2500 m from the depth predicted 
by the Parsons and Sclater [1977] plate cooUng model were excluded from the final age regression. 
Although each SS wave samples the upper mantle at a finite range of Uthosphere ages, we expect 
diat tire different travel time anomalies contributed by die SS path segments on the younger and 
older sides of the bounce point approximately cancel so that the age at tiie SS bounce point is 
appropriate to the associated SS-S residual. 

The SS-S residuals for die nortii Atiantic are consistent with the expectation of an increase in 
seismic velocity with seafloor age. For bounce points between 0' and 60-N latitude, the coefficient 
derived by Unear regression of residual with square root of age is -0.68 ± 0.08 s My-l/2 from to 



100 My. with a linear correlation coefficient of -0.85 (Figure 4). However, residuals from 60 - 
90-N do not seem to be strongly correlated with lithospheric age. This may be due to the fact that 
this area is more tectonically compUcated than 'normal' oceanic lithosphere [e.g.. White, 1988; 
ZehnderandMimer, 1990], includes several ridge jumps, is in close proximity to continental 
regions, and does not closely follow the age-depth relation of Parsons and Sclater [1977]. 
Compared with the residuals for 0-60-N, those from 60-90-N are anomalously negative at young 
ages and anomalously positive at older ages. The slope of SS-S residual vs. square root of age for 
data from to 60-N is smaller than that inferred from S delays of intraplate earthquakes in the 
Atlantic by Duschenes and Solomon [1977] (two-way S delay = -1-2 s Myi/^) and that reported by 
Kuo et al. [1987] (-1 s Myi^^). It is larger, however, than the global average obtained by 
Woody^ardandMasters [1991] (-0.51 s My^/^). We find that the residual-age relation is not 
constant over the entire north Atiantic, so that some of these variations in slope may reflect real 

geographic differences. 

We may compare Uie variation of SS-S residual versus age witii tfiat due only to litiiospheric 
cooling. For a Utiiospheric structure given by the plate cooling model of Parsons and Sclater 
[1977], we may convert temperature variations to differences in shear velocity vs by adopting a 
value for dvs/aT, which we take to be uniform and equal to -0.6 m/s K-l [Mcmt and Judge, 
1990]. For a horizontal slowness typical of the teleseismic S and SS waves of tiiis study (0.1375 
sAon), tiie slope of the Une best fitting tiie SS-S travel time delay versus age given by die plate 
cooling model over 0-100 My is Uien -0.73 ± 0.07 s My-l/2, a result indistinguishable from tiie 
observed slope. This agreement indicates that the dependence of travel time residual on plate age 
can be explained entirely by lithospheric cooUng. 

The trend of tiie travel time residual versus lithospheric age relation changes at about 100 My. 
After 100 My. tire residuals appear to flatten out (Figure 4). in die same sense as die plate cooHng 
model oiParsonsar^Sclater [1977]. Such a pattern may reflect tire unmodeled effect of increased 
sediment or crustal titickness, or, as suggested by Parsons and Sclater [1977] may be partially the 



10 



„s^.„f scoondaryconvecion .Mch supplies h«. . .he base of *e pia. a.oU,erages. Toavcd 
possibleWasesassccia^dwim any of U,ese effects we shall res^c.curanalysis»dau.wi,h wee 

poincs on UUK>sph«e .ess ,han 100 My. To .<K,k for od,er systemaoc variations in 0« «sidua.s. we 
co^foragebyren^ng .he linear^laHon shown by ..e solid Unein Figured mseo^don 

is effectively a no^aHzation of residuals .o 22.My-o.d U*osphere m »o cussing of ti.e 

regression line). 

Anisotropy 

Anoti«r sys,e,»tic velocity variation ti,a, has ^n suggested as a possible contnbu.or to 

^ual SS-S .avel titt^s is aximutital anisotropy. Kuo e, aL [1987, exatnined this phenotnenon u. 

detail and concluded that alignn«n. of olivine oystals in the asthenosphere ceated a significant 

pauetn of azimuthal aniso^py in SS-S residuals measured in the AUantic region. We have also 

searched for evidence of azimuthal anisotropy with our dau set. 

Bactm [1965, and Cranpin [1977] de.,»nstrate4 from the genetal form of body wave 

anisooopy in a weaay anisotropic medium, that the Unear form of the azimuthal variation of 

velocity is given by 



V2 = Ao + AiCos2e + A2sin2e + A3COs4e + A4sin4e 



(1) 



whereVis the body wave velocity.the An are linear funcnons of the elasdcHKKluli,^^ 
a.i.uth,definedforourp.>blernbytheanglel.tweentheg.atcirclepathandthedh^^^ 
geographic north measured at the SS bounce point. Equation ( 1 ) was further simpimed by Kuo et 
cd. [19871 and parameterized in terms of travel time residuals: 



R = RO + Ricos2e + R2sin20 + R3cos40 + R4sin4e 



(2) 



11 



whcRisU^ttavel time residual and fteR„ arc consents. By Httingafunction of «sfcn„.o our 

ag«or«ctcd measurement we can detenrine if our data are consistent with the presence of 

anisotropy. 

we have conducted several tests of azimuthal anisotropy with our travel time data. We 
performed leas, squares inversions to determine 29 and 48 patterns which provide best fits to d,e 
age-corrected SS-S residuals. The anisotropy inacated by our regression experiments differs 
significantly fiom the pteferred model of *:«>«<.;. 1 19871 bom in magnitude and in pha» (Figure 

5). Our results indicate that for *e 26 model the slow direction for SS-S is N4-W and the peak-,^ 
peak magnimde of the effect is less than 1 s; for the 49 model the slow directions are N32-W and 
N58-E and the magnimde is 2.5 s; for the joim 29 and 49 model the slow direction is N3rW and 
the magnimde is jus. under3s. ««.««(. 119871 obtainedapeak-tcpeak variation with azimuth of 

5-7 s and a slow di«=ction at N13»W. The slowest residuals in the Kuo «a/. [19871 smdy were 
ton nortit-soud, padts. i.e.. nearly along the ridge, and the fastest tesiduals w«e ftom norti«as.- 
soumwesftrending paths with bounce points north of the Azores-Gibraltar plate boundary (an area 
noted to be anomalously fast in their study), so theirreported anisotropy may have been at least 
party the result of onmodeUed upper mantie heterogeneity. Our inversion for a 29 pattern of 
anisotropy provWed a vahance reduction of only 2%, compared with 20% for a 49 pattern, and 
22% for a comHn«i 29 and 49 pattern. On the basis of titese values of variance reduction and the 
number of free parameters involved, our results suggest dtat ti.ere is no single coherent pattern of 
upper mande anisotropy in the north AUantic. The latest anisottopic upper mande models obtained 
ftom surface wave tomography [Mon«g«r and Tammou,, 19901 also show a complex pattern of 
anisotropy in the region. Any azimuthal anisotropy in dte asthenosphere induced by plate motions 
in U« north Adantic may be hetetogeneous because the th.ee plates in the tegion are slow-moving 
and the remm flow is not closely related to plate divergence [Haier and OVonnell. 1979. 1981; 
Parmender and Oliver, 1979]. 



12 



Spaial Patterm (^ Age-corrected Residuals 

Mtcr removal of fte dependence on seafloor age, a plo> of SS-S navel time residuals a. U,e 
SS surface ^flection poim (Figux 6) shows several interesting features. PeAaps the most striking 
is that residuals in the westen. Adantic north of about 35- N a., on average nearly 4 s mote negative 

than those to the south. TOs feature is also noticeable in Figure 3 bu, is more obvious after age- 
dependence is removed. A similar change at appmximately this latitude was nottd for SS-S 
^uals with bounce positions on tite eastem side of the Mid-Atlantic Ridge by Kuo e, al. [ 1987] 
and was attHbutcdtoachange in upper n^tiesmacnue across the A««es-Gib..lu. plate boundary. 

•n„ signal we observe is ptedominantly from dau witi. bounce points on the western side of the 
ridge A map view of the azimuthal distribution is shown in Figure 7 and serves as an aid » assess 
Cualitively the geometry of wave paths to ti« soutit and north of 35-N. We examined tite possibility 
.hat this signal may b« fiom the Caribbean anomaly , a region of anomalously high velocity in the 

™„,fle be^veen 600 and 1400 km depti, beneati. tite Caribbean originally reporied by Jordan and 
Lynn 119741 and further confirmed by Grand [1987]. If the first leg of tite SS rays pn,pagating to 
western Europe we.« to botiom in tite high velocity Caribbean region. ti« result would be early SS- 
S residuals. This would pr«iuce a feantre of opposite sign from Uta, observed, so we discount it as 
an influence h«e. Another possible explanation for the long-wavelength signal could be azimutital 
anisotmpy. but tite «tamination above of possible patterns of azimutital anisom>py does not suppori 

this suggestion. 

Anod«r distinctive featme of the n=siduals in Figure 6 is a mw of negative values which 
trends nonhwest to soutiteas, along Uk tiend of U.. New England Seamounts and across tite ridge 
» UK vicinity of the Great Meteor Seamount. This feanne comes from event-station pairs at a 
number of diffen=n. arimuths and distances so cannot be attributed to a sou.ce or receiver effea. 
We do not observe distinctive anomalies in the vicinity of the Bermuda. Azores. Iceland or Canary 
islands hotspots. The data density is poor for the Bemtuda region and Iceland, however, and any 
signal associated with the Canary Islands may be obscured by tite ocean-continent tnmsition. 



13 



Recently active hotspot islands might be expected to display strong positive (late) residuals, such as 
Stewart and Keen [1978] observed for PP-P residuals at the FogoSeamounts. In contrast. 
Woodward and Masters [1991] found mosUy negative (early) SS-S residuals in the vicinity of the 
Hawaiin hotspot, and yordan [1979] md Sipkin and Jordan [1980] have suggested that the net 
effect of hotspots may be to produce early arrivals because of the presence of high velocities in a 

depleted mantle residuum. 

There is a systematic variation of SS-S residual with latitude, i.e., effectively along the 
direction of the Mid-Atlantic Ridge axis. Age-corrected SS-S residuals with SS bounce points on 
Uthosphere younger than 100 My are shown versus latimde in Figure 8. The along-axis variations 
show a variety of scales, notably at wavelengths of about 1000 - 2000 km in the region from 15* to 
35*N, and at about 6000 km wavelength from late (positive residuals) in the south (20-35*) to early 
(negative residuals) farther north (45-55'N). The largest of these variations are robust with respect 
to selective removal of portions of tiie data. The Iceland region appears as a local maximum 
(positive SS-S delay) on the profile, but Uie Azores hot spot does not have a distinct seismic signal. 

JOINT INVERSION OF TRAVEL TIME RESIDUALS AND GEOID AND DEPTH ANOMALIES 

Long-wavelength variations in shear wave velocity of the son depicted in Figure 8 
presumably are a consequence of some combination of variations in temperature and composition of 
the upper mande. Such lateral variations should also have signatures in otfier physical quantities 
measurable at these wavelengths, notably gravity (or geoid height) and topography (or residual 
bathymetry), because of the dependence of these quantities on bulk density. Travel time residuals, 
geoid anomaUes, and residual depth anomalies are independent quantities dependent in different 
ways on temperature, bulk composition, and tiieir variation with depth. We therefore seek a 
quantitative procedure for treating travel time residuals jointiy with geoid and batiiymetry data and in 
particular for a combined inversion of all three quantities for horizontal variations in upper mantle 



14 



temperature and composition. 

To ensure complentarity of data sets, bathymetry and geoid height values are obtained at each 
SS bounce point, and both arc corrected for subsidence with seafloor age by means c. the plate 
cooling model [Parsons and Sclater, 1977; Parsons and Richter, 1980]. In this manner we 
effectively normalize all observations to zero age. Batiiymetric data arc obtained from the corrected 
Digital Batiiymetric Data Base (5' grid) [US. Naval Oceanographic Office, 1985]. Geoid data arc 
taken from a combined set of Seasat and GEOS3 altimeter data [Marsh et al., 1986]. Data north of 
70" N were not included in die Marsh et al. [1986] data set due to die high probabiUty of being over 
sea ice, so our analysis below is confined to latitudes less than 70-N. We find tiiat die correlation 
of SS-S residuals witii the low order geoid is negative, but that at high order tiie coirelation is 
positive (Figure 9). This relationship may indicate a depth dependence of contributions to geoid 
and travel time (e.g., the long wavelengtii signal may be a lower mantie effect). Low degree 
harmonics are likely linked to deep-seated density heterogeneities and subducting slabs [Hager, 
1984; Hager et al., 1985]. Since we are interested in upper mantle processes, we filter out die long- 
wavelength component of the geoid by subtracting a reference field [Urch et al., 1979] expanded in 
spherical harmonics to degree and order 7 and tapered to degree and order 1 1. To provide a 
comparable batiiymetric data set, batiiymetry is high-pass filtered (comer at 4000 km, cutoff at 6000 
km) to remove long-wavelengtii d^nds. Along-axis profiles are constructed from die age-corrected 
and filtered geoid and bathymetry data. 

Profiles of age-corrected travel time residuals, geoid, and bathymetry are compared in Figure 
10. While qualitative correlations among profiles are apparent, we seek to quantify possible models 
of temperanire and compositional variations tiiat can match tiiese observations. Oceanic batiiymetry 
and geoid height are both sensitive to variations in mantie density at depth. Such variations can be 
eitiier tiiemial or compositional in origin and, like seismic velocity, are presumably related to mantie 
convection and differentiation. For a given density change, tiie seismic signature of tiieimal and 
compositional heterogeneity are of opposite sign, so tiavel time residuals constitute key information 



15 



for distinguishing between mechanisms of heterogeneity. 

Inversion for Thermal Structure 

We seek to fonnulate an inversion for the distribution of temperature anomalies T(x,z) 
(where X is along-axis and z is depth) that can produce the along-axis geoid, bathymetry, and travel- 
time anomalies shown in Figure 10. Topography and geoid kernels were calculated for prescribed 
models of viscosity for an incompressible, self-gravitating, Newtonian mande with free slip at the 
surface and the core-mande boundary. The convecting region is assumed to be overlain by a high- 
viscosity layer 40 km tiiick. We performed calculations both for a mande of constant viscosity and 
for a mande widi a shaUow low-viscosity layer. Topography and geoid anomalies depend on the 
viscosity strucmre, but the predicted travel times do not. Kernels were calculated using a mediod 
similar to that of Richards and Hager [1984] except that the solution was direcdy integrated across 
die layers instead of being obtained via propagator matrices [McNutt and Judge, 1990]. 

The inversion is best conducted in the horizontal wavenumber domain. The Aermal 
anomalies AT(k,z) at depth are related to the predicted dynamic topography h(k) for wavenumber k 
via an integral of the form 

Ah (k) = -^5^ H (k,z) AT (k,z) dz (3) 

[Parsons and Daly, 1983] where a is the volumetric coefficient of thermal expansion, po and pw 
arc die densities of die mande and of water at standard temperature and pressure, and Zmin and Zmax 
arc die upper and lower boundaries of die layer in which temperatures are allowed to vary. Table 2 
contains a summary of die constants adopted here. The depdi and wavenumber-dependent 
topography kernel H(k,z) is calculated from die equations of continuity and motion given a set of 
boundary conditions, a viscosity model, and a constitutive relation between stress and strain 



16 



[Parsons and Daly, 1983]. Similarly, the kernel G(k,z) for the geoid relates the thermal anomalies 
to the geoid N(k) via 

AN(k) =^^^ JG(k.z) AT(k,z) dz (4) 

min 

[Parsons and Daly, 1983] where T is the gravitational constant, and g is the surface gravitational 

acceleration. 

Sample geoid and topography kernels calculated for different wavenumbers and viscosity 
structures art; shown in Figures 1 1 and 12. Cartesian kernels are used throughout this study 
because of their computational efficiency and straightforward application to Fourier transform 
techniques. We have compared extiema of the upper manUe portions of the geoid and topography 
kernels for a layered cartesian Earth and a spherical Earth for a number of wavelengths and different 
viscosity structures (Figure 12), and we note good agreement even at very long wavelengths 
(spherical harmonic order f = 6). This agreement suggests that the results presented here should be 
applicable to the spherical Earth without introducing unreasonably large eirors. 

Temperature perturbations at depth can be convened to a seismic velocity perturi>ation by 

assuming a value for the partial derivative of shear wave velocity with respect to temperature, 

dvs/3T. The resulting two-wave travel time perturbation is given by 

^dvs f" AT(k,z)dz .ex 

At(k) = 2-=^ 2-^ 2172 ^^^ 

^J v,(z)' (1 - p^s(z) ) '^ 

min 

where vs(z) is from the reference shear velocity model [Dziewonsid and Anderson, 1981] and p is 
the ray parameter, generaUy taken to be a representative value for the range of epicentral distances 
considered here. We use a value of -0.6 m/s K'l for 8vs/9T. This value is higher than the values 
of Anderson et al. [1968] and Kumazawa and Anderson [1969] at standard temperature and 



17 



pressure but is similar u. *e value of -0.62 m/s K-ldeKnmned by McNm adjudge [1990] by a 

leas, squares fi. of Love-wave phase velocities «, predicted ■en.perature of U.e liAosphere. Such a 

value is consistent with U,e change in P-wave velocity with temperature. 8vpOT = -0.5 m/s K', 

found from modeUng wave prapagation along suMucdng slabs [Creagcr <uulJord^ 1986; Fiscl^r 

e,al.. 1988] if we assume that 3vsflT= 1.1 dy^ [Woodhouse and Dziewonski. 1984]. Pardal 

melt would increase the value of avs/3T[S(«p, WA: Sou, a^ Sacks. 1989], but simultaneous 

analysis of both shear and compressional differential travel times by Wooded cul Masurs [1991] 
indicates that significant partial meldngisnottequired to explain thedifferendal travel time residuals 

in the north Atlantic region. 

The forward problem consists of calculating geoid, topography, and travel time residual 
pK,files given a starting twc^dimensional temperature structure T(x,z). The inverse problem 
consists of finding a temperature structure that predicts (via equations 3 - 5) geoid, topography, and 
travel time profiles which best fit those observed. The familiar matrix equation d = A m is formed 
from discrete versions of equations 3 - 5. The data vector d consists of the topography, geoid, and 
travel time residuals, the model vector m contains the temperature variations for which we are 
solving, and die matrix A contains the coefficients and kernels which relate the data to the model. 
As a check on our procedure, we constructed a forward problem for geoid and topography and 
found good agreement with the modelling results ofMcKenzie et al. [1980]. 

The bathymetry, geoid. and travel time pK,files of Figure 10 are interpolated to a constant 
spacing, demeaned, tapered at both ends with a 10% sine squared taper, and Fourier transfonned. 
Since our profile extends from 10 to 72-N, the first and last 10% of the profile (10 - 160N and 66 - 

7rN) wiU be affected by the taper. The 3n x 1 data vector d is then constructed, using the complex 
(to retain both ampUtude and phase) bathymetry, geoid, and travel time data sampled at n discrete 
wavenumbers: 



d = [ Ah(ki)....,Ah(kn).AN(ki) AN(kn),At(ki) At(k„) ] 



(6) 



18 



.He^Tdenotestn^spose. per thecase where temperature penurba.^^^ 
single layer, the n x 1 model vector m is given by 

(7) 
m= lAT(ki),...,AT(kn)P 



For the more general case 



of a multi-layer system, the nj x 1 model vector m is given by 



whe.e.istHclayer'inde.anajisthetotaln.mberof.ayers.lnthisp.perweperforminversio„s 
for singWayer .nodels only. The "layers" of temperamre variadons are independent of .he 

••,ay«ing" system of lid. low viscosity zone, and mantle which we use for the calculadon of 
.eme^a..hou.hn.Jorchan.esinviscositywouldtendtosesmen,.Taswell.Thetempe«n« 

layering simply refers to that region bounded by ..in and .„„ in the integrals of equattons 1-3. 

m 3n X „ nutrix A contains the cc^fftcients and kernels that relate the temperature 
penurbations to the observations, which tor the single-layer case is given by 



19 



■ P°° T H(ki^) Az 
po-p- «*- 



P°° 5;, Hfez) Az 
po-p. 



A = 



^"^P"" T G(k,.z)Az 
gki ^ 



^"^P°° T G(kj^)Az 



23]iy ^■(')" Az 

aT-»*.(i.p2v.(z)*)i 



3T -**■ (l-p^'.(z)*)2 



P°" 5^ H(k«.z) Az 

Po-Pw wmnH 



2"rp'>° "5 G(k..z)Az 



2avi^ _Ji!(£ll_jAz 
dT -.*. (i.pJv.(z)^)5 



(9) 



T^e^atrixAcontainsbothbathy^etry and topography .en.elsandisa.usvisc^^^^ 
U..aviscosity struct, mustbc assumed. Wesolve 0.0 e.uation<i = An,by least squares 



m = (AR:lA)-UR> 



(10) 

<: th. matrix A ConstTuction of the data covariance 
where A is the complex conjugate transpose of the matrix A. Constru 

.A Aw-R Fnuation (10) is solved for the solution vector m. and 
matrix Rdd is discussed in Appendix B. Equation uu; 

variance reduction is calculated via 



20 



. , (d-Am)R;l,(d-Ain) 

vanance reduction = i ~ j v. 1 1 ; 

d Rdd" 

The resulting model vector m is inverse Fourier transformed back to the spatial domain to produce 
an along-axis temperature profile. The solution m is also substituted into equations 3 - 5 to 
compare predicted geoid, bathymetry, and travel time residuals with those observed. 

Six inversion experiments for temperature structure were performed (Table 3). Inversions 
were carried out for two different viscosity models and for three different tiiicknesses of the layer in 
which lateral temperature variations were assumed to occur. Because topography and geoid 
anomalies depend only on the ratios of viscosity in different layers [Robinson et al., 1987; Hong et 
al., 1990], we set the dimensionless viscosity of tiie layer representing the bulk of the mantie to 
unity. In one viscosity model, termed the "constant viscosity mantie." a ACkm-thick high-viscosity 
Ud overlies a unit viscosity mantle. We set the viscosity in the lid to 10*, which effectively mimics 
rigid behavior. In a second model, a 160-km-thick low-viscosity zone is present beneath a 40-km- 
thick Ud; the viscosity in the low-viscosity zone is a factor of 100 less than in tiie underlying mantle. 
The tiiickness of the layer of temperature perturbations was taken variously to extend from 0-150 
km deptii, 0-300 km depth, and 0-650 km depth. The matrix A is different for each of these cases, 
as it involves viscosity-dependent geoid and topography kernels and also a summation over depth. 

Inversion results for tiie constant-viscosity-mantle cases are shown in Figure 13. The 
"observed" piofUe is actually a filtered version of the observations, containing only the wavelengtiis 
used in the inversion (1400 to 7100 km). Predicted profiles were calculated from equation 5. For 
these solutions, the long-wavelength fit to geoid is better than at short wavelengtiis. The fit to 
batiiymetry is poor. The ^edicted magnitude of the SS-S residuals range from a factor of 5 too 
small for tiie 650-km-thick layer to a factor of about 1.5 too small for tiie 150-km-tiiick layer. 
Increasing the temperature variations to improve tiie fit to tiie SS-S residuals leads to predicted 
geoid variations tiiat are too large. The highest total variance reduction and best fit for die constant- 
viscosity cases come when lateral variations are constrained to shaUow (0-150 km) deptii. The 



21 



variance reduction is 25% for bathymetry. 79% for geoid, and 58% for travel times. The total 
variance reduction is 53%. The variation in temperature is 180 K for the 150-km-thick layer, and 
only 60 K for die 300-km-thick layer. 

Figure 14 shows inversion results for the models with a thin low-viscosity zone. A good fit 
to both geoid and travel time is found, although the alignment in phase of predicted and observed 
geoid is not as good as for the constant-viscosity case. The fit to bathymetry is again poor. The 
total variance reduction for the 150-km-thick and 300-km-thick layers are botii 57%, altiiough die 
shallow model provides sUghUy higher variance reduction for batiiymetry (27% for 0-150 km deep 
layer, 24% for 0-300 km deep layer) and the 300-km-tiuck-layer model provides higher variance 
reduction for geoid (79% for 0-150 km deep layer, 85% for 0-300 km deep layer). The variation in 
temperature for the 150-km-thick layer is 230 K and in the 300-km-thick layer is 1 10 K. 

We have explored the hypothesis that the lack of correlation of predicted and observed 
topography is an indication that the source of variations in the geoid and travel time anomalies is 
deep. To test this hypotiiesis. we performed inversions with temperature variations restricted to 
deeper layers and found that fits to topography were still poor. It is possible that the bathymetric 
signal is dominated by crustal thickness variations which are not included in our calculation of dy- 
namic topography. An assessment of such thickness variations is discussed further in Appendix B. 

Inversion for Compositional Variations 

A possible alternative to along-axis variation in mantle temperature is lateral variation in bulk 
mantie composition, due perhaps to a variable extent of melt extraction or different degrees of 
mixing of compositionally distina volumes of mantie material. The dynamical effects of 
compositionally induced density variations can be large [O'Hara, 1975; Boyd and McCallister, 
1976; Oxburgh and Parmentier, 1977; Sotin and Parmentier, 1989]. The fraction of mantie 
potentially extractable as basaltic melt is thought to be 15-25% [t.g.. Green and Uebermann, 
19761. Thus, for every volume of basalt removed from tiie mantie. a volume of residuum several 



22 



times larger is left behind. TTe effec, of basal, depletion is «> increase the molar rado Mg/(Mg * Fe) 
(or Mg#) in a.e nisiduum, which reduces ti,e density and increases the seismic velocities [e.g.. 
Liebermann. 1970-. Akimow. 1972]. For example, subtraction of 20 mole % olivine basalt from 
py„,lite can decrease the density of the residuum by nearly 2%, equivalent to a dtermal per«rtation 
of nearly 500 K IJordan, 1979]. Thus compositional changes need only be sUght to produce effects 
on the order of 100 K, comparable to values obtained from the inversions for temperamre 
variations. In this section we explore the effects of compositional variations parameterized in temts 
of d« variation in the Mg# in the upper mantie along the ridge. Our motivation for parameterizing 
compositional variations simply in terms of Mg# is that differences in this quantity yield significant 
variations in seismic velocity and density, in contrast to most other measures of degree of melt 

extraction. 

Partial derivatives of density and seismic velocity with respect to Mg# are obtained ftor. 
Akimoto [19721. TTicse values were measured on a suite of samples ranging from pure forsterite 
(Mg2Si04) to pure fayaUte (Fe2Si04). While these partial derivatives are at standard temperature 
and pressure, it is expected that a change to elevated temperature and pressure wUl have only a 
second order effect, since temperature and pressure corrections work in opposite directions [Jordan, 
19791. Above tiie soUdus temperature, however, the amount and distribution of partial melt, which 
may depend strongly on composition and particularly volatile content, is important The presence 
ofmelt islikelytohavealargereffectonshearwavevelocitiesthanonbulkdensity. Calculations 
of melt migration, however, suggest that once created, melt segregates rapidly by a percolation 
mechanism [e.g. Scott and Stevenson, 1989]. so that the melt fraction present in the mantie at any 
given time is probably small. Studies of mantle peridotites [Johnson et al, 19901 also support the 

importance of fractional melting. 

It is straightforward to convert equations (3) and (4) to relations between geoid or 
topography and a compositionally induced density perturbation by means of the relation 



23 



Ap = -PoaAT (12) 

Compositional anomalies at depth yield a dynamic topography h(k) given by 

Ah(k) = --^ ^ f H(k,z) AMg(k,z) dz (13) 

Po~Pw oMg J 



z 

mm 



where AMg represents the fractional change in the Mg#. Compositional anomalies yield a geoid 
anomaly 

AN(k) = ^^ J G^l''^) AMg(k,z) dz (14) 

nrnn 

For a compositional perturbation at depth the resulting two-wave travel time perturbation is given by 



8vs f AMg(k.z)dz ^^5) 



Atrv^-9 ^^» f AMg(k.z) dz 



Using equations (13) - (15), an inversion scheme similar to that used for tiiennal 
perturbations is forawd. The solution vector now has the form 

m = [AMg(ki) AMg(kn)]T <16) 

The data vector remains tiie same as in equation (6). while the matrix of coefficients, A, changes to 
reflect tiie relation between the data and mantie composition, rather than temperature, as ouUined in 

equations (13)- (15). 

The results of tiie inversions for compositional variations are summarized in Table 3 and in 
Figures 15 and 16. We are unable to match simultaneously both SS-S travel time residuals and 



24 



.eoid and ba*ymcmc a«,manes with solely n^Ue co^fosidonal variadons for cither a constant 
viscosity .nanUe « one »ith a low viscosity zone. TOs is not surprising, as the ..vc, tin«s are for 
^ nK,st par, positively cotrelated with gcoid and bathyn^try, but composidonal varradons (at least 
for the M«SiO. - Fe.SiO. systen, exanuned here) have an opposite effect on .rave, .in« ».d geOK.- 

bathymetry. 

^ *e constant viscosity case, the fit to the geoid is exceUent, and the fit to bathymetry rs 
sUghUy better than in the inversion for tentperamre. The fit .oSS-Sresidualsis so poor thatthe 

variance reduction is negative for travel un«. Urge contpositiona. changes would be .^.uired to 
affect travel tin«s, whereas only small com,»sidonal changes are needed to produce significant 
density contrasts to match the geoid signal. The total variance reducdon for the constant viscosity 
casedoes not vary greatly (from32-33%)for composidonal changes constrained to beover 

aiffetcn. depth intervals, though dte variance reducdons for individual data sets (badtymetry, geotd. 
traveldmOvarysignificandyftommcKleltomodeKseeTableS). m range in Mg# is about l%.f 
*e variadon is consuained to the depd, range 0-150 to and only 0.1% for the 0-650 km depU, 

range, 

Hgure 16 shows inversion ..suits for the model with a low viscosity zone. A good fit to 
U^ g«,id and bathyme^ is found, although d« alignment of predicted and observed geoid .s no. 
- .^^asind-econstantviscositycase. m fit to bathymetry is me best of any models so far. 
TV total variance reducdon is sdU low (43 to 49%), due to the poor fi, to travel dmes (negattve 

variance reducd™, in all cases except d,e 0-650 km model). The rang, in Mg# is 2.4% rf 
oo„s.rained,oO-.50km depd,, 1.3%overO-3<X.kmdepd,,and0.5*over0.650km depd,. 



yoinr Inversion for Temperature and Composition 

Wenex,explo..whethera«>mbinadonof«mpera.u.tandcomposi.ionalvariadonscan 

p„v.de a good ma.h to d,e observed geoid, travel dme, and bad,ymetry. Join, inversions prov.de 
tapmved fi« .0 all dau at d,e expense of inmxiucing additional fee parameun. For ftese 



25 



taver^ons d,e dau vecu. r^m^ns U,e same as in equation (6). U,e soluaon veocr is modified «, 
include bod, «mpe«n»c and oomposidon, and d,e mamx of coefficients. A, includes .he effect of 
bo* «n,penm« and composition. The matrix-building equations become, for example, for 

topography^ 



*Tna 



Po« f"u.u ^ ATrt r\ Av + ^ -^ f H(k,z) AMg(k,z) dz (17) 

Ah(k)=-^^^ J H(k,z) AT(k,z) dz + p^_p^ aMg J 

^ Z min 

mm 

which is simply a combinauon of equations (3) and (13), The new geoid equation comes ftom a 
combination of equations (4) and (14) and the tmvel time equation from a combination of equations 
(5) and (15). Cross terms, such as compositional changes induced by incn^ses or decreases in 

temperature, arc neglected. 

The results for the join, inversion for temperature and composition are summarized in Table 3 
and Hgures 16 and 17. The travel time residuals are well-modeled in all cases, as are the geoid 
data. Thetopographyisbestmforthecasewidtalowviscosityzone. Resolution of the depth 
interval of the most impomnt lateral variations is ratiier poor. The topography is fit marginally 

better for dK case whet* temperanare and compositional anomalies are constrained to be shallower 

Utan 300 km. For die constant viscosity mantie, the temperamrt variations range firom 210 K. if 

c^tstrained to 0- 150 km depd.. to 55 K if over 0-650 km depth; variations in Mg# range ftom 1.5« 

if over 0-1 50 km depdt to 0.4% for 0-650 km depth. For the case wid, an upper mande low 
viscosity zone. d,e temperantre variations are similar ,0 those in tite constant viscosity case, but d,e 

variationsin Mg# are larger, from over 2% forO-150km depth to neariy 1% for 0.650km depd,. 

The travel time residuals ate perfectiy fit in d,e joint inversions for temperanne and 
composition fTable 3). This occut. because of d,e way d,e model parameter, aa in a similar 
manner on bod, geoid and baUtymetry. producing a singular matrix if only geoid and baUtymetry 
dau are inverKd for bod, temperature and composition. Undamped leas, squares always ptovdes 
perfect solutions when d,e number of equations is equal to ti,e number of unknowns unless d,e 



26 



namx u, be inver»=d is singular. If we perform an inversion including only m.vel time and geoid 
daa v,t have the same number of equations as unknowns, the matrix is nonsingular. and we obtain 
perfect fits to both travel time and geoid. Similarly, if we perform an inversion of travel time and 
bati.yme.ry dau. we again obtain perfect fits to both data sets. If we perform an inversion of geoid 
and bafltyn^try data, however, we a«= unable to obtain solutions without applying damping. In tite 
join, inversion of tiavel time, geoid, and bathymetry, we have more equations titan unknowns and 
tite inversion is overdetermined. However, ti,e ttavel times are perfectiy detennined in this case 
because of ti« nonuniqueness inhen:nt witi. geoid and batitymetry. We have performed undamped 
inversions witi. various weightings on the geoid, batiiymetry, and travel time data, and in all cases 

the travel times remain perfectly fit 

Wc have also performed joint inversion for temperature and composition with Mg# variations 
constrained to be in the upper 50 km of the lithosphere so as to mimic compositional variations due 
solely to variable melt extraction at the ridge. Temperature perturbations were allowed to remain 
within the depth ranges adopted earlier. The results for this inversion are summarized in Table 3 
and Figures 19 and 20. The variance reduction was similar for the constant viscosity case and for 
the model with a low viscosity «,ne. In general, tiie geoid is fit very well, the predicted ampUtudes 
are a bit low for travel time residuals, and the topography fit is sUghtly out of phase. For the 
constant viscosity mantie, tiie range in temperature is 210 K over 0-150 km depth and 25 K over 0- 

650 km, while Mg# variations constrained to be confined to 0-50 km depth were over 5%. For the 
case with a low viscosity zone, the temperature variations were not dramatically different from those 
ir, the constant viscosity case, and variations in Mg# were about 4.5%. The inversion solution 
shows high temperamres near SO'N and low temperatures in the region from 5(>-60-N. Iceland also 
appears to be underlain by high-temperature mantle. Going from south to north along the ridge, 
compositional variations indicate low Mg# in the vicinity of 20-30-N, high Mg# in the Azores 
region (AO'N), low values near 50-N. and high values near 60-N. 



27 



DISCUSSION 



The temperature and compositional variations in Figures 13-20 are broadly consistent with 
observed travel time, geoid. and bathymetry anomalies in the north Atiantic region. Temperature 
variations alone can account for most of the observed anomalies. In contrast, compositional 
variations alone cannot match all anomalies simultaneously. We infer that a component of die 
observed anomalies is due to long-wavelength variations in upper mande temperature. Joint 
inversions for temperature and composition provide better fits than single-variable models, but at 
the expense of introducing additional free parameters. 

It is difficult to select a 'best' model from the suite of inversions presented. TTie variance 
reductions in Table 3 serve as a guide, but independent criteria may aUow us to reject some of tiie 
models, even diose with high variance reductions. In particular, those models with large 
temperature variations (well in excess of 100 K) can be seriously questioned. Lateral temperature 
variations at upper mantle levels beneath oceanic ridges are thought to be no more than about 300 K 
globally [Klein and Langmuir, mi', Johnson et ai, 1990], so a variation in temperature of 230 K 
(as in the inversion with a low-viscosity zone and a 1 50-km-thick layer of temperature 
perturbations) solely within a section of die north Adantic is probably unreasonably large. Further, 
as White and McKenzie [1989] have noted, relatively small increases in manUe temperature above 
values typical for the mid-ocean ridge are sufficient to cause large increases in melt production. 
Their models indicate tiiat, for fixed bulk composition, an increase of 100 K above normal doubles 
the amount of melt while a 200 K increase can quadruple it. Such increased melt production should 
lead to approximately corresponding increases in crustal tiuckness. Variations in oceanic crustal 
thickness away from fracture zones, however, are generally thought to be small, widt thicknesses 
typicaUy 6-7 km and ranging from 4.5 to 8.5 km [Spudich and Orcutt, 1980; White, 1984; Purdy 
ondDetricK 1986]. In the joint inversion for temperature and composition, temperature variations 
if confined to 150 km depth are excessive (over 200 K) and if the variations extend over 0-650 km 



28 



U,efl.«>u,pogn,>hyispcor,«pcciallyfor*econsa„.-viscosi.y™3nde, On .he basis of tee 
„s»l.sw« prefer *e models wUhtemprnture variations <xcumngoverO-300kmdepd,, For Uie 

consmn. viscosiqr numUe, fte tempemmn: variadon is ! 10 K. and .he variation in Mg# is 0.75%. 
For d,e case wid, an .^per mande low viscosity zone, d,e prediaed temperance variadon is 125 K, 
and d>e variadon in Mg# is 1 . 1 %. -IKe «..al variance reduction is greater in the model with a low 

viscosity zone. 

Even a temperanire variation of about 100 K is high for a manfle of constant composition, 
since we do not observe increased crustal tinckness in regions ti>at ourmodels indicate have high 
temperannes. Tlte assumption of approximately constant upper mande composition warrants 
discussion. In particular, lateral variation in trace amounts of mantle volatiles may have a large 
effect on seismic velocity at a given temperamre. Tire presence of even a slight amount of water, 
for instance, is sufficient to cause a significant decrease in dte initial melting temperati«e of 
peridotite \V/yUU, 1971]. Estimates of volatile contents and their lateral variations in d« norti, 
Atlantic region have been made ftom measurements of abundances of halogens. SiOj, KjO. and 
H,0 in basalts and from the volumes of vesicles in basalts iSMlin, e, a,.. 1980, 1983; ScMUim. 
1986; Michael. 1988). These studies indicate that Q, Br. F, and HjO contents incease toward Ute 
Azc^ and Iceland and that H^O is two to three times note abundant in Mid-Adantic Ridge basalts 
erupted over d« Azores platform ti«n at adjacent nonnal ridge segments. Tlte effect of volatiles on 
density and shear wave velocity wiU be sUght at subsolidus temperatures but can be major over the 
melting interval tG««, 1977]. Tlte presence of melt wiU act to decease signiHcandy Ute seismic 
velocity [Duschenes and Solomon. 1973] and. to a lesser extent, lower the density of tite mantie. 
To dte extent tiiat seismic velocity depends on proximity of the temperantre to the soUdus 
temperamre l&to « a/., 1988, 1989], volatile content can n»ie off with temperature in its effect on 
velocity at subsoUdus conditions. Thus, variation in volatile content could lessen Ute variations in 
melt production impUed by die inversion solutions. 

Even widtout significant variations in volatile content, it is cleariy an ovendmpMcation to 



29 



p,„™«erize manUc composition in .cnns of only a single quann,y. Fn«her v« have assun«d fta, 
^ partial derivatives of bulk density ami seismic velocity with tespec. ,0 Mg# to a« tiiose for 
olivine [Mimou,. W2]. TTe workof/»rdl.n [1979] indicates that these derivatives Vemain nearly 
constant for .nany diffe«« mantle compositions (i.e.. pyn>li.e-type compositions witi, various 
amounts of olivine, ortiiopyroxene. clinopymxene. spin... and game,), so the latter assumption is 
sound. Ho«ev.r. a. any given Mg*. orthopyroxene and dinopyn>xene have lower velocities and 
are less dense Uuu, olivine, whUe game, a.^ spinel an= seismicaUy faster and denser than olivine 
[Jordnn. 1979], so an inaease to the weigh, percent of ortiiopyroxene and clinopyioxene or a 
decrease in ,he weigh, percen. of game, and spinel witt, respec. ,0 olivine in *e mande could 
coun.e.ac. some of U« Kmperamrc variations obtained under U,e assumption of effectively uniform 
minendogy. Several studies IWood. 1979; Jaa,ues and Green, 1980; Dick e,al., 1984) have 
suggested *a. contpositional variations in fte manfle are plausible. Indeed a number of workers 
(e.g.. Dovto. 1984; AUegre e, al.. 1984] favor dynamic models for Uk mantie in which dispersed 
hettmgeneities of various sizes and shapes are passively embedded in a continually mixed, 
convecting mande. Variations in modal fractions of olivine, orihopyroxene. and cUnopyroxene in 
peridoti«s .ecovered along ti,e Mid-Atiantic Ridge have been reported in several snidies IDick e, al.. 
,984; Mich^andBonam. 1985]. These variations are wically ""buted to dUferem degrees of 
meh exoaction bu. could also be partially due .0 tatrinsic upper manUe heKn.genei.y. For example, 
^ relative fractions of olivine, cUnopymxene. and orihopyroxene indicated by Michel and Bcnam 
1 1985) a. 26-N and SO'N. if extended to deptii, could counteract a ponion of the tempeianm; 
differences indicated by die invereion solutions for these regions. 

Chemical analysis of dredged peridotites in the norih Atiantic indicate a range of about 2.5% 
variation in Mg#tM.c*«/<mdi"»"'^. '9851. TOs value is intem«liate tetween wha. we find for 
„«Jels wid, compositional variations constrained .0 be shaUow (4.5 .0 6% variation) and diose 
models wid, compositional variations to ti,e same depfl. ranges as U,e ti-emal variations (1-2%). 
This suggesB that compositional variations may be concenu^ttd sUghdy shallower d.an U.e 



30 



„™pen.«« variations. Af;c/«(u~liio'««ai9851p«sem an along-axisp,xrfile<rfMg#variado„s 
f,<K„ dn^dged peridod^s which can be compared wi* our calcula^d profile. -me main feanu. in 
d,eir profile is a «,ne of high values of Mg# in U,e Azo^s .gton, from 34^5-N, relative .o d.e res, 
of ti,eridge,consis«n,wid, our modellingresults. Their daasampUngis ,00 sparse .odehneate 

oU«r long-wavelengd, features. Their average value for 26-N also has a high Mg# relative u, 
adjacen, data. Tl.is is consistent with our observation of early SS-S travel times and low geoKl m 
titisregion. This anomaly is of too short a wavelength « 1000 km), however. .0 resolve in our 
inversions. We shodd note tita, comparisons men, caution, as small scale featines. such as titose 
due ,0 ridge segmentation, can produce large diffetenccs in composition between peridotites over 
scales of tens of kilometers. In addition, dredged peridotites are mosUy from fracmre zone 
environments, which may not be representative of typical ridge mande \DM. 1989]. 

On fl,e SS-S residual profile tiie Iceland region appears as a local maximum (late SS) bu, die 
Azotes hotspo, does not show a distinct seismic signal. Tlte inversion results for titese two regions 
are also maritedly different Tite results of Ute joint invetsion for temperature and composition 
p^Uct a high Mg# in Ute Azores region while indicated tempetamres are no, anomalously high. At 
Iceland, in contiast. high temperatures dominate. Work by 5c«/«n« [1986, and Bcmmf (19901 
ouUines tite differences in gcochemical signages be,ween <he Azo«s and Iceland ho, sp«s. TTese 
woricen suggest that Iceland is a "traditional" plume hot spot, with a predominantiy titemtal origtn, 
but that the Azores might be more aptly named a "we, spot" because of ,he presence of excess 
hydrousphases and Ute lack ofathemal anomaly. Bomni [1990] suggests that t«cause the 
Azores hotspot is rich in volatiles,enha„cedmeltprodu=tioncouldoccur with Utdeornoincrease in 

tempemture. TTk high Mg# indicated in our inversions allows tite region ,0 be seismically fas, (as 
we obs«ve) bu. of low densi,y (as geoid and bathymetiy tequire). The results are consistem wtth 
the hypoUtesis titat *e Azores hot spot is no, ass<«iated witi, a plume-Uke Utemml anomaly, 
inversion of surface wave disp^sion dau can poKntiaUy provide furiher «s,s of these ideas, bu. 
studies todat. have yielded apparendyconflictingresults-Resultsof several such investigations 



31 



A««s .gion is seis^ically slow a. dcpU,s less 0«o 300 to, bu. a sn.dy udUzing SCms-penod 
Ray.eigh»avcsbyM<,c,«,«./.[.989,d<.s„o,.T.eseditfe.nces™aybcpa«ial.ya»bu.a«e 

^UKdifferencsi. wav.pcri.xise.ployedandn.xic of analysis fton,s»Kiy«.s«,dy.Umay be 

p„ssib.e,....ha.appea..o^lowvel<.i.esa.,hcA.resa.aresu.,of,K^n^snKK,*in,of 

^,o.ve.ocides..on,*eridgeandhaveiinie,odowiU,d,eacu.ais»«u«in0.eA««sreg.o. 

Noneot^ese .ong-period surface waves,^ies.soiveadis.„aive anomaly ..Iceland, aea^iy, 

„K„wc*is„eeded,„res„lve*cuppcrnunUevcloci,ys.uc,.«ofh„,spo,«gio„s. 

»-H „Tr.r,iP. of the equilibrium temperature of dredged pendotites 
Bonatti [1990] has constructed profiles oi tne equuiui »- 

•c ft^m n to 60-N bv means of two different geothermometers 
along the Mid-Atiantic Ridge axis from to W is oy mc^i 

lWe„s ,977; Z.-*,.y. 1983,. Comparison of .hcsc profiles with .he along-axis .n,pcn,nne 
«Haulnsob,ained.^ourinve.ionsrevealsanun,berofqualiunveco™ia.o.aswei.asafe. 

aiscepancics. T.e range of .en,pe,an.re variadons in .he p^filc based on d« L.-^-^ 11983, 
^.Henno^e^-is abo«.150K,neglecUnghigh values ,enned"ano™alon."W,.enU.cMghvalues 
a„i„c.oded*e«ngeinaeases»>400K.ThepK.fileuaiizingU,e,Ve,M.977,geo.i,«n,on,e«r 

Has a range of 100 K negleciing *e anomalous values and 350 K including d,em. The highes. 
^peotures in our inversions are near 30-N (Figures 17-18), a region showing a sligh, peak u, 
Bona,d-s«n,pera.urc^mces,ima.edaccording.oti-u.,^[1983,andaveryweal.risein*e 

p„,me udlizing d,e We,, (1977, geod,er„»me,er, "nrere is a smal dip in «n,pe,a„ne a. 26 N (a 

. • • 11 fo=t^ in the Linds/ev [1983] and M^€//s [1977] profiles, but 
region which we find to be seismically fast) m the Ljnd5/0' U^ 

U,ediffere„cemaynorbesignificanrconsidering*eerrorbars.B.,^a«<.o,<».«ll989,als„ 
found OK uppernunUe near 26-N » be seismically fas. fion, an analysis of .eleseismic P-w.ve 
,„ve. ^ ^siduals .*om e3r.h,ualces in to region recorded by a local ocean-bouom scsnuc 
ne^or. ■n,elowes.«n,pera»es on d,e profiles ofB..mt.990, are a. 43-N. Ten,peran.res 
^„„„rinve.ionsoludonsarealsolowind,is,.gion,al*ough.heB.»a«<I1990,p.files 
U,dica«a„increasein«mpera.ureproceedingnor*fton,43-K.o53-N,wHer.asourresu,.sfavor 



32 



^^ low «n,«a«^. P« of *= diffe^nce be,w=.n our .suUs »d U,e gecchenuoa, sn»iies 
^y b. amib„«d «. *e fac, *a. the d.ptf. sanmled by basalu and peridoftes is likely «> be 

sHallowe, «,an U« .aye. U,ic.„esses of n,os, of our nxxJels. Assun.„g e.a, U« <.kn.-*ick oceanic 
crus, w^ fomKd by 9 K, 22 % parnal mcldng of me mantle l/r/./-"^ /-'■«'«^. "^1. *" *» 
volutne of residual peridodte wiU extend fron, the base of the crus, to so««where between 30 and 
70 tan depth. Tbe anx,un, of depletion will vary with depth if we assun« a pactional melung 
^odel. our nxxiels with compositional variations confined to depths less than 50 Ion are nK». 
representative of shallow fractionation and differentiation. 

Several improvements in future sntdies of the ^ presented here may be envisioned Our 
Uriels thus far have t«en limited to simply panuneteh^ed one-dimensional variations in 
.en^rure and composition within a single layer. It is likely that these lateral variations are not 
constant within a given layer and that there are two-dimensional latent variati^ts independent of 
Uthospheric agine. T^ tech^ques outiined in this paper can be generalized to a multilayer system 
and to two-dimensional wavenumber (see equation 8). but we do no. feel d,a. the resolution of our 
data can Justify more con^Ucated models at this time. Kernels for seismic surface waves are 
strongly peaked in Ute upper manUe. and such data would provide a useful constraint in future 
n^el. m inclusion of surface wave dau would help to distinguish between Uthospheric and 
asthenospheric effects and may allow for two or m.« independenUy resolved layers. Extension of 
Ute modelUng to tht^e dimensions would penni. an assessment of tite degree to which manUe 
anomalies beneath the ridge extend off axis. Implicit in our age-correction is the assumption that the 
^alousptopertiesoftheridgemantiearesteadystateonatimescaleof lOOMy. Recent 

«an«. surveys and theoretical studies [e.g., Poc^lny e, ai.. 1988; Scou ani S.e.e,^n. 1989] 
bring this assumption into question and suggest that at least on short time scales « 1 My) and at 
slow spreading rates (as in the Atlantic) intermittent peritxis of melting and cntstal fonnation may be 
separated by periods witi, Uttie or no melt production. These temporation variations are likely to be 
averaged ou. however, over the typical h<»i«>n,al wavelength (100 km) of a long-period SS wave. 



33 



Another limitation of our models is that they depend on the assumed values of several 
physical constants. It is straightforward, however, to estimate the effect of choosing different 
values. The viscosity structui^s we employ are also quite simple but have been chosen to represent 
two models widely invoked in other studies - a constant or nearly constant viscosity mantle [e.g., 
Peltier, 1989] and a mantie with a thin low viscosity layer [e.g.. Craig and McKenzie, 1986; 
Robinson et aL, mi]- The viscosity structure of the Earth may be temperature and pressure 
dependent or vary laterally, but we have not considered viscosity structures of this type. Nor have 
we modelled the effects of partial melting which could accompany the temperature variations we 
predict The effect of retained melt on the physical properties of the mantie depends critically on ti.e 
melt fraction and geometry, characteristics presendy poorly known. Sato et al. [1988. 1989] 
downplay the importance of partial melt and suggest that most mantie seismic velocity anomaUes 
can be explained by temperature variations at subsolidus conditions. The combined analysis of both 
shear and compressional differential travel times also suggest tiiat significant partial melting is not 
required to explain ti»e travel time residuals in the north Atiantic region [Woodward and Masters, 
1991]. . 

CONCLUSIONS 

We have measured 500 SS-S differential travel times for paths in the north Atiantic region. 
The SS-S travel time residual decreases linearly witii square root of age. in general agreement witii 
the plate cooling model to an age of 80-100 My [Parsons and Sclater, 1977]. Azimutiial anisotropy 
is not clearly resolved, and tiie azimutiial patterns of our data are not consistent with tiie preferred 
upper mantie anisotropy model ofKuo et al. [mi] for tiie nonh Atiantic. An along-axis profile of 
age-corrected travel time residuals displays significant long-wavelengtii variations, notably at 
wavelengtiis of 1000-2000 km. The largest of these variations are robust witii respect to selective 
removal of portions of the data. 



34 



We have fon„ul««)ajoin. inversion of tmveltin»..siduals and geoid and baAymrrto 
anon^csforlawai variation in upper n^de ,en,pera.m. and compodtion. Ond« basisof 
variance .eduction, inve^on for «n,pera,ure favors *e presence of an upper n^nde^ow viscosiR, 
^ and »np«atin. anomalies conce„,ra«d a, depd. less d,an 300 te,. We are unable » march 
^vel time residuals simuUaneously witi, geoid ^ ba>hym=»y solely witi. lareral variations in bulk 
c„nn»sition (Mg#). Join, inversions for «mperan«e and composition provide good fi« <o boti, 
travel tinK and and geoid regardless of viscosi^ sm.aure or layer depth and ti,iclc„ess, bu, ti,c bes. 
f,B K, badrymetiy come from models wiA a low-viscosiry zone and .hennal or composrtional 
variations confined to shallow depth. The Mg# variations predicted in tite joint inversion for 
remperantre and composition are comparable to ti,ose found by Mic^K^Bo^ [1985] m a 
sttrfy of dn=dged peridoti.es along the Mid-Adantic Ridge and may be related to variations m mel, 

production along the ridge. 

mprefened inversion solutions have variations in upper manUeKmpemnne along tite Mid- 
Atlantic Ridge of about 100 K. For a constant bulk composition, such a Kmperanue variation 
would prxxluce about a 7 km variation in crustal thickness IWHi^ an, McKemU. 1989), larger dtan 
is generally observed \Spu0ch and Ormu 198ft 1VW«, 1984; />»■«. and Demck. 1986). 
intioducing compositional variations as well as temperamre variations in the inversions does not 
change derange of temperan^ appreciably. -n^pt^sence of volatiles in titemande can havea 

strong effec. on temperatures required for melting, and variations in volatile con«n. along ti,e ndge 
„uy .educe *e U^ge variation in melt production impUed by ti,e lateral ,empera«re variati«,s 

indicated in our models. 



35 



APPENDIX 



A: ESTIMATION OF ERRORS FOR SS-S DIFFERENTIAL TRAVEL TIMES 



It is important to quantify the uncertainties in the differential travel time measurements. After 
cross-correlation, the "quality" of each individual SS-S measurement is rated and a grade is 
assigned. The cross correlation coefficient, which describes the degree of fit between the synthetic 
and real SS phases, is used as an objective aid in the assignment of quality. However, our final 
assignment of quality is largely subjective and based upon visual inspection of the "synthetic" SS, 
leal SS. and cross correlogram, taking into account the sharpness of the arrivals and their 
alignment, the clarity of the seismogram, and the appearance of a single clear peak in the cross 
correlation function. An "A" quality grade indicates an excellent fit, "B" quality indicates good 
phase aUgnment but only a fair fit, and a "C" quality grade indicates a poor fit or some ambiguity as 
to phase alignment In addition to A, B, and C grades, there were data that were rejected due to 
pcx>r signal to noise ratio for either the S or SS phases. 

Assuming that the uncertainty in an individual measurement comes from a combination of 
measurement error, unmodeled lower mantle structure, and epicentral error, we write, for example, 
for the measurement variance of an "A" quality datum: 

where Oa is the total uncertainty. ©Am is the measurement error, Oi™ is the uncertainty due to 
unmodeled lower mantie structure, and Oepi is the epicentral error. We assume that c^ and Gepi 
are the same for A, B. and C quality measurements, but the measurement error is obviously a 
strong function of data quality. 

Effect of Epicentral Error 

In general, epicentral errors affect the travel times only sUghtly. The events used in this 

C-3 



36 



SI 

e 

error 
error in 



„K,y were «cll ^corded by a iargc number of stadons over a wide .ang^ of azimud,s. and typcal 
epieen^I nnslocuons a. pn^bably less *an 10 km (which would yield a diffe.e„dal «avel-toe 
of 35 s « 75- distance). Tl-e .ravel tfmes are even less sensitive to enors in focal depth; an 
depth of 25 km conmbutes only al>ou, 0.3 s .0 the SS-S tesidual. Using die rule of U,umb 

thatonestamiard deviation is aboutone half of the estimated extremes, we adopt Oe^=0.75sasa 
conservative estimate of epicentral enor. 

EffeaofUnmodelkdLower Mantle Helerogeneiri: 

We estimate the likely magnitude of latend variadons in the shear wave velocity of the lower 
mantle from tnodels of lower mantle hetetogeneity in P wave velocity (such as ^^ U.2.56 of 
D.ie^ns,u [1984],. m average variadon in »vel dmes of direct P waves bodoming in the lower 
mantle is in the range ± 0.5 s. Global ton»graphic studies by D^ie^onsla an, Woo<U.use [1987, 
ir^icatedtatthe scaling ratio (6V^,) /(5V^p) " 2 in d,e lower mande. Such a scaHng ts also 
suggested by comparison of lower mande P wave mcdels with the tecent lower mande S mode, of 
Taninu,.o (1990]. Assuming such an S to P velocity anomaly scaUng, dte resulting variation tn S 
wave amval dme contributed by dte lower mande would likely be about ± 1.5 s, a faction of the 
observed nutge in SS-S residual. WhUe dte major features of lower mantle model L02.56 
IDne^nski. 1984) and d,e lower mande pordons of Tanimo'o' s 1 1990] mode, are for the most 
par, similar, enough differences exist dta. dte appUcadon of a lower mande "co^cdon" to our data 
might a« more uncertainty dtani, removes. Furdter, absolute S-wavedavel dmes do not show 
enough variance for us to suspect large lower mantle effects [e.g., Ran^U. .971; CarSn an, 
Foupine.. 1974; Har, an, Bu.ler. 1978; VI.Hantn.r. 1978. 1979), and the work of Ou^un^son 
e, a, 119901 indicates that most of the variance from dte ISC ubles is attributable to dte shaUow 
mande. i.e.. most of the Eardt's heterogeneity is in d,. upper mande and dte lower mande is fairly 
homogeneous. On dte basis of the above information, we set au„ = 0.5 s for our study. 



37 



Measurement error 

As an objective means to obtain error estimates, we examine the scatter in A, B, and C 
quality picks in a small region. We measured the root mean square (rms) difference between travel 
time residuals of the same grade (A. B, or C) with bounce points separated by less than 80 km and 
with differences in path azimuth at the bounce pointofless than 10'. An 80-km distance is less 
than the horizontal wavelength of SS (which is about 1 80 km at 25 s period) so we do not expect 

much contribution to the rms difference from actual lateral variations in stmcture. The rms 
difference for the 16 A quality residual pairs which were within 80 km of each other was 1 .1 5 s. 

. .aUty picks, an mis difference of 2.08 s was measured using 20 residual pairs, and for C 
quality picks 44 residual pairs yielded an rms difference of 2.96 s. 

We interpret these estimates of the rms diffences as representing the average overall errors in 
the A, B, and C grade measurements. (Unmodelled lower mantle stmcture should be nearly 
identical for data witii bounce points within 80 km and at similar azimuths). Under this 
interpretation we can write, for A-quality residuals, 

SubstitutingvaluesofaA™sandaepiinto(A2)yieldsaA.= 0.87s.Similarly,forBandCquality 
n^easurements. we find Cb. = 1-94 s and ac. = 2.86 s. From (Al), the total uncertainty for A, B, 
and C quality is, respectively, Oa = 1-25 s, Og = 2.14 s, and ac = 3.00 s. 

In the weighted regression experiments the A, B, and C quality measurements ar^ weighted 
inversely by their measurement variance. 



38 



..preNDCB: E«,ORS.N™HALONO-AX,SPKOPn^ANDCONS™uCnONOP-mBDATA 

CovARiANCE Matrix 

ErrorsinBa,hyme,ry.Geoid.cmdTravelTmePraftles 

U-K^ainties i. ^ aiong-axis p^fUes of geoid, ba*yn,e.:y, and »v=. d™s a. -n-pona.. 
U,o™a.o„inU«inv«sio„.Th.gridaedtaa.yn«,.cda.,..S.Nav.,Oc««<,..<^«cq9r« 

„85,i„o,«ie«»,^o„sfor*edevia.on„fwa«rco.u™nacous.c«,«i.yfn».*cass„n«d 

^„eof.500™s-..-n«geoidda.,p™vid«ii„*efo™cfa0.25-x0.25-grid,M.«*«a., 

1,86,. include colons for o« eno. insm.n,en, and ao^ospheHc p«,pagado„ effect, and 

solid Earth and ocean tides. 

W.have.v«agedU,eba.hyn,e^ and geoidhcigh, values wUhinarxl-boxocn^a. 

..HSSbounoepoi„.T.eave.gingyie.dsa.p,ese„«.vevaluefora.gionoverapp™^»..y 

onehcH«.nuawavc.e„gd,ofU,eSSwaveandac.sK.sn,o„.hou.shon-wave.eng.hva^uons 

Bod,baU,yn«»yandgeolda.cc™c.edforsubsidencewiU,seaflo„rage,usingd»p.a.coo.u,g 

r^nForso.a^Sc,a.er^^^Parsonsan.mc^r.^m. Enorin»«iucedin»depd.and 
,eoidanon«liesbyiscctao„n..oca«onisdifr.cuu«,es.,na.epreci«.y.bu.foranenorlnageof 

.My.depd,andgeoidenorsa.80Mywou,dbeabou.30n,andO..,«s^ve.y.wbdea.2 

My ane^rinageoflMywouldhavea^uehUrger affect. givingdepd, and geoidem>rsof350 

„a„d0.3m.T1..n«.gni»dcof«ser™rhighUgh.d,ein,ponanceofaccu..eagede.e™.nauo„. 

especially at young ages. 

T^ p^sence of oceanic scdin«n« is another source of error. In *e AUandc Ocean, .he 
«<^„.d.ic^essi„creasesreguIar„..n,lessdraniOOmaIongU«Mid.A-an.c Ridge .oward 

c„„d„en.a.™argins.herei,can„ceedito[E..>..«a,..973.,ruc*<„^..9S6,.A...an 

«<.™en.«c>a..ss.eads«,correcUons.oresidu.depd,andgeoid„fa.»u.500.an0.3. 

respec«ve.y,Ca«„ave«a,..1988;5^.*<«.<.«*McNu„.1989,. OnAdandCid-osphereonOO 

Myageor,ess,hesedin«n.d.cb,essislessU,an500minn,os.areas.Hence.neg.ecdngU,e 



39 



sedtaent loading comction should not be cmcial in this region. 

■n« along-axis prafile of SS-S residual is a weighted moving average of 10 adiaeen. data 
points group«l by ladtude, using the weights discussed in Appendix A. m same weights and 
n»ving average a« appUed to geoid and bathyn^tty values a, a given SS t»ance point, even 
though bathyn«ny and geoid data ate ptesumed to ^ of equal quaUty, in otder that these ptofUes 
will be consistent with the SS-S residuals. The standard ettor of the tnean values for SS-S tesidual 
™,ges from 0.2 sto 1.6 s. For bathymetry the range of standard deviadons from dte mean value ts 
from 24,0 370 m, and for geoid. 0.08 to 1.0m. m largest variances in the bathymetry and geotd 
data come fmm the Iceland region (north of W'N). and may be due to the more complicated 

tectonics of this region (IVWie. 1988]. 

Before Fourier transforming, the along-axis pmffles must be interpolated to a constant 
spacing We use a simple linear interpolation scheme to estimate values at a 0.5- spacing. We 
estimate thatdte typical error in d,e interpolated data iscomparabletotita. in thealong-axismoving 

averages, which for batitymetry is on the order of 125 m. for geoid 0.4 m. and for travel time 1 s. 

Effect ofCrustal Thickness Variations 

our poor fit to topography in the inversion experiments can be at least partially attributed to 
unmodelled effecu such as crustal thickness differences. Variations in oceanic cmsuU thickness 
about *e typical valueofMkm[Sp«dicA.«/Orc.«, 1980; H'W<e.l984;P»r*,<«<fD«rict. 

,986) are generally d»ught to be smaU a. horizontal scales of 100 km and greater. However, tire 
crust beneath Uk Azores plateau is estimated to be between 8 and 9 km thick [SearU. 1976; 
WHi:nu.rsH e, aU 1982) and to beneatit Iceland is at least 8 to 14 km thick iBjornsson. 1983). By 
simple isostatic mass balance, the depth anomaly due to excess cmstal thickness in d>e Azotes 
region would be about 400 m, and a. Iceland, 200 m to 1.6 km In general, simple variations m 
crustal thickness are insufficiem to produce a signiftcant SS-S residual. For custal and manUe S 
wave velocities of 3.5 and 4.4 km/s. a 2-km variation in crustal thickness would contribute less 



40 



U,a„ 2 s «. an SS-S di«c«„.al »vc. tin« coveted for d.ff«ences in t»«hyn«»y. However, at 
,cc..nd,whe.U«cn,s.iscs.™a.cd.obeas.uchasl4^*icMheaadidona.SS-S«ave.an,e 

could be up to 0.8 s. 



Dam Covariance Matrix 

The data covariance matrix Rdd is of the form 



Rdd = 



/ ah(ki)2 








































Oh(kn)^ 





























ON(ki)2 





























... 





























aN(kn)^ 





























at(ki)2 





























... 





\ 























a,(k 



IW 



where 0.2 Cr?. and o.^ are the no^nal variances of *eba,hymeay,geoid. and BaveUunc 
data, ^specdvely. We n.y choose to constnrc. the data covariance n^trix no, » reflect the true 
variance of Ut. dam but rather to aUow weighting t^tween the different data sets. In this way. the 
<^ covariance n,a»ix can t« altered to test t.« reladve con^budons of different dau sets to .he 

inversion results. 

to aU of our inversions, the covariance matrix is constmcted to weigh, the Uuee dau seu 
approxinutely equally. For example, exanunadon of Figure ,0 indicates .hat a. 3000-1™ 
wavelength the an.pUtude of *e geoid signal is approximately 4 m. bad.yme,ry 1 km, and »vel 
dme2s Thusifavalueof imischosenfor on, d,en a value of 0.5 s for o, andO^Slcmfor a, 
^uld yield approximately equal weighting of dau sets. T.e corresponding 1/c^ values are d«n 1 
for geoid. 4 for ffavel dme, and 16 for bathymetry. 



41 



Acknowledgements. We thank Marcia McNutt for suggesting the inverse problem, and Anne 
Judge for providing codes for computing geoid and topography kernels. Bob Woodward and 
Justin Revenaugh provided advice and subroutines for measuring travel times. We thank John 
Woodhouse and Adam Dziewonski for allowing us access to tiie digital data archives at Harvard 
University and Lind Gee for setting up the data retrieval software at MTT. This research was 
supported by the National Science Foundation under grant EAR-9004750 and tfie National 
Aeronautics and Space Administration under grant NAG 5-814. 



42 



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Figure Captions 



Figure 1. An example of the measurement of SS-S differential travel time for the event 
of December 24, 1985 (10 km focal depth), at GDH (63* epicentral 
distance), (a) "Synthetic" SS pulse generated from S. The S pulse is 
windowed and attenuated to account for the additional time that SS travels in 
die mantie (t* = 3 s), and a 7c/2 phase shift is applied, (b) Windowed SS 
wave pulse, (c) Cross-correlation of tiie trace in (b) with that in (a). The 
differential travel time residual is -5.04 s. 

Figure 2. Distribution of earthquakes (triangles) and seismograph stations (circles) 
used to measure SS-S differential travel times. Stations are firom the 
GDSN, NARS, and GEOSCOPE digital arrays. Earthquakes are from the 
Harvaid CMT catalogue (generally mb > 5.0) from tiie years 1977-1987. 
Lambert equal area projection with pole of projection at 45*N, 40*W. 

Figure 3. (a) Map view of SS-S residuals relative to PREM [Dziewonsid and 

Anderson, 1981], corrected for Earth elUpticity and seafloor bathymetry. 
Residuals are plotted at the SS bounce point The size of each symbol 
scales linearly with magnitude of the residual. Lambert equal area 
projection with pole of projection at 40-N, 60' W. Negative residuals 
indicate either early SS or late S. Plate boundaries are from DeMets et al. 

[1990]. 

(b) Same as (a) but including data only for SS bouncepoints on lithosphere 

younger than 100 My. 



55 



Figure 4. SS-S travel time residual versus square root of seafloor age for data from 0- 
60-N. Each plotted point represents the weighted mean of 14 adjacent data 
points. Weights are constructed from variances determined as discussed in 
Appendix A. Horizontal and vertical bars are standard errors of the means 
of the travel time residuals and (age)l/2. Linear regression yields a slope of 
-0.68 ± 0.08 s/ (My)l/2 for a 0- 100 My age range (solid line) or -0.76 ± 
0.09 s/ (My)l/2 for a 0-80 My range (dashed line). 

Figure 5. Age-corrected SS-S residual (see text) versus azimuth 9. Each plotted point 
represents the weighted mean of 10 adjacent data points. The soUd curve 
shows the best-fitting 40 variation derived from these data. The dashed 
shows the preferred model ofKuo et a/. [1987], which corresponds 
, alignment of the a axis of oUvine in the approximate direction N13°W. 



curve 
toani 



Figure 6. (a) Map view of age-corrected SS-S residuals. 

(b) Same as (a) but including data only with SS bounce points on 
lithosphere younger than 100 My. 

Figure 7. Map view of the distribution of sampUng azimuths. Lines indicate the wave 
path azimuth at the SS bounce point. Mercator projection. 

Figure 8. Age-corrected SS-S residual versus latitude along the Mid-Adantic Ridge 

from 10 to 90'N. The residuals shown are moving averages (such tiiat each 
point is used twice) of 12 adjacent data points. Bounce points on 
Uthosphere of age 0-100 My are used. The approximate locations of several 
fracture zones (Fifteen-Twenty, Kane, Atiantis, Oceanographer. and 
CharUe-Gibbs, denoted by abbreviations) and of the Iceland and Azores 



56 



hotspots are indicated 

Figure 9. Linear correlation, by highest harmonic degree removed ftom the geoid, of 

observed SS-S residual with geoid height measured at the corresponding SS 
bounce point. Both travel time and geoid residuals arc age-corrected. First 
the raw [Marsh et al, 1986] geoid data arc correlated with SS-S residuals 
and a slope and correlation coefficient determined. Then a gedd reference 
field [Urch et al, 1979] up to degree and order 2 (with taper to degree and 
order 6) is calculated and removed from the geoid data, the slope and 
correlation coefficient with SS-S calculated, and so on for higher harmonic 
degrees rremoved from tiie geoid data, witii appropriate tapers (up to U 4). 
(a) Linear correlation coefficient between geoid and SS-S residuals vs. 
highest harmonic degree and order removed from the geoid. (b) Slope of 
the correlation between geoid and SS-S data, as a function of highest 
harmonic degree and order removed from the geoid. Extra points at degrce 
and order 10 arc obtained by using differcnt tapers (no taper, taper to r= 14, 
and taper to t= 15). 

Figure 10. Comparative plots of age-corrected (a) bathymetry, (b) geoid, and (c) SS-S 
residual along tiie Mid-Adantic Ridge, 10-65'N. Bathymetry and geoid 
have been high-pass filtered (see text). All of the residuals shown are 
moving averages of 10 adjacent data points. Bounce points from 
Uthosphere of age 0-100 My arc used, except that data from the Labrador 
Sea region are omitted. 

Figure 11. Uppermantleportionof the kernels for geoid and topography at two 

wavelengths X = 2nAc for two viscosity models. The convecting region in 



57 



both models is overlain by a high-viscosity layer 40 km thick, with 
viscosity 10^ that of the underlying mantle. 

(a) High-viscosity Ud is underlain by a mantle of uniform viscosity and 
other physical parameters. 

(b) High-viscosity Ud is underlain by a zone extending to a depth of 200 km 
having a viscosity equal to 0.01 that of the underlying mantic. 

Figure 12. Upper mantle portion of the kernels for geoid and topography at two 
wavelengths in spherical versus cartesian coordinates. The convecting 
region is overlain by a high-viscosity layer 40 km thick in each of two 
models for viscosity structure. 

(a) Underlying mantle is of uniform viscosity. Cartesian kernels are for 
4000 km wavelength (solid lines) and spherical kernels are for C= 10 

(dashed lines). 

(b) High-viscosity Ud is underlain by zone extending to 200 km depth 
having a viscosity equal to 0.01 that of the underlying mantle. Cartesian 
kernels are for 4000 km wavelength and spherical kernels are for 1= 10. 

(c) Same as (a) but with Cartesian kernels for 6667 km wavelength and 
spherical kernels for [= 6. 

(d) Same as (b) but with Cartesian kernels for 6667 km wavelength and 

spherical kernels for [= 6. 

Figure 13. Results of combined inversion of geoid, bathymetry, and SS-S travel time 
residuals for upper mantle temperature variations. The viscosity structure is 
taken to consist of a thick high-viscosity Ud overlying a constant-viscosity 

halfspace. 

(a) Three solutions for along-axis temperature variations: Dotted line: 



58 



Temperature perturbations constrained to be uniform over 0-150 km depth. 
Long-dashed line: Temperature perturbations constrained to be uniform 
over 0-300 km depth. Short-dashed Une: Temperature perturbations 
constrained to be uniform over 0-650 km depth. 

(b) Observed (solid line) and predicted along-axis profiles of SS-S travel 
time residual. The "observed" profUe is actually a filtered version of die 
observations, containing only the wavelengths used in the inversion (1400 
to 7100 km). Predicted profiles were calculated from equation 5. Line 
types correspond to those of the temperature models. 

(c) Observed and predicted along-axis geoid profUes. Same treatment as in 

(b). 

(d) Observed and predicted along-axis bathymetry profiles. Same treatment 

as in (b). 

Figure 14. Same as Figure 13 except for tiiat the viscosity structure includes a zone 
extending from the base of the Ud to a depth of 200 km with a viscosity 
equal to 0.01 tiiat of die underlying mande. 

Figure 15. Results of combined inversion of geoid, batiiymetry, and SS-S travel time 
residuals for variations in upper manUe composition (Mg#). The viscosity 
structure is taken to consist of a thick high-viscosity lid overlying a 
constant-viscosity halfspace. 

(a) Three solutions for along-axis composition variations: Dotted line: 
Composition perturbations constrained to be uniform over 0-150 km depth. 
Long-dashed Une: Composition pertuitations constrained to be uniform 
over 0-300 km depth. Short-dashed line: Composition perturbations 
constrained to be uniform over 0-650 km depth. 



59 



(b) Observed (solid line) and predicted along-axis profiles of SS-S travel 

time residual. 

(c) Observed and predicted along-axis geoid profiles. 

(d) Observed and predicted along-axis bathymetry profiles. 

Figure 16. Same as Figure 15 except for that the viscosity structure includes a zone 
extending from the base of the Ud to a depth of 200 km with a viscosity 
equal to 0.01 that of the underlying mantle. 

Figure 17. Results of combined inversion of geoid, bathymetry, and SS-S travel time 
residuals for both upper mantle temperamre and composition variations. 
The viscosity structure is taken to consist of a thick high-viscosity Ud 
overlying a constant-viscosity halfspace. 

(a) Three solutions for along-axis temperature variations: Dotted line: 
Composition perturbations constrained to be uniform over 0- 150 km depdi. 
Long-dashed line: Composition perturbations constrained to be uniform 
over 0-300 km depth. Short-dashed line: Composition perturbations 
constrained to be uniform over 0-650 km depth. 

(b) Three solutions for along-axis composition variations: Dotted line: 
Composition perturbations constrained to be uniform over 0-150 km depth. 
Long-dashed Une: Composition perturbations constrained to be uniform 
over 0-300 km depth. Short-dashed line: Composition perturbations 
constrained to be uniform over 0-650 km depth. 

(c) Observed (solid line) and predicted along-axis profiles of SS-S travel 

time residual. 

(d) Observed and predicted along-axis geoid profiles. 

(e) Observed and predicted along-axis batiiymetry profiles. 



60 



Figure 18. Same as Figure 17 except for that the viscosity structure includes zone 
extending fh)m the base of the Ud to a depth of 200 km with a viscosity 
equal to 0.01 that of the underlying mande. 

Figure 19. Same as Figure 17 but compositional variations constrained to be from 0-50 
km depth only. 

Figure 20. Same as Figure 1 8 but compositional variations constrained to be from 0-50 
km depth only. 



TABLE 1. Digital Seismograph Stations Used 



Station Code 


Network 


T atinide (°N) 


Longitude (°E) 


ALQ 


DWWSSN 


34.942 


-106.458 


ANMO 


SRO 


34.946 


-106.457 


ANID 


SRO 


39.869 


32.794 


BCAO 


SRO 


4.434 


18.535 


BER 


DWWSSN 


60.387 


5.326 


BOCO 


SRO 


4.587 


-74.043 


COL 


DWWSSN 


64.900 


-147.793 


GAC 


CAN 


45.70 


-75.47 


GDH 


DWWSSN 


69.250 


-53.533 


GRPO 


SRO 


49.692 


11.222 


JASl 


DWWSSN 


37.947 


-120.438 


KBS 


DWWSSN 


78.917 


11.924 


KEV 


DWWSSN 


69.755 


27.007 


KOti 


HGLP 


59.649 


9.598 


KDNO 


ASRO 


59.649 


9.598 


LON 


DWWSSN 


46.750 


-121.810 


NE04 


NARS 


52.810 


6.670 


NE06 


NARS 


50.100 


4.600 


NB09 


NARS 


44.850 


0.980 


NEIO 


NARS 


43.090 


-0.700 


NEll 


NARS 


41.480 


-1.730 


NE12 


NARS 


40.640 


-4.160 



NE13 


NARS 


38.690 


-4.090 


NE14 


NARS 


37.190 


-3.600 


NE15 


NARS 


50.810 


5.780 


NE16 


NARS 


45.763 


3.103 


NE17 


NARS 


39.881 


-4.049 


RSCP 


R^TN 


35.600 


-85.569 


RSNT 


RSTN 


62.480 


-114.592 


RSNY 


Ksm 


44.548 


-74.530 


RSON 


RSTN 


50.859 


-93.702 


RSSD 


RSTN 


44.120 


-104.036 


SCP 


DWWSSN 


40.795 


-77.865 


SSB 


GEOSCX)PE 


45.280 


4.540 


TOL 


DWWSSN 


39.881 


-4.049 


WFM 


GEOSCDPE 


42.610 


-71.490 


ZDBO 


ASRO 


-16.270 


-68.125 



TABLE 2. Adopted Constants 



Variable 


Description 


Value 


a 


volumetric coefficient of thermal 
expansion 


2.5 X 10-5 K-l (a) 


PO 


average mantle density 


3300 kg m'^ 


pw 

r 


density of seawater 
gravitational constant 


1000 kg m"^ 

6.67 X 10-11 Nm2kg-2 


g 

avs/3T 


surface gravitational acceleration 
thermal coefficient of 


9.8 m s"^ 

-6.0 X 10-^ km/s K-1 


dvs/9Mg 

dp/aMg 


shear velocity 

variation of shear velocity with Mg# 

variation of density with Mg# 


1.8 X 10-2 km/s/Mg#(*') 
.12kg/m3/Mg#W 


p 


average SS ray parameter at 70* 


0.1375 s/km 



(a) Stacey [1911], Duffy and Anderson [1989] 

(b) Akimoto [1972] 



TABLE 3. Inversion Models and Variance Reduction 



Model: Temperature variations only 






Variance reduction, 


% 


Layer 

thickness 


Viscosity 
structure 


^T range 


total 


25 


&?oid 

79 


ss-s 


0-150 km 


cvm 


180 K 


53 


58 


0-150 km 


Ivz 


230 K 


57 


27 


79 


66 


0-300 km 


cvm 


60K 


47 


21 


85 


41 


0-300 km 


Ivz 


llOK 


57 


24 


85 


65 


0-650 km 


cvm 


20 K 


41 


14 


91 


25 


0-650 km 


Ivz 


33 K 


49 


17 


83 


51 



Model: Compositional variations only 



Variance reduction, % 



Layer 
thickness. 

0-150 km 


Viscosity 


AM p# ranee 


total 


tODO 


feoid 


SS-S 


cvm 


1.1 


33 


46 


74 


-9 


0-150 km 


Ivz 


2.4 


44 


75 


76 


-9 


0-300 km 


cvm 


0.4 


33 


29 


87 


-6 


0-300 km 


Ivz 


1.3 


43 


73 


73 


-7 


0-650 km 


cvm 


0.1 


32 


19 


93 


-3 


0-650 km 


Ivz 


0.5 


49 


65 


86 


+5 



Model: Thermal and compositional variations in same layer Variance reduction. % 



Layer 
thickness 



Viscosity 
smicftire 



AT 

rangg 



AMg# 

, rangg 



0-150 km 
0-150 km 



cvm 
Ivz 



210 K 
235 K 



1.5 

2.1 



t(7tfll top n geoid SSiS 

75 44 78 100 
86 75 80 100 



0-300 km 


cvm 


llOK 


0.7 


73 


28 


89 


100 


0-300 km 


Ivz 


125 K 


1.1 


84 


74 


76 


100 


0-650 km 


cvm 


55 K 


0.4 


71 


18 


94 


100 


0-650 km 


Ivz 


60K 


0.8 


85 


66 


88 


100 



Model: Thermal inversion in layers as noted, compositional variations 0-50 km only 

Viscositv AT AMg# Variance reduction % 

l^yer Viscosity " & ^ ^ ^ ggpid — SSiS 

Thirhnr-i'i ^"^^^"^ ^^^^ ^^^ 

210 K 5 5 84 83 77 91 

0-150 km cvm 21U k o.j 

1 240K 4 5 85 85 70 96 
0-150 km Ivz 24UK 

80 K 5 9 80 84 86 72 

0-300 km cvm »" k D.y 

1 120K 4 7 86 90 77 89 
0-300 km Ivz 12U K 

9SK 6 73 85 92 47 

0-650 km cvm 25 K o.u 

, 35K 4 6 75 82 73 71 
0-650 km Ivz ^^ ^ 



cvm = constant viscosity mantle 
Ivz = mantle with low viscosity zone 



CO 



CO 

if) 



o 
o 

I 

X 








60 



-60 



120 





Time, s 



60 



h^ 



eo^N 



30*»N 




90*W 



hf 



2- 



60°N 




eo^w 



h) 



?" 



60°W 



60°N 




<"•) 



>^ 



6 



1 r 



T r 



4 



GO 



CO 

• 1—1 

m 

CD 

I 

CO 
CO 



2 - 







-2 



-4 



-6 








:i 



11 






4 8 

VAge, VMy 



12 



- 



Z^;^ 



/ 



6 



1 r 



1 \ 1 r 



w 



cd 

•r-l 

CD 

I 

m 
m 

0) 

o 

(D 

;-. 
o 
o 

0) 







Kuo et al. (1987) 



-2 




-4 



[} 



-6 



-80 



J L 



-40 

Azimuth 



40 



80 



/^> 



r 



60°W 



60°N 




/T^ / 



60°W 



60°N 




/r> 



u 



kf 




ecN 



- 30* 



90"W 



^) 



t 



Along-axis SS-S Residual 



N 




10 



20 



30 



40 50 

Latitude, °N 



^> 



f 



Geold/SS Correlation Coefficients 



d 
a> 

•■H 
O 

«M 

^-1 

0) 

o 

o 

d 
o 

05 

0) 

t: 

o 
a 




-0.5 



2 4 6 8 

Highest degree and order removed 

Geoid/SS slope 



10 



a 

d 
o 

^ -1 






a -2 



I -at 



CO 



-4 



8 



2 4 6 

Highest degree and order removed 



10 



h^ 1 



SS-S RESIDUAL 




O 4 
2 




»^T * i i 



iW"'^ f "^ 



ft 



{ 



i»* 



1 



^ll 



10 



20 



30 



40 



50 



60 



70 



2000 



1000 



BATHYMETRY 



§ 



i 






■p— 



5/'. 



OQ -1000 



-2000 



o 






I 



.. W 



10 



20 



30 40 50 

LATITUDE, °N 



60 



70 



A ^^ 



(a) CONSTANT VISCOSITY 

GEOID KERNEL 



-0.4 




TOPOGRAPHY KERNEL 

-0.4 0.0 0.4 0.8 



— X=3500 km; 
--X=1000 kmi 



100 



200 



300 



Q 400 



500 



600 




(b) LOW VISCOSITY LAYER 



GEOID KERNEL 

-0.4 0.0 0.4 



TOPOGRAPHY KERNEL 

-0.4 0.0 0.4 



100 



200 



. 300 



a, 

Ed 

1=1 400 



500 



600 



— X=3500 knd 

1 

--X=1000 kmj; 




-I L. 




h 



II 



SPHERICAL VS. CARTESIAN 

(a) CONSTANT VISCOSITY (X = 4000 km) 



GEOID KERNEL 



-0.4 
I 



0.0 

I 



0.4 

— r— 



- 



100 - 



200 



. 300 



Oi 
Ed 
Q 400 



500 



600 



— X=4000 km 
-- i = 10 




TOPOGRAPHY KERNEL 

-0.4 0.0 0.4 0.8 




(b) LOW VISCOSITY LAYER (A = 4000 km) 
GEOID KERNEL TOPOGRAPHY KERNEL 

-0.4 0.0 0.4 0.8 




100 



200 



300 



O 400 



500 



600 



T \ 1 — T 1 1 1 T- 







II - 



(. 



GEOID KERNEL 

-0.4 0.0 0.4 



SPHERICAL VS. CARTESIAN 

(c) CONSTANT VISCOSITY (X = 6667 km) 

TOPOGRAPHY KERNEL 





GEOID KERNEL 

-0.4 0.0 0.4 



(d) LOW VISCOSITY LAYER (X = 6667 km) 

TOPOGRAPHY KERNEL 

-0.4 0.0 0.4 0.8 




T r^ 



100 



200 



300 



o 400 



500 



600 



I I 



f-^ 



II 



J 



CONSTANT VISCOSITY MANTLE 



....AT 0-150 km 
_AT 0-300 Jan 
_. AT 0-660 km 




10 



20 



80 40 00 

LATTTUDE, ^N 



i^'d 



/,? 



W 100 



a 



50 



-50 



LOW VISCOSITY ZONE 

TdlPKRlTURE 
AT 0-lBO km 

AT 0-300 Ion 

AT 0-660 km 



i' ■^^ //:::§ 



-100 






//,''— -~s^ 






A 



// 



/ 



a 








^.-^ 


a 


-I 


■ 


o 






^ 


-8 


. 


o 








-3 






30 40 60 

LATITUDE, "N 



f,^/^ 



CONSTANT VISCOSITY MANTLE 



couposmoH 

fCiig 0-160 km 
^llg 0-300 km 
^^ 0—660 km 




15 80 30 «> 

lATTTUDE. ^'N 



A; /^ 



LOW VISCOSITY ZONE 



=«= 


1.0 


«0 




a 




< 


0.5 


S5 




O 


0.0 


i-4 




n 




o 


-0.5 


Si 




O 


-1.0 


O 





ooliPosmoN 

Alls 0-160 km 

£Mg 0-800 km .. 

AUg 0-660 km/ 



^-"^^ 




10 



20 



30 40 60 

lATTTUDE. "N 



60 



70 



h 



/6 



COMPOSITION. A Mg# 



A TEMPERATURE, K 



^. 



W 



O 

!z: 




S s 



s 



g-i 



8 



I 
8 



8 S 



-v. 

.'/ / 
'A--.. 



y 



n 



>--•• 



/ y 



I I 1 
??? 

9 (A tl 



TOPOGRAPHY, km 

J, 

01 



GEOID, m 



SS-S. s 



t 



o 
25 




A^/? 



COMPOSITION, A Mg# 



A TEMPERATURE. K 



1 

b 



I 

o 



o 
b 



o 
b 



I 

8 






s 



I 



W 



o 

2: 



8 



J 

it / 

/// 






I 



o o O o 

1 I I g 
• 5fi ti a 

s s s i 

HI* 



/ 



8 



/J 






^ 



y> 






s 



•/7 










■v 



TOPOGRAPHY, km 



GEOID. m 



SS-S, s 




CO 

o 

o 

CA 



tS3 
O 



A5 « 



I 
to 



COMPOSITION. A Ug# .A TEMPERATURE. 

o 8 



^ O 



i>A W ' 



I 
8 






,;> 



' I 







???§ ° 

9 CA tt H 

lss| 

ffffl 






"^/S-) 



o 
\ 



i C •: 



S fe 



o 



I> 8 



»>*•* 



i.|*U> 



/■;^/' 



i ■■~^~- 



-v.. 

\ \ ••• 
\ \ 

! ) 
/ / . 

/i 

/ / 
/ / 

V ! 
...\ \ 



K 

8 



; I 



^^6 



I I I 



TOPOGRAPHY, km 



GEOID. m 



w 

o 




^ /9 



COMPOSITION. A Mg# 



A TEMPERATURE, K 



o 
— r- 



I 

8 



I 



!S 



,<- 



> 






! I I 

h b h 8 
? ? ? I 



^ O 



o 



8 



8 



•a 



V--. 



\ 



o 



8 



% 



J^ 



^-■v 
^--S* 



O 
I 
Ol 

o 



o 



t- 



..^ 



g 



N 
y 



y..- 






\ 



\ 



II 

?? 
S8 



\l 



■•••.. ^!^ 



O 






TOPOGRAPHY, km 



GEOID, m 



SS-S, s 

bi b b( o 01 o w o 

I 




CO 

o 
o 



o 




zo