Mobility of continental mantle: Evidence from postseismic

geodetic observations following the 1992 Landers earthquake

Fred F. Pollitz

Department of Geology, University of California, Davis

Gilles Peltzer

Jet Propulsion Laboratory, Pasadena, California

Roland Bu .. rgmann

Department of Geology and Geophysics, University of California, Berkeley

Abstract. The crust around the rupture zone of the 1992 Landers
earthquake has continued to

deform in the years following the earthquake at rates •3 times greater
than pre-earthquake rates.

We use a combination of Global Positioning System (GPS) and synthetic
aperture radar

(InSAR) data collected during a •3-year epoch following the earthquake
in order to investigate

postseismic mechanisms responsible for the high transient velocities. In
order to maximize the

potential signal from viscoelastic relaxation we evaluate and model
postseismic relaxation

following the first few months of documented accelerated deformation.
The combination of

GPS and InSAR data allows us to establish viscoelastic relaxation of the
lower crust and upper

mantle as the dominant postseismic process and to discriminate among
possible viscoelastic

models. The data particularly require the presence of a highly ductile
uppermost mantle

beneath the central Mojave Domain, with temperature between the wet and
dry basalt solidus.

This is consistent with independent seismic and geochemical inferences
of a regionally warm

uppermost mantle. Further consideration of seismic velocity variations
in conjunction with

faulting patterns within the Mojave Desert suggests that the primary
faulting characteristics of

the Mojave Desert, namely, the pervasive late Cenozoic deformation
within the Eastern

California Shear Zone versus the near absence of faults in the Western
Mojave Domain, are

controlled by the rheology of the uppermost mantle.

1\. Introduction

The strength of the Earth's lithosphere is of central

importance for understanding mountain building \[Chery et al.,

1991\], continental rifting \[e.g., Buck, 1991; Zeyen et al., 1997\],

and the propagation of stresses through continental lithosphere

\[Kusznir, 1982\]. Continental lithosphere is thought to be

characterized by a brittle upper crust, a ductile and weak lower

crust, and a ductile but much stronger mantle lithosphere. This

picture is based on the correlation of cutoff depth in continental

seismicity with the onset of thermally activated processes in

crustal materials \[Sibson, 1982\], the seismic and geological

evidence for a weak lower crust \[Kay and Kay, 1981; Hacker et

al., 1992; Brocher et al., 1994\], and the mechanical properties

of the primary constituents of the crust and upper mantle

\[Brace and Kohlstedt, 1980\], and it is often summarized in

terms of strength envelopes \[Brace and Kohlstedt, 1980;

Molnar and Tapponier, 1981; Chen and Molnar, 1983\]. A

relatively cool geotherm is expected to result in a less ductile,

\"strong\" uppermost mantle, as occasionally directly manifested

by mantle seismicity \[Chen and Molnar, 1983\]. The expectation

that higher-than-normal temperatures in the mantle should

increase its ductility is consistent with the association of high

topography with warm and likely convecting mantle \[e.g., Jones- 2 -et

al., 1996; Wernicke et al., 1996; Lithgow-Bertelloni and

Silver, 1998\] and the association of highly thickened crust with

thermally weakened mantle \[Chery et al., 1991; Wdowinski and

Bock, 1994\].

A direct way of characterizing the ductility of the uppermost

mantle is to infer its viscosity from geodetic observations made

after large earthquakes. This method is based on the

supposition that the coseismic stresses generated by an

earthquake cannot be sustained by the ductile lower crust and

upper mantle, leading to postseismic relaxation of these

materials which is, in turn, transferred to the upper crust,

producing observable transient geodetic signals. Such signals

have a predictable, essentially space- and time-transgressive

diffusive behavior \[e.g., Bott and Dean, 1973; Nur and Mavko,

1974; Rydelek and Sacks, 1990; Cohen, 1992; Pollitz, 1997\]

consistent with observations in a number of cases. Triangulation

and leveling data collected after large earthquakes in Japan and

California have been successfully (but not uniquely) explained

in terms of postseismic relaxation behavior \[e.g., Thatcher et

al., 1980; Miyashita, 1987; Tabei, 1989; Pollitz and Sacks,

1992, 1994\]. The large uncertainties, infrequent time sampling,

and configuration of triangulation and leveling networks have

made it difficult to distinguish between broadscale, deep

relaxation processes versus localized crustal afterslip.

Moreover, for the special case of a very long strike-slip fault,

both deep afterslip and deep viscoelastic flow can produce the

same horizontal surface deformation \[Savage, 1990\]. Horizontal

geodetic data complemented by vertical data, however, remove

this ambiguity and allow discrimination between afterslip and

viscoelastic flow mechanisms for a rupture of finite dimension.

Uppermost mantle viscosity is thought to play a fundamental

role in the style of regional crustal deformation in both the

short and long term \[e.g., Furlong et al., 1989; Kusznir, 1991;

Jones et al., 1996\], yet it has not been directly estimated even

in relatively well-monitored regions because of nonuniqueness

in interpreting available geodetic data as well as the paucity of

seismic sources of sufficient strength to excite observable

postseismic signals. For example, Global Positioning System

(GPS) and leveling data around the rupture zone of the Mw =

6.9 1989 Loma Prieta earthquake were recently considered by

Pollitz et al. \[1998\] in order to establish the possible

importance of various postseismic processes. Interpretation of

this postseismic velocity field strongly suggests that shallow

afterslip is the dominant postseismic process. Although the

data also appear to resolve a tangible signal from deep

viscoelastic relaxation, the trade-offs with relatively shallow

afterslip are substantial and there is not enough resolution to

distinguish among even grossly different (but equally viable)

viscoelastic stratifications such as strong versus weak uppermost

mantle. A study of geodetic velocities collected in the 2 years

after the Mw = 6.7 Northridge earthquake \[Donnellan and

Lyzenga, 1998\] confronts similar difficulties. Near-field

horizontal and vertical GPS measurements (and far-field

measurements at one site) point to shallow afterslip as the

dominant postseismic process. Although lower crustal

viscoelastic relaxation alone is ruled out by the data, it is

possible that a slow (and as yet undetectable) viscoelastic

relaxation signal is imposed on a larger afterslip signal. Thus,

in both the post-Loma Prieta and post-Northridge cases, the- 3
-domination

of shallow afterslip in the immediate (2 5 years)

postseismic epoch, as well as the relatively small size of these

earthquakes and the distribution and type of data, have made

detection of a deep viscoelastic relaxation signal problematical.

The Mw = 7.3 1992 Landers earthquake, a larger event,

involved an average of 3 4 m of right-lateral slip on long-dormant

faults of total length •80 km traversing the Eastern

California Shear Zone (ECSZ) in the central Mojave Domain

\[Hart et al., 1993; Sieh et al., 1993\] (Figures 1a and 2). In the

months and years following the earthquake the epicentral region

has been monitored with GPS networks, trilateration arrays,

creep meters, and interferometric processing of synthetic

aperture radar (InSAR) data. These types of data (covering

time periods ranging from several days to years) have been

previously considered by several investigators, and several

postseismic processes have been proposed. These include (1)

fault zone collapse \[Massonnet et al., 1996\], (2) afterslip \[Shen

et al., 1994; Massonnet et al., 1994; Wdowinski et al., 1997;

Savage and Svarc, 1997\], (3) poroelastic rebound \[Peltzer et

al., 1996, 1998\], and (4) viscoelastic relaxation of the lower

crust and upper mantle \[Ivins, 1996; Yu et al., 1996; Deng et

al., 1998\]. The studies by Massonnet et al. \[1996\], Peltzer et

al. \[1996\], and Peltzer et al. \[1998\] utilize InSAR data alone;

that of Wdowinski et al. \[1997\] utilizes GPS data recorded by

remote (\>65 km) stations of the southern California Permanent

GPS Geodetic array (PGGA), and the remaining studies utilize

campaign GPS measurements. With the exception of the

continuous GPS measurements at remote stations of the PGGA,

the GPS studies have provided no or poor estimates of vertical

deformation. By the same token, the InSAR range change is

shaped primarily by the vertical displacement field.

Both vertical and horizontal deformation information together

are critical for addressing uniqueness in interpretation of

postseismic processes. In this paper we analyze a joint data set

consisting of GPS and InSAR data collected in the 3 years after

the Landers earthquake. This combination proves to be

effective in discriminating among the above candidate

postseismic processes. We find that the long-wavelength

(horizontal scale larger than •5 km) postseismic deformation

pattern is dominated by deep viscoelastic relaxation. This data

combination is also effective in discriminating among different

models of regional viscoelastic stratification, and we infer a

very weak uppermost mantle beneath the central Mojave Desert.

Viscosity structure provides important constraints on the

physical state of the crust and upper mantle. The Mojave

Desert lies at the southwestern edge of the Basin and Range

province, which has experienced substantial horizontal

extension over the past 20 Myr \[Stewart, 1978\], and it

encompasses the transition from rifting to strike-slip faulting

within the modern San Andreas fault system. Intense debate

centers on whether significant thinning or erosion of the mantle

lithosphere has occurred there during the Cenozoic, either

during the epoch of low-angle Farallon plate subduction or

following the transition to a dominantly strike-slip Pacific-North

America plate boundary zone. Geochemical analyses of

mantle-derived alkali basalts in the late Cenozoic volcanic fields

of the Mojave Desert yield a strong similarity to Pacific mid-ocean

ridge basalt (MORB) source rocks \[Glazner et al., 1991\],

suggesting the existence of an underlying asthenosphere no- 4 -deeper

than 50 70 km \[Livaccari and Perry, 1993\].

Consideration of the elevation difference between the northern

and southern Basin and Range province, however, suggests a

relatively cool upper mantle beneath the southern Basin and

Range and eastern Mojave Desert \[Saltus and Thompson, 1995\].

The former view is supported by upper mantle seismic

velocities in the eastern half of the Mojave Desert (Figure 1b)

\[Humphreys and Dueker, 1994\], while the latter view is

supported by the crustal geotherm derived by Williams \[1996\].

The present study may shed further light on the state of the

uppermost mantle beneath the east central Mojave Desert.

In subsequent sections we present the data, give arguments

for the dominance of viscoelastic relaxation over other possible

postseismic processes, and discuss the implications of our

estimate of regional mantle viscosity.

2\. Data Set

This study utilizes both GPS and InSAR collected in the 3

years following the June 28, 1992, Landers earthquake (Plates

1a and 1c). The GPS data (Table 1) consist of horizontal

velocity vectors and corresponding covariance matrices Ch

determined over the following networks and occupation times:

\(1\) 14 sites released by the Southern California Earthquake

Center (SCEC) and analyzed by University of California, Los

Angeles, for the period September/November 1992 to December

1995 (SCEC Release 2, 1998, available at

http://www.scecdc.scec.org/group e/ release.v2), and (2) 12

U.S. Geological Survey (USGS) sites analyzed by Savage and

Svarc \[1997\] for the period November 1992 to December 1995

(Emerson transect). All horizontal velocities are with respect to

the fixed site GOLD (Table 1). These two GPS data sources

combined provide good coverage (primarily west of the rupture

zone) of average horizontal velocity in the near field (within 30

km of the rupture zones), intermediate field (30 60 km), and

far field (\> 60 km). In Table 1 we separate these data into

near-field and far-field categories. The InSAR data represent

total range change over the period September 27, 1992, to

January 23, 1996. The interferogram was computed using pairs

of SAR images provided by the European Space Agency, and it

contains a substantial vertical displacement signal in both the

near field and intermediate field. Further details are given by

Peltzer et al. \[1998\]. Although postseismic observations

beginning within days of the Landers earthquake are available

\[e.g., Shen et al., 1994; Massonnet et al., 1994; Savage and

Svarc, 1997\], we restrict attention to postseismic observations

made in September 1992 and thereafter in order to avoid

complications associated with possible rapid afterslip or

relaxation during the first three months after the earthquake

\[Shen et al., 1994; Massonnet et al., 1994; Ivins, 1996; Yu et

al., 1996\].

Formal error estimates are readily available for the GPS data

in the form of a covariance matrix Ch provided by J. Svarc

(personal communication, 1998) and SCEC Release 2. A

covariance matrix CR carrying information about statistical

correlations of errors among the InSAR range change estimates

is not available. Although this issue is not critical for our study

(we do not require absolute error estimates of any data subset

for our analysis), we have nevertheless taken a first-order- 5 -approach

in addressing this issue. We have defined a

covariance matrix CR for the InSAR image designed to

accommodate small uncertainties in both regional tilt and local

observation error. Small unknown errors in orbital position

translate into an unknown additional regional tilt upon forming

phase difference images in InSAR analysis. We account for

possible correlations between the observed and calculated range

change images due to possible broadscale regional tilt. We

represent range change R over a rectangular x •y grid as

R (x ,y ) =R0 (x ,y ) +a x +b y +c (x ,y ), where R0 is

deterministic signal, a and b represent unknown tilt, and c

represents local noise. Assuming in a statistical sense

Var a =• a

2 , Var b =• b

2 , and Var c =• c

2 , and that a , b , and c

have zero expectation value and are uncorrelated with one

another yields the covariance between two points (x 1 ,y 1 ) and

(x 2 ,y 2 ) in the interferogram:

CR (x 1 ,y 1 ;x 2 ,y 2 ) =• a

2 x 1 x 2 +• b

2 y 1 y 2 +• c

2 . (1)

The full covariance matrix includes the covariances between

each measurement in the interferogram. This covariance matrix

with values • a =• b =1.5 •10 •7 /(3.31 years) and

• c =0.75cm/(3.31 years) will be subsequently employed in

equation (6).

3\. Interpretation

3.1. Dominance of Deep Viscoelastic Relaxation

A whole array of postseismic processes likely contribute to

varying degrees to the observed postseismic deformation field.

The GPS and InSAR measurements may be interpreted as the

product of (1) fault zone collapse \[Massonnet et al., 1996\], (2)

afterslip on or beneath the Landers seismogenic rupture zone

\[Shen et al., 1994; Savage and Svarc, 1997\], (3) poroelastic

rebound \[Peltzer et al., 1996, 1998\], (4) viscoelastic relaxation

of the lower crust and upper mantle driven by the coseismic

stress changes \[Ivins, 1996; Yu et al., 1996; Deng et al., 1998\],

and (5) interseismic strain accumulation.

Interseismic strain accumulation is modeled here using the

slip-at-depth model specified by Feigl et al. \[1993\] and Table 3

of Savage and Svarc \[1997\]. Figure 3a shows the strike-slip

fault traces used, and Figure 3b shows the interseismic velocity

field calculated at the 26 GPS sites relative to a fixed Gold-stone,

as tabulated in Table 1. The interseismic velocity field

relative to a fixed Goldstone does not, with the exception of

PIN1, exceed 6 mm/yr and is generally a fraction of the

observed relative velocity (Table 1). This is also seen by com-parison

of Figure 3b and Plate 1c.

The observed postseismic velocity field is therefore shaped

primarily by processes which are unique to the Landers postse-ismic

epoch. These are processes 1 to 4 above, and we now

evaluate the relative merits of these processes. Poroelastic

rebound alone, assuming drained pore fluid conditions over the

entire region following the Landers earthquake (with values of

0.27 and 0.31 for the drained and undrained Poisson's ratio,

respectively \[Peltzer et al., 1998\]), predicts horizontal velocities

of only very small magnitude and thus cannot explain the

observed GPS velocity field, even if it explains remarkably well

the observed InSAR image (Plate 2b). It appears to be a- 6 -particularly

important postseismic process around localized fault

bends where sharp gradients in range change pattern are

observed (Plate 1a). Afterslip alone, if it does not extend deeper

than 30 km depth, can adequately explain the near-field GPS

velocity field, as demonstrated by Savage and Svarc \[1997\]

using the Emerson transect data, but the predictions of their

model are practically anticorrelated with the observed InSAR

image (Plate 2a). A combination of poroelastic rebound and

afterslip can adequately explain the near-field GPS velocity

field and the northern portion of the InSAR image (Plate 2c).

Neither the persistence of significant horizontal postseismic

deformation up to 100 km from the rupture zones (Plate 1c) nor

the southern portion of the InSAR image (Plate 1a), however,

can be explained with this combination. Fault zone collapse

alone is similarly unable to produce the significant far-field

deformation which is observed. If postseismic relaxation plus

interseismic strain accumulation are invoked to explain the far-field

observations, then we find that they are sufficient to

explain the near-field observations as well. These arguments

suggest at most minor contributions of fault zone collapse,

poroelastic rebound, or afterslip to the long-wavelength postse-ismic

deformation pattern during the 3-year epoch beginning

3-5 months after the Landers earthquake, and we shall hen-ceforth

focus on postseismic relaxation and interseismic strain

accumulation only.

3.2. Viscoelastic Stratification of Central Mojave Domain

We intend to construct a model of the regional viscoelastic

stratification which satisfactorily explains both the horizontal

GPS and InSAR range change observations during the Landers

postseismic epoch. In order to clarify the importance of various

subsets of the data we shall subdivide the total data set (Plates

1a and 1c) into four distinct subsets reflecting the different

influences of data type and distance from the rupture zones

(i.e., near-field versus far-field). In order to evaluate misfit with

respect to these data subsets we shall present the forward prob-lem

in terms of the summed effects of interseismic velocity

plus viscoelastic relaxation of the lower crust and mantle. The

latter is completely specified by the Landers coseismic rupture

model, which is assumed known, elastic stratification (also

assumed known), and unknown viscoelastic stratification (which

includes the influence of the initial stress field; see section 5.1).

After defining our model parameter space, we shall evaluate

misfit of these data subsets within this model space and discuss

which combinations of viscoelastic parameters yield the best fit

to all data considered.

Let t1 and t2 denote the start and end time, respectively, of

repeated geodetic surveys. We work with 26 horizontal GPS

velocity vectors vh (ri ;t 1,t2) (i =1,2, . . . ,26) and InSAR range

change pattern R (r;t 1 ,t 2 ) covering a continuous 90 •70 km 2

area. Predicted horizontal velocity and range change are

expressed as follows:

v(r;t 1,t2) =t 1 t 2

????????????????????????????

Equation (2) represents the vector velocity v as a sum of post-seismic

relaxation and interseismic strain accumulation, respec-tively,

each expressed as a convolution of a Greens function

and slip defined over appropriate dislocation planes. For the

postseismic component the Landers earthquake fault area and

coseismic right-lateral strike-slip distribution s (r0 ) are

prescribed by Wald and Heaton \[1994\]. For the Big Bear seg-ment

we use a fault length of 12 km striking N50°E, a dip of

90°, a width of 8 km (7 15 km depth range), a uniform slip of

2.50 m, and a total seismic moment of 9 •10 18 N m. These

values are appropriate for the main shock of the Big Bear

sequence \[Jones and Helmberger, 1993\]. The Greens function

G (ps ) is prescribed by Pollitz \[1997\]. For the interseismic
com-ponent

the distribution of deep slipping segments and the

corresponding velocity distribution d (r0 ) are prescribed by

Feigl et al. \[1993\] and Table 3 of Savage and Svarc \[1997\],

and the Greens function G (is ) is prescribed by Okada \[1985\] (a

half-space elastic medium is appropriate for calculating the

interseismic component because such a medium is assumed by

Feigl et al. \[1993\] in order to match regional geodetic surface

displacements). The unit vectors zˆ and • ˆ point toward the

locally up direction and the line-of-sight direction of the satel-lite

used in the InSAR analysis, respectively. The azimuth • ˆin

local east-north-up coordinates is (0.381, -0.088, 0.920) \[Euro-pean

Space Agency, 1992\].

Given a fault model of the Landers earthquake, surface defor-mation

resulting from viscoelastic relaxation of the lower crust

and mantle is determined by the viscoelastic stratification (Fig-ure

4). In our modeling, we choose elastic parameters

appropriate for the region \[Qu et al., 1994, Table 1\] and allow

the following parameters to be variable: • c , • m1 , and • m2

(lower crust, uppermost mantle, and deeper mantle viscosity,

respectively) and µ•(the long-term strength of the lower crust)

\[Cohen, 1982; Ivins and Sammis, 1996\]. A value µ•=0

corresponds to a Maxwell viscoelastic fluid, and a finite value

of µ•corresponds to a material which can maintain a certain

amount of shear stress, nominally a fraction of its short-term

strength, over indefinitely long periods of time. A significantly

nonzero µ•in the northeast Iceland lower crust was strongly

suggested in the postrifting study of Pollitz and Sacks \[1996\]

around the Krafla rift. This parameter is found to exert a

moderate influence on the present results as well. A viscosity

decrease of about one order of magnitude within the top 100

km of the mantle is dictated by the increase in dislocation

mobility of olivine with depth \[Karato et al., 1993\]. If, as is

suggested by isotopic compositions, asthenosphere is present no

deeper than 50 70 km depth in the area \[Livaccari and Perry,

1993\], then the mantle viscosity below the dehydration boun-dary

(65 km depth, where melt extraction alters the water con-tent

\[Hirth and Kohlstedt, 1996\]) should be •10 18 Pa s, about a

factor of 5 lower than the mantle viscosity that would be

inferred in our study if an isoviscous mantle were assumed

(section 4.1). As will be justified shortly, we represented this

viscosity decrease by prescribing a mantle viscosity ratio

• m1 ⁄• m2 =3, i.e., a threefold decrease in mantle viscosity at

50 km depth. - 8 -Values

of µ•=6, 12, 18, 24, and 30 GPa were considered

and evaluated. Best results were obtained with µ•=12 GPa,

but our main conclusions are robust with respect to the choice

of µ•. We shall therefore restrict attention to the two cases:

µ•=0 and µ•=12 GPa. We calculated vh and R for these

values of µ•and over the range • c ⁄• m1 =3.6 •10 •2 •10 1 and

• m1 =10 18 •10 20 Pa s. In order to compare modeled and

observed deformation, we define misfit • 2

( j ) for each of four

data subsets \[Savage and Svarc, 1997; Peltzer et al., 1998;

SCEC Release 2\], far-field SCEC GPS (j =1), near-field SCEC

GPS (j =2), USGS GPS (j =3), and JPL InSAR (j =4) as fol-lows:

• 2

(1,2, or 3) =(\[vh \])T C •1

h (\[vh \]) (5)

• 2

\(4\) =•

••\[R (r;t 1 ,t 2 )\] +const •

T

C •1

R •

••\[R (r;t 1 ,t 2 )\] +const •, (6)

where •\[ \] denotes the difference between a calculated and

observed quantity and Ch and CR are covariance matrices of

GPS and InSAR data, respectively. Far-field and near-field sub-sets

of the SCEC GPS data set are realized by retaining

nonzero vh in (5) according to whether the GPS site lies out-side

of or within, respectively, the small boxed region of Plate

1c. In order to employ consistent reference frames for all cal-culations

and observations all calculated and observed horizon-tal

deformation is referred to the fixed site GOLD (Table 1) by

subtracting its observed and modelled velocity from all

observed and modelled site velocities, respectively. Mathemati-cally,

this means that the adjustments

vh (ri ;t 1 ,t 2 )obs •••vh (ri ;t 1 ,t 2 )obs •v(Goldstone;t 1 ,t 2
)obs (7)

vh (ri ;t 1 ,t 2 )cal •••vh (ri ;t 1 ,t 2 )cal •v(Goldstone;t 1 ,t 2
)cal (8)

have been performed for all horizontal deformation discussed in

this report. Also, the constant in (6) is always chosen such that

the mean of the bracketed quantity is zero.

Misfit patterns log10 2

( j ) (j =1,2,3,4) for µ•=12 GPa are

shown in Figure 5 (left). Corresponding results for a Maxwell

viscoelastic fluid lower crust (•=0) are shown in Figure 5

(right). We note that for each data subset j , there is a local

minimum in • 2

( j ) in the neighborhood of the following model

(indicated by solid circles in Figure 5):

• m1 =8.0 •10 18 Pa s

• m2 =2.7 •10 18 Pa s

• c ⁄• m1 =2.0

µ•=12 GPa

(Mojave Block model). Calculated range change and horizontal

velocity field for the Mojave Block model are shown in Plates

1b and 1c. This simple viscoelastic coupling model duplicates

the main long-wavelength features of both the range change and

horizontal velocity fields. The calculated range change (Plate

1b) does not include any tilt, and we found that a substantial

portion of the remaining misfit could be explained by a tilt of

20 mm per geocentric degree \@S60°W.

We now consider which other models perform comparably

with this one. Acceptable models must provide a good fit to all

data subsets simultaneously. The most straightforward way to

evaluate the suite of models would be to consider the statistic- 9 -

2 =

j =1 •

4

• 2

( j ) . (9)

Unfortunately, this measure is sensitive to the absolute error

scaling of the various data subsets. Although both the GPS and

InSAR data can be fit at the level of •80 90% variance reduc-tion,

the residual misfit of the three GPS data subsets averages

between 2 and 3 (where • represents one standard devia-tion),

whereas the InSAR data are fit closer to the level of 1 .

The InSAR data are consequently grossly under-represented in

• 2 as written in (9). We choose an approach which avoids the

issue of absolute error scaling. For each data subset j we con-sider

the set of models (m1 ,c ,•) such that the improvement

in • 2

( j ) obtained by the parameter combination of the Mojave

Block model is significant at the 95% or 99% confidence level.

Then F • obeys the F •distribution, where F • is given by

F • = • 2 (Mojave Block model) ⁄(N •3)

•

•• 2 (m1 ,c ,•) •• 2 (Mojave Block model) •

•⁄3

\_
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
, (10)

where N is the number of independent data in data subset j .

Define (F )j to be the region in the model space such that

F • \< P (F •3,N), where P (F • • 1 ,2 ) is defined by equation

26.6.1 of Abramowicz and Stegun \[1984\]. Finally, define ΩF to

be the intersection of the sets (F )j , i.e., that part of the model

space which fits each data subset at probability level P . Since

each (F )j is independent of the absolute error scaling, ΩF is

as well, so we consider it to be a useful objective definition of

the best fitting models. Figure 6 shows ΩF at probability levels

P =0.95 and P =0.99 at the model slices µ•=12 GPa and

µ•=0. We conclude that uppermost mantle viscosity beneath

the central Mojave Domain equals 8 ±4 •10 18 Pa s (99%

confidence interval), corresponding to a maximum characteristic

relaxation time of • m1 ⁄µm =•3.6 years, i.e., a mobile upper-most

mantle. It is noteworthy that consideration of near-field

GPS data alone would render models of low µ•, high • m1 , and

low • c plausible. The additional information provided by far-field

GPS and near-field InSAR data rules out this possibility.

4\. Discussion

4.1. End-Member Mantle Viscosity Models

We find that if the statistical analysis of section 3.2 is

repeated using mantle viscosity ratios • m1 ⁄• m2 equal to 1 and

10, sharp local minima similar to those seen in Figure 6 are

obtained with a shift toward lower • m1 =5 •10 18 Pa s or higher

• m1 =1.1 •10 19 Pa s, respectively. This is illustrated for the

isoviscous mantle model • m1 =• m2 in Figure 7. In both these

end-member cases and for intermediate ratios (such as the

Mojave Block model), average mantle viscosity within the top

40 km of the mantle is about 5 •10 18 Pa s. Regardless of the

details of the viscosity decrease with depth, a low-viscosity

uppermost mantle is a robust result.

Our analysis with • m1 ⁄• m2 =3 yields a low uppermost man-tle

viscosity • m1 near 8 •10 18 Pa s, but lower crustal viscosity

• c may lie near either 5 •10 18 Pa s or 2 •10 19 Pa s (based on

the bimodal distribution exhibited in Figure 6). In addition, the

analysis can not discriminate among low and high µ•, though a

nonzero µ•=12 GPa generally yields slightly smaller residual- 10
-misfits.

We favor the larger possible crust-to-mantle viscosity

ratio of •2, in the Mojave block model because the local

minimum in data misfit is strongest for that value. For pur-poses

of discussion, we will consider the ratio • c ⁄• m1 and µ•

fixed at the values determined for the Mojave Block model and

focus on the resolution of the mantle viscosity stratification.

We may examine in greater detail two end-member models

constructed with mantle viscosity contrasts of 1 and 10. Two

forward models using these ratios are presented in Plate 3. The

first end-member model is prescribed by • m2 =• m1 =6.0 •10 18

Pa s and is found to yield a good fit to the horizontal velocity

field, but it does not predict the observed substantial decrease in

range change from west to east across the Johnson Valley fault

(Plates 3a and 3b). From comparison with Figure 1c, the

InSAR data thus favor a factor •3 decrease in mantle viscosity

below 50 km depth. A decrease in mantle viscosity with depth

is also suggested by the USGS Emerson transect data, where

systematic misfits between observed and calculated horizontal

velocities are large for • m1 ⁄• m2 =1 (Plate 3b), small for

• m1 ⁄• m2 =3 (Plate 1c) and smaller still for • m1 ⁄• m2 =10

(Plate 3d). It should be noted, however, that allowance for

numerous unmodeled factors could modify our predictions

enough to remove the requirement for this viscosity decrease.

These include (1) afterslip on the Eureka Peak and southern

Johnson Valley fault segments \[Behr et al., 1994\], (2) poroelas-tic

rebound \[Peltzer et al., 1998\], and (3) lateral variations in

poroelastic and viscoelastic stratification. All of these may also

contribute to many shorter wavelength features on the observed

InSAR image (Plate 1a).

4.2. Modeling of Emerson Transect Data

As noted above, a systematic offset of about 4 mm/yr toward

the southwest is apparent in the calculated vectors at the USGS

Emerson transect sites on the Mojave Block model (Plate 1c).

As demonstrated in Plate 3, this offset is found to increase or

decrease substantially when models with smaller or larger

• m1 ⁄• m2 , respectively, are considered. Rather than use this to

argue unequivocally for a sharp mantle viscosity decrease with

depth, it is worthwhile to explore alternative causes. The offset

could be caused by inaccuracies in calculated deformation at

the reference site GOLD arising from the interseismic velocity

correction or the calculated viscoelastic relaxation. The latter

could result from a very different viscoelastic stratification

north of the study area compared with that within the study

area. All of these possibilities, however, would be expected to

produce systematic offsets at all GPS sites, and the SCEC GPS

sites do not exhibit the offset. Unmodeled postseismic

processes on the Emerson and Camp Rock faults are another

possibility. Fault zone collapse would be expected to produce a

symmetric velocity pattern with respect to the fault trace, in

contrast with the uniformity of the offset. Relaxation following

dip-slip coseismic motions on the Emerson and Camp Rock

faults, as advocated by Deng et al. \[1998\], is another possibil-ity,

but the additional velocity produced by the suspected dip-slip

components is toward the southwest, which would degrade

the offset of our model even further. These considerations raise

the possibility of a solid body rotation between the SCEC and

USGS data sets. The two data sets have no sites in common

except GOLD for the time period modeled here- 11 -(

September/November 1992 1995). For a •3-year period begin-ning

in mid-late July 1992, the USGS data \[Savage and Svarc,

1997\] and SCEC data (SCEC Release 2) have two sites in com-mon

(in addition to GOLD): PIN1 and SANH/SAND (Table 1).

The velocity vectors with respect to GOLD in the two data sets

are for PIN1, -6.8 mm/yr east, 12.6 mm/yr north (SCEC) and

-2.6 mm/yr east, 14.4 mm/yr north (USGS); for SANH/SAND,

9.3 mm/yr east, -9.1 mm/yr north (SCEC) and 17.3 mm/yr east,

-6.0 mm/yr north (USGS). Sites GOLD and PIN1 are both

continuous PGGA sites, while SANH/SAND are campaign

sites. Both sets of velocities disagree by several millimeters per

year. Although this may be partly due to the slightly nonover-lapping

time intervals involved in this comparison, this suggests

sizable discrepancies between the two data sets. A reviewer (L.

Hearn) has pointed out similar discrepancies at these two sites

within the early postseismic epoch alone. If the discrepancies

continued into the later postseismic epoch, then they may be

related to the offset exhibited in Plate 1c. We will not attempt

to resolve the origin of the offset in this paper, if it exists at all.

In any case, the magnitude of the offset in our preferred model

is fairly small, and our preferred viscoelastic model reproduces

quite accurately the strain field represented by the USGS GPS

data.

4.3. Temporal Variation in Effective Viscosity

A power law relationship between stress and strain rate in the

upper mantle can be used to express effective viscosity • eff in

terms of strain rate at a given temperature:

• eff •• . (1 n )n

, (11)

where n •3.5 \[Karato and Wu, 1993\]. The large transient

velocities observed in the first few months following the

Landers earthquake have been interpreted in terms of very low

effective viscosity • eff •10 17 Pa s \[Yu et al., 1996\]. The fact

that this estimate is much smaller than our estimate of

• eff =8.0 •10 18 Pa s for the 3-year period following the initial

postseismic phase may indicate (1) rapid afterslip during the

initial postseismic phase \[Shen et al., 1994\], (2) a biviscous

lower crust with •5% concentrations of oblate spherical inclu-sions

of viscosity 3 •4 •10 15 Pa s \[Ivins, 1996\], or (3) a rapid

decrease in crust and/or mantle strain rate with time following

the earthquake, based on equation (11). Discrimination among

these possibilities will require an integrated analysis of both the

early and later postseismic geodetic data, with consideration of

viscoelastic relaxation (and other) processes within both a com-posite

lower crust and the mantle. It appears likely, in any

event, that the early postseismic epoch is shaped by numerous

postseismic processes of comparable importance.

4.4. Thin Channel Model

A very different model for the regional viscoelastic relaxation

\[Deng et al., 1998\] possesses a very low-viscosity lower crust

(10 18 Pa s) and high-viscosity mantle (\> •10 20 Pa s). It was

derived on the basis of the USGS GPS data which included the

early (first 3 months) postseismic epoch after the Landers earth-quake.

Deng et al. \[1998\] included both horizontal and vertical

component data and examined a model space consisting of vari-able

elastic plate thickness and lower crustal viscosity. In- 12 -support

of their viscoelastic model they invoked substantial

dip-slip coseismic offsets on the Emerson and Camp Rock

faults extending from the surface to •10 km depth. We can test

their viscoelastic model against the larger data set considered

here by prescribing a viscoelastic upper crust of the same thick-ness

and viscoelastic lower crust of the same thickness and

relaxation time • =• c ⁄µc 2 (the actual value of • c prescribed

for this test will differ from the corresponding value in their

model simulations because they assumed uniform elastic param-eters

with depth, in contrast to the layered model of Figure 4),

embedded between a purely elastic upper crust and upper man-tle.

We find that this model, regardless of whether the extra

dip-slip components are included or not, yields a serious misfit

to the entire southern portion of the observed InSAR image

(compare Plate 1a and Plate 4f; this misfit is obscured in the

first-order comparison with similar data presented in Figure 1 of

Deng et al. \[1998\]) and cannot explain the far-field horizontal

velocity patterns. This is reflected in the large • 2 of InSAR

data and far-field GPS data obtained at large • m1 and low • c

(Figure 5). The shortcomings of such a high-• m1 model have

their physical origins in the fact that (1) a thin low-viscosity

layer cannot transmit postseismic stresses efficiently into the far

field \[Cohen, 1992; Pollitz, 1997\] and (2) the vertical postse-ismic

deformation predicted with such a model is invariably

positively correlated with the coseismic uplift pattern, precisely

the opposite of what is observed (Plates 1a and 4b). The con-tribution

of the horizontal velocity field to the total range

change is similar for the low-• m1 and high-• m1 cases (Plates 4c

and 4d). (Large differences between the horizontal velocity vec-tors

for the two cases are, by chance, nearly perpendicular to

the range-change azimuth • ˆ, and crustal viscosity for the high-

m1 case was chosen to match the observed fault-parallel velo-cities.)

The difference between the low-• m1 model and the

high-• m1 model (Plates 4e and 4f) thus arises from the differ-ence

in the predicted vertical postseismic response. Given these

differences and the fact that either rapid afterslip or extremely

low crustal viscosities (\< •10 17 Pa s) have been deduced from

the early postseismic epoch \[Ivins, 1996; Yu et al., 1996; Shen

et al., 1994\], we believe that our analysis of the longer-term

postseismic relaxation pattern using more data constraints

clarifies the regional viscoelastic stratification.

4.5. GPS Uplift Data

We have examined whether available uplift data covering the

same 3-year period on the Emerson transect may help distin-guish

among different candidate viscoelastic models. The

observed uplift with respect to a fixed GOLD and correspond-ing

predictions for the Mojave Block model and the high • m1

model discussed above are shown in Figure 8. Savage and

Svarc \[1997\] suggest that the standard deviation has been

underestimated by a factor of 2. The large scatter in the data

does not reveal a clear pattern, and signal at the level of the

competing viscoelastic models cannot be resolved.

5\. Temperature

5.1. Mantle Temperature Inferred From Post-Landers

Geodetic Data- 13 -Our

estimate 8 ±4 •10 18 Pa s lies within the range of

dynamic viscosity 3 •10 18 Pa s to 3 •10 19 Pa s determined by

Zandt and Carrigan \[1993\] for the upper mantle under sections

of California where conditions for convective instability were

apparently satisfied between 5 and 25 Myr ago. One of the

competing interpretations of the eastern Mojave Desert mantle

discussed in section 5.2 invokes a relatively shallow astheno-sphere

beneath the region, so that its mechanical similarity with

regions of suspected small-scale convection within California

may be physically meaningful.

We obtain a first-order estimate of the mantle temperature

beneath the central Mojave Domain by considering the

Arrhenius relation which represents effective viscosity:

• eff = • . • \_ \_ = • n •1

A •1

\_ \_\_\_\_ exp

•

•

•RT

Q +PV \_ \_\_\_\_\_\_\_ •

•

•

. (12)

Here • and • . are the second invariant of the stress and strain

rate tensor, respectively, A is a constant, Q and V are the

activation energies for temperature and pressure, respectively, R

is the gas constant, and T is the absolute temperature. The

parameter n =1 for diffusion creep and n =3 for dislocation

creep. The value n •3.5 is thought to be appropriate for the

continental upper mantle \[Karato and Wu, 1993\]. The parame-

ters A , Q, and V all depend on the material, and • eff further

depends on • . Once these parameters are chosen, (12) provides

a direct relation between effective viscosity • eff and temperature

T . One property of this relation employed with n =3.5 is that

at a given temperature, effective viscosity decreases as •

increases; equivalently, for a given effective viscosity, tempera-

ture decreases as • increases. Two potential contributors to •

in the mantle are the value accumulated during the interseismic

interval and the addition of coseismic stress changes from the

Landers earthquake itself. The former could be potentially high

after the long interseismic period leading up to the Landers

event if crust-mantle coupling were assumed to be strong. It

cannot be estimated without knowledge of the rheological

behavior of the mantle itself, but a reasonable upper bound on

it is provided by the stress change at lower crustal depths pro-

duced by the Landers coseismic rupture. At a depth of 20 km,

• estimated over the region covered by our geodetic data varies

from 0.02 to 3 MPa and averages 0.8 MPa. At uppermost

mantle depths (\> •30 km depth), maximum coseismic • over

the region diminshes to 0.57 MPa and continues to diminish

rapidly with depth. Therefore a conservative estimate of • in

the subcrust of the central Mojave Domain during the Landers

postseismic epoch is 3 MPa. Since a lower bound on T will

depend primarily on the upper bound to • , we adopt this value

of • for use in (12).

From the viscosity value of 8.0 •10 18 Pa s beneath the cen-

tral Mojave Domain and • =3 MPa, we estimate an uppermost

mantle temperature of 1120°C. This temperature is based on

the parameters for wet dunite (Fo90) rheology given in Table 2

of Hirth and Kohlstedt \[1996\]. Wet dunite is practically the

weakest material that can be used as a proxy for the uppermost

mantle, so that temperatures estimated from (12) using its rheol-

ogy should be minimum estimates. We have neglected the pos-

sible effects of pyroxenes and garnet/spinel and iron depletion

due to partial melting. Hirth and Kohlstedt \[1996\] summarize

studies which suggest that aggregates composed of olivine and- 14
-orthopyroxene

(the most important secondary mineral) are, in

fact, slightly stronger than dunite at a given temperature. An

increase in the Mg/Fe ratio such as could be produced by the

extraction of basaltic melt would also increase the strength of

the material, Fo85 being about 15% stronger than Fo90 \[Hitch-ings

et al., 1989\]. Such an iron depletion, even if it could

result in a weaker material, would lead to a seismic velocity

increase \[Humphreys and Dueker, 1994\], contrary to the low

seismic velocities imaged in the central Mojave Domain (Figure

1b). Since Fo90 is nearly the pure forsterite end-member of the

olivine series, iron enrichment cannot play a significant role in

producing the low mantle viscosity. These arguments taken

together strongly suggest that the low-viscosity mantle inferred

in the central Mojave Domain has a thermal, rather than a
com-positional,

origin.

5.2. Additional Constraints on Sub-Mojave Upper Mantle

Temperature

The temperature estimate of 1120°C is between the wet and

dry basalt solidus and is generally consistent with high heat

flow \[Sass et al., 1994; Williams, 1996\], the occurrence of

Quaternary volcanism \[Wise, 1969\], and low seismic velocities

beneath the central/eastern Mojave Domains (Figure 1b). The

shallow mantle viscosity range delineated by the data (Figure 6)

yields a temperature of 1100 1140°C. The end-member models

discussed in section 4.2 suggest deeper mantle viscosity • m2 •

one-third of the shallow mantle viscosity • m1 , in which case the

deeper upper mantle would be sufficiently high temperature to

reach adiabatic conditions. This suggests that convection has

shaped the evolution of the sub-Mojave mantle, consistent with

the fact that the sub-Mojave mantle has evolved completely

from a subcontinental lithosphere to an oceanic mantle geo-chemical

composition from Miocene to Quaternary time

\[Musselwhite et al., 1989\]. This agrees with the fact that tem-poral

geochemical patterns in Miocene to Quaternary basalts in

the central Mojave Desert cannot be explained in terms of frac-tionation

of a closed system, but, rather, they reflect sampling

of a mantle component similar to that sampled by ocean island

basalts \[Glazner et al., 1991\].

The high uppermost mantle temperature agrees well with low

seismic velocity at shallow upper mantle depth (30 to 200+ km

depth) in the central Mojave Domain (that is, east of about

117°W) based on the detailed seismic velocity profile of Hum-phreys

and Dueker \[1994, Figure 10i\]. The mantle portion of

this profile is depicted in Figure 1b. This low-velocity pattern

also appears in recent tomographic images obtained in the Los

Angeles Region Seismic Experiment \[Kohler, 1999, Figure 5\].

Our temperature estimate strongly suggests that the low-velocity

region is of thermal rather than compositional origin. The

-2.5% velocity differences exhibited here would correspond to a

•200°C elevation in temperature relative to typical southern

California upper mantle. This high temperature is, however, at

odds with two independent observations. Saltus and Thompson

\[1995\] showed that the elevation difference between the north-ern

and southern Basin and Range can be explained by differ-ences

in mantle bouyancy between the two regions, implying a

relatively cool uppermost mantle (800°C at 40 km depth).

This view is consistent with the crustal geotherm derived by- 15
-Williams

\[1996\] on the basis of heat flow measurements \[Sass

et al., 1994\] and estimation of radiogenic heat production,

which points to a similarly low mantle temperature.

Isotopic compositions from late Cenozoic alkali basalts in the

Cima volcanic field in the east central Mojave Desert display a

strong affinity with Pacific MORB and late Cenozoic basalts of

the California Coast Ranges \[Farmer et al., 1995\]. From these

similarities, Farmer et al. \[1995\] suggest that an upwelling

MORB asthenosphere has been present beneath this part of the

Mojave Desert for at least the past 8 Myr. Indeed, both the

Mojave Desert and Coast Ranges lie at the margin of the

Pacific-North America plate boundary which has undergone a

transition from a convergent to strike-slip regime during the

Neogene \[Atwater and Stock, 1998\]. Northward migration of

the Mendocino triple junction is postulated to have resulted in a

\"slab window\" developing in its wake \[Dickinson and Snyder,

1979; Lachenbruch and Sass, 1980\]. The existence of a local-ized

upwelling, rather than a broad thermal disturbance such as

would be produced by an upwelling mantle plume, may help

reconcile the competing interpretations. An upwelling MORB

asthenosphere beneath both the east central Mojave Desert and

the Coast Ranges is consistent with their similarities in

present-day heat flow \[Lachenbruch and Sass, 1980; Sass et al.,

1994\]. Owing to its localized nature, the uplift generated by

this upwelling is likely less than that generated by a broad ther-mal

disturbance, so it may not conflict with the •500 m eleva-tion

difference between the northern Basin and Range and the

east central Mojave Desert. More work is clearly needed to

quantitatively verify the conceptual model proposed by Farmer

et al. \[1995\]. It appears to be the most promising explanation

for the low mantle seismic velocities (Figure 1b), low viscosity

(Figure 6), and the additional geodynamic and geochemical

constraints discussed above.

5.3. Nature of Possible Thermal Boundary Layer

A possible temperature structure based on the crustal geoth-erm

of Williams \[1996\] and the mantle temperatures inferred

here is depicted in Figure 9. This structure is intended as a

guide for understanding the many types of geophysical con-straints

which bear on the state of the sub-Mojave crust and

mantle. Since these constraints each carry considerable uncer-tainties,

the structure depicted may be most useful for qualita-tively

outlining the different temperature domains which exist at

various depths.

The suggestion that upwelling asthenosphere exists •50 70

km depth beneath the east central Mojave Desert raises the pos-sibility

of small-scale convection beneath the region. This idea

has been explored in the southern Sierra Nevada \[Liu and Shen,

1998\], the Transverse Ranges \[Humphreys and Hager, 1990;

Jones et al., 1996\], and elsewhere in California \[Zandt and

Carrigan, 1993\]. Our preferred upper mantle temperature

structure deduced from the Mojave Block model implies an

upper layer from 30 to 50 km depth of \"average\" temperature

1120°C underlain by a slightly hotter mantle, though the data

considered here cannot resolve the precise nature of the viscos-ity

decrease/temperature increase with depth. If the temperature

at the base of the crust is indeed only about 600-700°C \[Willi-ams,

1996\], then our model can be interpreted in terms of a

thermal boundary layer of uncertain thickness (30 km) - 16
-accommodating

a 500-600°C vertical temperature difference.

The top few kilometers of the boundary layer may have tem-perature

below 975°C (Figure 9), and there the material may be

quasi-rigid, but below that depth the material behaves viscously

with a low average viscosity. The value •5 •10 18 Pa s would

represent an effective average viscosity over the boundary layer.

This picture is similar to that described by Zandt and Carri-gan

\[1993\] for the uppermost mantle which has flowed as

upwelling asthenosphere and interacted with the cooler litho-sphere,

forming a thin thermal boundary layer at that contact.

This model has, in turn, been adapted from consideration of

Rayleigh instability beneath older oceanic lithosphere \[Parsons

and McKenzie, 1978\]. Depending on the Rayleigh number of

the mantle flow region, which will depend primarily on the

viscosity of the mantle and the temperature difference between

the asthenosphere and the cooler lithosphere, this volume of

mantle will develop a mature thermal boundary layer, and

small-scale convection may be encouraged. If the east central

Mojave Desert has reached the conditions for small-scale con-vection,

then we should expect to find a corresponding

\"downwelling\" region. The only candidate downwelling in the

region is the high seismic velocity feature beneath the

Transverse Ranges imaged by Humphreys and Hager \[1990\]

and Kohler \[1999\]. Although they have attributed this feature

to convective downwelling of the lithosphere produced by con-vergence,

we suggest that it may be part of a convective system

driven by an upwelling asthenosphere beneath the east central

Mojave Desert. Alternatively, the viscosity and temperature

structure beneath the east central Mojave Desert may be close

to, but not satisfy, the conditions for Rayleigh instability.

The presence of a thermal boundary layer within the upper-most

mantle is consistent with average lower crust viscosity

being about a factor of 2 higher than average uppermost mantle

viscosity in our preferred model. Flow parameters for several

possible materials which may comprise the lower crust are sum-marized

in Table 3 of Freed and Lin \[1998\]. These parameters

lead to a large range of possible mechanical behavior of lower

crustal materials depending on several factors, particularly water

content. Two representive scales of crustal viscosity as a func-tion

of temperature are included in Figure 9 using wet and dry

Westerly granite. Figure 14 of Freed and Lin \[1998\] shows

that most other crustal materials are intermediate between these

two. Lower crustal temperatures prescribed by the Williams

\[1996\] geotherm appear adequate to explain the lower crustal

viscosity of 1.6 •10 19 Pa s obtained in the Mojave Block

model with • c ⁄• m1 =2, provided that a hydrous crustal rheol-ogy

is chosen. Without a strong thermal boundary layer the

estimated viscosity of the lower crust could be obtained with a

dry rheology and higher temperatures •900°C, but this would

compromise the geotherm of Williams \[1996\]. There are many

factors which should be considered in such an evaluation, such

as uncertainty related to the extrapolation of surface heat flow

to depth, the assumption of dislocation creep, the appropriate

differential stress, the extrapolation of laboratory data to low

geologic strain rates, and the effects of grain size, melt fraction,

and interconnectedness of the weakest consituent of a biviscous

lower crust \[Ivins and Sammis, 1996\]. The relative importance

of these factors may be better established with more detailed

examination of the early and late post-Landers deformation- 17 -process.

6\. Geologic Implications

On the basis of the likely thermal origin of the low viscosity

and seismic velocity of the uppermost mantle beneath the cen-tral

Mojave Domain, we suggest that the existence, location,

and width of the ECSZ are genetically related to the weakness

of the upper mantle beneath it. We arrive at this proposition by

considering the variations in mantle strength across the region

together with the distribution of crustal faulting. Figure 1b

shows that the mantle beneath the east central Mojave Domain

possesses low velocity, whereas that beneath the western

Mojave Domain possesses very high velocity. The viscosity

structure derived in this paper together with the geochemical

evidence strongly suggests a thermal origin for the low seismic

velocity region. It is likely that the high seismic velocities

beneath the western Mojave Domain, particularly the

southwestern portion, can be attributed to a correspondingly low

mantle temperature. They have been interpreted as a convec-tive

downwelling of subcrustal lithosphere beneath the

Transverse Ranges \[Humphreys and Hager, 1990; Kohler,

1999\]. From the relation between strength and temperature

(equation (12)) it follows that mechanically weak and strong

mantle must be present beneath the east central and western

Mojave Domains, respectively. If we extrapolate current

mechanical behavior to the time when late Cenozoic heating

began affecting the region (26-18 Ma) \[Dokka, 1986\], then

since this heat input the mantle beneath the east central Mojave

Domain has been thermally weakened and caught in a newly

formed dextral shear zone (the San Andreas fault system)

bounded to the west by the stronger western Mojave Domain.

It appears that these attributes of the Mojave Desert region are

fundamentally responsible for (1) the pervasive dextral faulting

and block rotation which have shaped the east central Mojave

Domain region since middle to late Miocene time \[Dokka and

Travis, 1990\] and continue to the present day \[Sauber et al.,

1994\] and (2) the almost total absence of active faults beneath

the western Mojave Domain \[Unruh et al., 1994\].

Our results thus lend credibility to the idea proposed by

Kusznir \[1982\] that much of the western United States consists

of a thin horizontal stress guide; that is, it has been sufficiently

thermally weakened that the upper lithosphere is effectively thin

and subject to large amplications of externally applied stresses,

making it a locus of large scale faulting. The ECSZ represents

the natural boundary between the southern Great Basin, which

possesses a weak uppermost mantle and the western Mojave

Domain/San Gabriel Block, which possesses a strong uppermost

mantle.

This association between the distribution of active surface

faults and the strength of the mantle may be applicable to other

regions as well. For example, the northern Coast Ranges, Cali-fornia,

are underlain by warm uppermost mantle material \[e.g.,

Benz et al., 1992\] and contain a denser network of faults than

the surrounding California lithosphere. The continuation of the

ECSZ farther north of the Garlock fault may be related to the

presence of warm, buoyant material beneath the southern Sierra

Nevada that continues eastward into the southern Great Basin

\[e.g., Wernicke et al., 1996; Pollitz, 1999\], in contrast to the- 18
-unfaulted

nature of most of the Sierra Nevada block which is

underlain by relatively high-velocity (and presumably low tem-perature)

material at uppermost mantle depths \[Benz et al.,

1992; Humphreys and Dueker, 1994; Pollitz, 1999\].

7\. Conclusions

We have analyzed a combination of GPS and InSAR data

collected during the 3.5 years following the 1992 Landers earth-quake

in the central Mojave Domain. The GPS data set covers

near-, intermediate-, and far-field distances away from the

Landers rupture zones and provides a discrete (but nevertheless

fairly dense) sample of the horizontal postseismic velocity field.

The InSAR data set covers near- and intermediate-field dis-tances

and adds essentially spatially continous coverage of the

vertical postseismic velocity field. The interseismic velocity

field is dwarfed by the observed postseismic velocity field, so

that the observed velocity field must be the product of

processes which are unique to the Landers postseismic epoch.

The combination of GPS and InSAR that we have considered

allows us to discriminate, first, among competing postseismic

processes, particularly afterslip versus deep viscoelastic relaxa-tion

driven by the coseismic stress changes; and second, to

discriminate among possible models of deep viscoelastic relaxa-tion.

Once we establish the importance of deep viscoelastic relaxa-tion,

our study examines essentially a two-dimensional model

space consisting of crust and mantle viscosity. We find that the

shallow mantle viscosity beneath the central Mojave Domain is

low (8 ±4 •10 18 Pa s) in agreement with independent infer-ences

of a warm regional uppermost mantle. The deeper (\>50

km) upper mantle viscosity is estimated at 2.7 •10 18 Pa s in

our preferred model. Although the inferences we can draw

about the deeper viscosity are limited, the end-member models

discussed in section 4.1 suggest that the broadest range of

deeper upper mantle viscosity consistent with the geodetic data

is about 1 6 •10 18 Pa s. This is in the range expected for

young oceanic mantle below the dehydration boundary \[Hirth

and Kohlstedt, 1996\], in agreement with the inference of an

asthenosphere no deeper than 50 70 km based on isotopic com-positions

of late Cenozoic alkali basalts \[Livaccari and Perry,

1993\]. This is further consistent with the interpretation of a

slab window having developed beneath this part of the Mojave

Desert following the transition from a convergent to a strike-slip

plate boundary during the Neogene \[Farmer et al., 1995\].

Slow seismic velocities beneath the eastern Mojave Domain

are likely thermally induced. If seismic velocity variations

between the western and eastern Mojave Domain are also attri-buted

to temperature, then this implies correspondingly large

variations in uppermost mantle strength. In that case, there is a

strong correlation between uppermost mantle strength and the

distribution of surface faults within the Mojave Block, the east

central Mojave Domain being permeated with numerous faults

that form the ECSZ and the western Mojave Domain being

nearly devoid of faults.

Our inference that mantle relaxation explains most of the

long-wavelength post-Landers transient velocity field carries

additional implications. First, at similar temperature, crustal

materials should be weaker than mantle materials. Although a- 19
-composite

crustal rheology with polymineralic rock types is

complicated to assess, a weaker mantle may imply a strong

thermal boundary layer within the shallow mantle. Heat flow

data around the Landers rupture zone imply a lower crustal

temperature no greater than •700°C, which is consistent with

available geodetic estimates of lower crustal viscosity for most

wet rheologies. A dry lower crust combined with a much

weaker temperature gradient in the uppermost mantle could

explain available crust and mantle viscosity estimates only if

lower crustal temperature were far greater than heat flow data

suggest. Clarification of the state of the lower crust must await

more a detailed integrated study of the early and late postse-ismic

epochs, with focus on the mechanical behavior of a

biviscous lower crust. Second, a weak mantle encourages

small-scale convection, which may have a substantial effect on

crustal stresses. This idea has been previously explored

throughout California (e.g., southern Sierra Nevada, northern

Coast Ranges, Transverse Ranges, the Southern Great Valley

seismic \"anomaly\"), and it may also play a role in localization

of faulting in this part of the ECSZ.

Acknowledgments. This work was supported by the

Cooperative UC/Los Alamos Research program and the IGPP

program of Lawrence Livermore National Laboratory. We

thank Yehuda Bock, Jishu Deng, Liz Hearn, Barry Parsons, and

Jim Savage for helpful discussions. We thank Zheng-Kang

Shen and Jerry Svarc for helping us acquire the SCEC and

USGS GPS data, respectively; Evelyn Price for scrutinizing a

preliminary draft; and Jean Chery, Ruth Harris, and Liz Hearn

for their incisive reviews.

References

Abramowitz, M., and I.A. Stegun, Pocketbook of Mathematical

Functions With Formulas, Graphs, and Mathematical Tables,

468 pp., Natl. Inst. of Stand. and Technol., Gaithersburg,

Md., 1984.

Atwater, T., and J. Stock, Pacific-North America plate tectonics

of the Neogene southwestern United States: An update, Int.

Geol. Rev., 40, 375-402, 1998.

Basaltic Volcanism Study Project, Experimental petrology of

basalts and their source rocks, in Basaltic Volcanism in the

Terrestrial Planets, pp. 493-630, Pergamon, Tarrytown, N.Y.,

1981\.

Behr, J., R. Bilham, P. Bodin, and S. Gross, Eureka Peak Fault

afterslip following the 28 June 1992 Landers earthquake,

Bull. Seismol. Soc. Am., 84, 826-834, 1994.

Benz, H.M., G. Zandt, and D.H. Oppenheimer, Lithospheric

structure of northern California from teleseismic images of

the upper mantle, J. Geophys. Res., 97, 4791-4807, 1992.

Bott, N.H.P., and D.S. Dean, Stress diffusion from plate boun-daries,

Nature, 243, 339-341, 1973.

Brace, W.F. and D.L. Kohlstedt, Limits of lithospheric stress

imposed by laboratory experiments, J. Geophys. Res., 85,

6348-6252, 1980.

Brocher, T.M., J. McCarthy, P.E. Hart, W.S. Holbrook, K.P.

Furlong, T.V. McEvilly, J.A. Hole, and S.L. Klemperer,

Seismic evidence for a lower-crustal detachment beneath San

Francisco Bay, California, Science, 265, 1436-1439, 1994.

Buck, W.R., Modes of continental lithospheric extension, J.

Geophys. Res., 96, 20,161-20,178, 1991.

Chen, W.-P., and P. Molnar, Focal depths of intracontinental

and intraplate earthquakes and their implications for the- 20 -thermal

and mechanical properties of the lithosphere, J. Geo-phys.

Res., 88, 4183-4214, 1983.

Chery, J., J. P. Vilotte, and M. Daignieres, Thermomechanical

evolution of a thinned continental lithosphere under compres-sion;

implications for the Pyrenees, J. Geophys. Res., 96,

4385-4412, 1991.

Cohen, S.C., A multilayer model of time dependent deformation

following an earthquake on a strike slip fault, J. Geophys.

Res., 87, 5409-5421, 1982.

Cohen, S.C., Postseismic deformation and stress diffusion due

to viscoelasticity and comments on the modified Elsasser

model, J. Geophys. Res., 97, 15,395-15,403, 1992.

Deng, J., M. Gurnis, H. Kanamori, and E. Hauksson, Viscoelas-tic

flow in the lower crust after the 1992 Landers, California,

earthquake, Science, 282, 1689-1692, 1998.

Dickinson, W.R., and W.S. Snyder, Geometry of subducted

slabs related to San Andreas transform, J. Geol., 87, 609-627,

1979\.

Dokka, R.K., Patterns and modes of early Miocene crustal

extension, central Mojave Desert, California, Spec. Pap.

Geol. Soc. Am., 208, 75-95, 1986.

Dokka, R.K., and C.J. Travis, Late Cenozoic strike-slip faulting

in the Mojave Desert, California, Tectonics, 9, 311-340,

1990\.

Donnellan, A., and G.A. Lyzenga, GPS observations of fault

afterslip and upper crustal deformation following the

Northridge earthquake, J. Geophys. Res., 103, 21285-21297,

1998\.

European Space Agency, ERS-1 System, 87 pp., ESA Publ.

Div., Eur. Space Res. and Technol. Cent., Noordwijk, Neth-erlands,

1992\.

Farmer, G.L., A.F. Glazner, H.G. Wilshire, J.L. Wooden, and

W.J. Pickthorn, Origin of late Cenozoic basalts at the Cima

volcanic field, Mojave Desert, California, J. Geophys. Res.,

100, 8399-8415, 1995.

Feigl, K.L., et al., Space geodetic measurement of crustal defor-mation

in central and southern California, 1984-1992, J. Geo-phys.

Res., 98, 21,677-21,712, 1993.

Freed, A.M., and J. Lin, Time-dependent changes in failure

stress following thrust earthquakes, J. Geophys. Res., 103,

24,393-24,409, 1998.

Furlong, K.P., W.D. Hugo, and G. Zandt, Geometry and evolu-tion

of the San Andreas fault in northern California, J. Geo-phys.

Res., 94, 3100-3110, 1989.

Glazner, A.F., G.L. Farmer, W.T. Hughes, J.L. Wooden, and

W. Pickthorn, Contamination of basaltic magma by mafic

crust at Amboy and Pisgah craters, Mojave Desert, Califor-nia,

J. Geophys. Res., 96, 13,673-13,691, 1991.

Hacker, B.R., A. Yin, J. M. Christie, and G. A. Davis, Stress

magnitude, strain rate and rheology of extended middle con-tinental

crust inferred from quartz grain sizes in the Whipple

Mountains, California, Tectonics, 11, 36-46, 1992.

Hart, E.W., W.A. Bryant, and J.A. Treiman, Surface faulting

associated with the June 1992 Landers earthquake, California,

Geology, 46, 10-16, 1993.

Hauksson, E., L.M. Jones, K. Hutton, and D. Eberhart-Phillips,

The 1992 Landers earthquake sequence: Seismological obser-vations,

J. Geophys. Res., 98, 19,835-19,858, 1993.

Hirth, G., and D.L. Kohlstedt, Water in the oceanic upper man-tle:

Implications for rheology, melt extraction and the evolu-tion

of the lithosphere, Earth Planet. Sci. Lett., 144, 93-108,

1996\.

Hitchings, R.S., M.S. Paterson, and J. Bitmead, Effects of iron

and magnetite additions in olivine-pyroxene rheology, Phys.

Earth Planet. Inter., 55, 277-291, 1989. - 21 -Humphreys,

E.D., and K.G. Dueker, Western U.S. upper mantle

structure, J. Geophys. Res., 99, 9615-9634, 1994.

Humphreys, E.D., and B.H. Hager, A kinematic model for the

late Cenozoic development of southern California crust and

upper mantle, J. Geophys. Res., 95, 19,747-19,762, 1990.

Ivins, E.R., Transient creep of a composite lower crust, 2, A

polymineralic basis for rapidly evolving postseismic deforma-tion

modes, J. Geophys. Res., 101, 28,005-28,028, 1996.

Ivins, E.R., and C.G. Sammis, Transient creep of a composite

lower crust, 1, Constitutive theory, J. Geophys. Res., 101,

27,981-28,004, 1996.

Jones, C.H., J.R. Unruh, and L.J. Sonder, The role of gravita-tional

potential energy in active deformation in the

southwestern United States, Nature, 381, 37-41, 1996.

Jones, L.E., and D.V. Helmberger, Source parameters of the

1992 Big Bear sequence, Eos Trans. AGU, 74(16), Spring

Meet. Suppl., 215, 1993.

Karato, S.-I., and P. Wu, Rheology of the upper mantle: A syn-thesis,

Science, 260, 771-778, 1993.

Karato, S.-I., D. C. Rubie, and H. Yan, Dislocation recovery in

olivine under deep upper mantle conditions; implications for

creep and diffusion, J. Geophys. Res., 98, 9761-9768, 1993.

Kay, R. W., and S. M. Kay, The nature of the lower continen-tal

crust: Inferences from geophysics, surface geology, and

crustal xenoliths, Rev. Geophys., 19, 271-297, 1981.

Kohler, M.D., Lithospheric deformation beneath the San

Gabriel Mountains in the southern California Transverse

Ranges, J. Geophys. Res., 104, 15,025-15,041, 1999.

Kusznir, N.J., Lithosphere response to externally and internally

derived stresses: A viscoelastic stress guide with

amplification, Geophys. J. R. Astron. Soc., 70, 399-414,

1982\.

Kusznir, N.J., The distribution of stress with depth in the
litho-sphere;

thermorheological and geodynamic constraints, Phi-los.

Trans. R. Soc. London, Ser. A, 337, 95-110, 1991.

Lachenbruch, A.H., and J.H. Sass, Heat flow and energetics of

the San Andreas fault zone, J. Geophys. Res., 85, 6185-6222,

1980\.

Lithgow-Bertelloni, C., and P.G. Silver, Dynamic topography,

plate driving forces and the African superswell, Nature, 395,

269-272, 1998.

Liu, M., and Y. Shen, Sierra Nevada uplift: A ductile flank to

mantle upwelling under the Basin and Range province, Geol-ogy,

26, 299-302, 1998.

Livaccari, R.F., and F.V. Perry, Isotopic evidence for preserva-tion

of Cordilleran lithospheric mantle during the Sevier-Laramide

orogeny, western United States, Geology, 21, 719-

722, 1993.

Massonnet, D., K. Feigl, M. Rossi, and F. Adragna, Radar

interferometric mapping of deformation in the year after the

Landers earthquake, Nature, 369, 227-230, 1994.

Massonnet, D., W. Thatcher, and H. Vadon, Detection of post-seismic

fault-zone collapse following the Landers earthquake,

Nature, 382, 612-616, 1996.

Miyashita, K., A model of plate convergence in southwest

Japan, inferred from leveling data associated with the 1946

Nankaido earthquake, J. Phys. Earth, 35, 449-467, 1987.

Molnar, P., and P. Tapponier, A possible dependence of tec-tonic

strength on the age of the crust in Asia, Earth Planet.

Sci. Lett., 52, 107-114, 1981.

Musselwhite, D. S., D. J. DePaolo, and M. McCurry, The evo-lution

of a silicic magma system: Isotopic and chemical evi-dence

from the Woods Mountains Volcanic Center, eastern

California, Contrib. Mineral. Petrol., 101, 19-29, 1989.

Nur, A., and G. Mavko, Postseismic viscoelastic rebound, - 22 -Science,

183, 204-206, 1974.

Okada, Y., Surface deformation due to shear and tensile faults

in a half-space, Bull. Seismol. Soc. Am., 75, 1135-1154,

1985\.

Parsons, B., and D.P. McKenzie, Mantle convection and the

thermal structure of the plates, J. Geophys. Res., 83, 4485-

4496, 1978.

Peltzer, G., P. Rosen, F. Rogez, and K. Hudnut, Postseismic

rebound in fault step-overs caused by pore fluid flow, Sci-ence,

273, 1202-1204, 1996.

Peltzer, G., P. Rosen, F. Rogez, and K. Hudnut, Poro-elastic

rebound along the Landers 1992 earthquake surface rupture,

J. Geophys. Res., 103, 30,131-30,145, 1998.

Pollitz, F.F., Gravitational-viscoelastic postseismic relaxation on

a layered spherical Earth, J. Geophys., Res., 102, 17,921-

17,941, 1997.

Pollitz, F.F., Regional velocity structure in northern California

from inversion of scattered seismic surface waves, J. Geo-phys.

Res., 104, 15,043-15,072, 1999.

Pollitz, F.F., and I.S. Sacks, Modeling of postseismic relaxation

following the Great 1857 earthquake, southern California,

Bull. Seismol. Soc. Am., 82, 454-480, 1992.

Pollitz, F.F., and I.S. Sacks, Fault model of the 1891 Nobi

earthquake from historic triangulation and levelling, J. Phys.

Earth, 42, 1-43, 1994.

Pollitz, F.F. and I.S. Sacks, Viscosity structure beneath

northeast Iceland, J. Geophys. Res., 101, 17,771-17,793,

1996\.

Pollitz, F.F., R. Bu .. rgmann, and P. Segall, Joint estimation of

afterslip rate and postseismic relaxation following the 1989

Loma Prieta earthquake, J. Geophys. Res., 103, 26,975-

26,992, 1998.

Qu, J., T.L. Teng, and J. Wang, Modeling of short-period

surface-wave propagation in southern California, Bull.

Seismol. Soc. Am., 84, 596-612, 1994.

Rydelek, P.A., and I.S. Sacks, Asthenospheric viscosity and

stress diffusion: A mechanism to explain correlated earth-quakes

and surface deformations in northeast Japan, Geophys.

J. Int., 100, 39-58, 1990.

Saltus, R.W., and G.A. Thompson, Why is it downhill from

Tonopah to Las Vegas? A case for mantle support of the

high northern Basin and Range, Tectonics, 14, 1235-1244,

1995\.

Sass, J.H., et al., Thermal regime of the southern Basin and

Range province, 1, Heat flow data from Arizona and the

Mojave Desert of California and Nevada, J. Geophys. Res.,

99, 22,093-22,119, 1994.

Sauber, J., W. Thatcher, S.C. Solomon, and M. Lisowski, Geo-detic

slip rate for the Eastern California Shear Zone and the

recurrence time of Mojave Desert earthquakes, Nature, 367,

264-266, 1994.

Savage, J.C., Equivalent strike-slip earthquake cycles in half-space

and lithosphere-asthenosphere Earth models, J. Geo-phys.

Res., 95, 4873-4879, 1990.

Savage, J.C., and J.L. Svarc, Postseismic deformation associ-ated

with the 1992 Mw =7.3 Landers earthquake, southern

California, J. Geophys. Res., 102, 7565-7577, 1997.

Shen, Z.-K., et al., Postseismic deformation following the

Landers earthquake, California, 28 June 1992, Bull. Seismol.

Soc. Am., 84, 780-791, 1994.

Sibson, R.H., Fault zone models, heat flow, and the depth dis-tribution

of earthquakes in the continental crust of the United

States, Bull. Seismol. Soc. Am., 72, 151-163, 1982.

Sieh, K., et al., Near-field investigations of the Landers earth-quake

sequence, April to July 1992, Science, 260, 171-176, - 23 -1993.

Stewart, J.H., Basin-range structure in western North America:

A review, Mem. Geol. Soc. Am., 152, 1-31, 1978.

Tabei, T., Crustal movements in the inner zone of southwest

Japan associated with stress relaxation after major earth-quakes,

J. Phys. Earth, 37, 101-131, 1989.

Thatcher, W., T. Matsuda, T. Kato, and J.B. Rundle, Lithos-pheric

loading by the 1896 Riku u earthquake, northern

Japan: Implications for plate flexure and asthenospheric

rheology, J. Geophys. Res., 85, 6429-6435, 1980.

Unruh, J., W. R. Lettis, and J. M. Sowers, Kinematic interpreta-tion

of the 1992 Landers earthquake, Bull. Seismol. Soc. Am.,

84, 537-546, 1994.

Wald, D.J., and T. H. Heaton, Spatial and temporal distribution

of slip for the 1992 Landers, California, earthquake, Bull.

Seismol. Soc. Am., 84, 668-691, 1994.

Wdowinski, S., and Y. Bock, The evolution of deformation and

topography of high elevated plateaus, 2, Application to the

central Andes, J. Geophys. Res., 99, 7121-7130, 1994.

Wdowinski, S., Y. Bock, J. Zhang, P. Fang, and J. Genrich,

Southern California Permanent GPS Geodetic Array: Spatial

filtering of daily position for estimating coseismic and postse-ismic

displacement induced by the 1992 Landers earthquake,

J. Geophys. Res., 102, 18,057-18,070, 1997.

Wernicke, B., et al., Origin of high mountains on continents:

The southern Sierra Nevada, Science, 271, 190-193, 1996.

Williams, C.F., Temperature and the seismic/aseismic transition:

Observations from the 1992 Landers earthquake, Geophys.

Res. Lett., 23, 2029-2032, 1996.

Wise, W., Origin of basaltic magmas in the Mojave Desert

area, California, Contrib. Mineral. Petrol., 23, 53-64, 1969.

Yu, T.-T., J.B. Rundle, and J. Fernandez, Surface deformation

due to a strike-slip fault in an elastic gravitational layer over-lying

a viscoelastic gravitational half-space, J. Geophys. Res.,

101, 3199-3214, 1996. (Correction to \"Surface deformation

due to a strike-slip fault in an elastic gravitational layer over-lying

a viscoelastic gravitational half-space\", J. Geophys.

Res., 104, 15,313-15,315, 1999.)

Zandt, G., and C.R. Carrigan, Convective instability and upper

mantle viscosity under California, Science, 261, 460-463,

1993\.

Zeyen, H., et al., Styles of continental rifting: Crust-mantle

detachment and mantle plumes, Tectonophysics, 278, 329-

352, 1997.

\_\_\_\_\_\_\_\_\_\_\_

R Bu .. rgmann, Department of Geology and Geophysics, University of

California, Berkeley, CA 94720.

G. Peltzer, Jet Propulsion Laboratory, MS 183-501, 4800 Oak Drive,

Pasadena, CA 91109

F. F. Pollitz, Department of Geology, 1 Shields Ave. University of

California, Davis, CA 95616. (pollitz@geology.ucdavis.edu)

(Received May 13, 1999; revised September 27, 1999;

accepted October 21, 1999.)

Copyright 2000 by the American Geophysical Union.

Paper number 1999JB900380

0148-0227/00/1999JB900380\$09.00

POLLITZ ET AL.: POST-LANDERS MANTLE RELAXATION

POLLITZ ET AL.: POST-LANDERS MANTLE RELAXATION- 25 -Figure

1\. (a) Active faults around the Mojave Desert region.

Boxed region indicates the area covered in Figure 2 and Plates

1a, 1b, 2, 3a, 3c, and 4. (b) P-wave velocity anomalies in per-cent

of background velocity \[Humphreys and Dueker, 1994,

Figure 10i\] across the profile indicated in Figure 1a. The low

seismic velocity pattern underlying this portion of the central

Mojave Domain at uppermost mantle depths continues

northwestward to include essentially all of the central Mojave

Domain \[e.g., Humphreys and Dueker, 1994, Figure 9\].

Figure 2. Map of the June 28, 1992, Landers earthquake area.

Solid lines are the June 28, 1992, surface rupture \[Sieh et al.,

1993\]. Shade depicts topography from U.S. Geological Survey

(USGS) digital elevation model. White dots are aftershocks

between August 7, 1992, and January 23, 1996 \[Hauksson et

al., 1993\]. After Peltzer et al. \[1998\].

Figure 3. (a) Bold lines are the surface projection of buried

fault planes used by Feigl et al. \[1993\] and Savage and Svarc

\[1997\] to represent interseismic strain accumulation in southern

California. Dashed lines represent active faults in California.

\(b\) Interseismic velocity field evaluated at 26 GPS sites used in

this study relative to a fixed Goldstone.

Figure 4. Viscoelastic stratification used to model postseismic

deformation in the Landers epicentral area. A purely elastic

upper crust (base at 16 km depth) is underlain by a standard

linear solid lower crust \[Cohen, 1982\] (base at 30 km depth)

and Maxwell viscoelastic fluid upper mantle. Parameters • , µ,

and • are the bulk modulus, shear modulus, and viscosity,

respectively, and µ•is the long-term strength of the lower crust

(•=0 would correspond to a Maxwell viscoelastic fluid).

Elastic stratification is prescribed by values • c 1 =74 GPa,

µc 1 =41 GPa, • c 2 =95 GPa, µc 2 =53 GPa, and • m =150

GPa, µm =70 GPa. An additional elastic layer from 0 to 4 km

depth (not shown) is prescribed with • =65 GPa and µ=36

GPa. This stratification is essentially (with fewer discontinui-ties)

equivalent to the seismic structure for the eastern Mojave

Desert given in Table 1 of Qu et al. \[1994\]. Parameters • c ,

• m1 , • m2 , and µ•are variable.

Figure 5. (left) Misfit with respect to several data subsets in

• m1 •• c ⁄• m1 space for µ•=12 GPa and • m1 ⁄• m2 =3.

(right) Corresponding misfit pattern for the case µ•=0

(Maxwell viscoelastic fluid lower crust). Dashed lines indicate

lowest two contours associated with each subset. The Mojave

Block model is indicated by the solid circles in Figure 5 (left).

Figure 6. ΩF (defined in section 3.2) at probability levels

P =0.95 and P =0.99 through the model slices µ•=12 GPa

and µ•=0, for • m1 ⁄• m2 =3.

Figure 7a. Misfit with respect to several data subsets in

• m1 •• c ⁄• m1 space for µ•=12 GPa and • m1 ⁄• m2 =1. The

best isoviscous mantle model is indicated by the solid circles.

Figure 7b. ΩF (defined in section 3.2) at probability levels

P =0.95 and P =0.99 through the model slice µ•=12 GPa,

for the isoviscous mantle model. - 26 -Figure

8\. Observed uplift with respect to GOLD and

corresponding calculated uplift on the Mojave Block model and

the high • m1 model discussed in the text at the 10 GPS sites

on the Emerson transect (Plates 4a and 4b). Error bars denote

±standard deviation in measurement.

Figure 9. Possible temperature structure beneath the east central

Mojave Desert based on the crustal geotherm of Williams

\[1996\], the mantle temperature structure implied by the Mojave

Block model (section 5.1), and geochemical evidence for a

shallow asthenosphere. Two crustal geotherms of Williams

\[1996\] correspond to the range of heat flow values observed in

the Landers region. A thermal boundary layer between 30 and

60 km depth is envisioned to accommodate a 500-600°C verti-cal

temperature difference at the top of the mantle. The thin

subcrustal domain at temperature below 975°C may exhibit

quasi-rigid behavior, but the upper 30 km of the mantle as a

whole has an average temperature consistent with a viscosity of

•5 •10 18 Pa s. An adiabatic temperature gradient of 0.5°C/km

is assumed for the temperature in the asthenosphere below 60

km. Ranges of sub-Mojave mantle viscosity from depth 30-50

km (m1 ) and \>50 km (m2 ) determined in this study are indi-cated.

The dry and wet peridotite solidus are from Basaltic

Volcanism Study Project \[1981\]. Viscosity of the mantle and

crust as a function of temperature are indicated by the upper

tick lines. They are calculated from equation (12) with flow

parameters of wet dunite \[Hirth and Kohnstedt, 1996\], and wet

and dry Westerly granite \[Freed and Lin, 1998, Table 3\],

respectively, assuming 3 MPa differential stress. The pressure

dependence is included only for the mantle viscosity calcula-tion.

Plate 1. (a) Observed range change from September 1992 to

January 1996 \[Peltzer et al., 1998\]. (b) Calculated range change

(equation (4)) on Mojave Block model (see section 3.2). (c)

Observed average horizontal velocity with respect to fixed

Goldstone from November 1992 to December 1995 and

corresponding 1 error ellipses \[Savage and Svarc, 1997;

Southern California Earthquake Center (SCEC) Release 2,

1998, available at http://www.scecdc.scec.org/group e/

release.v2\]. Calculated horizontal velocity vectors (equation (3))

on Mojave Block model are shown as black arrows. The seven

SCEC GPS sites lying outside of the boxed region are referred

to as \"far field\"; all remaining GPS sites are considered \"near

field\" (Table 1).

Plate 2. Surface displacement predicted by (a) Savage and

Svarc \[1997\] afterslip model, (b) poroelastic model, and (c) the

combination of Plates 2a and 2b. One color cycle represents

5.6 cm of surface displacement towards the radar. Black

arrows depict horizontal displacement vectors. White lines

show fault geometry of Savage and Svarc \[1997\] afterslip

model (Plate 2a) and of Wald and Heaton's \[1994\] coseismic

model (Plates 2b and 2c). After Peltzer et al. \[1998\].

Plate 3. (a) Calculated range change and (b) horizontal dis-placements

on a model with an isoviscous mantle:

• m1 =• m2 =6.0 •10 18 Pa s, • c ⁄• m1 =2.0, µ•=12 GPa. (c

and d): Corrsponding calculated range change and horizontal- 27
-displacement

field on a model with a factor of 10 contrast in

mantle viscosity at 50 km depth: • m1 =1.1 •10 19 Pa s,

• m1 =1.1 •10 18 Pa s, • c ⁄• m1 =2.0, µ•=12 GPa. Superim-posed

in Plates 3b and 3d are the observed horizontal velocity

vectors from Figure 1c.

Plate 4. (a) Range change contributed from vertical postseismic

velocity field on the Mojave Block model. (b) Corresponding

range change on a thin channel model parameterized by

• c =5 •10 18 Pa s, • m1 =• m2 =•, and µ•=0 (c chosen to

duplicate observed near-field fault-parallel postseismic veloci-ties).

The pattern in Plate 4a is negatively correlated with the

coseismic uplift pattern and positively correlated with the

observed postseismic range change (Plate 1a), whereas the pat-tern

in Plate 4b is positively correlated with the coseismic uplift

pattern and negatively correlated with the observed postseismic

range change. (c and d) Range change contributed from hor-izontal

postseismic velocity field on the Mojave Block and thin

channel models, respectively. (e and f) Total range change pat-terns,

equal to the sum of Plates 4a and 4c or Plates 4b and 4d,

respectively. In Plates 4a and 4b, lighter dashed lines and tri-angles

denote the USGS sites on the Emerson transect.

Figure 1. (a) Active faults around the Mojave Desert region. Boxed
region indicates the area covered in Figure

2 and Plates 1a, 1b, 2, 3a, 3c, and 4. (b) P-wave velocity anomalies in
percent of background velocity \[Hum-phreys

and Dueker, 1994, Figure 10i\] across the profile indicated in Figure
1a. The low seismic velocity pattern

underlying this portion of the central Mojave Domain at uppermost mantle
depths continues northwestward to

include essentially all of the central Mojave Domain \[e.g., Humphreys
and Dueker, 1994, Figure 9\].

Figure 2. Map of the June 28, 1992, Landers earthquake area. Solid lines
are the June 28, 1992, surface rup-ture

\[Sieh et al., 1993\]. Shade depicts topography from U.S. Geological
Survey (USGS) digital elevation model.

White dots are aftershocks between August 7, 1992, and January 23, 1996
\[Hauksson et al., 1993\]. After Peltzer

et al. \[1998\].

Figure 3. (a) Bold lines are the surface projection of buried fault
planes used by Feigl et al. \[1993\] and Savage

and Svarc \[1997\] to represent interseismic strain accumulation in
southern California. Dashed lines represent

active faults in California. (b) Interseismic velocity field evaluated
at 26 GPS sites used in this study relative to

a fixed Goldstone.

Figure 4. Viscoelastic stratification used to model postseismic
deformation in the Landers epicentral area. A

purely elastic upper crust (base at 16 km depth) is underlain by a
standard linear solid lower crust \[Cohen,

1982\] (base at 30 km depth) and Maxwell viscoelastic fluid upper
mantle. Parameters • , µ, and • are the bulk

modulus, shear modulus, and viscosity, respectively, and µ•is the
long-term strength of the lower crust (•=0

would correspond to a Maxwell viscoelastic fluid). Elastic
stratification is prescribed by values • c 1 =74 GPa,

µc 1 =41 GPa, • c 2 =95 GPa, µc 2 =53 GPa, and • m =150 GPa, µm =70 GPa.
An additional elastic layer from

0 to 4 km depth (not shown) is prescribed with • =65 GPa and µ=36 GPa.
This stratification is essentially

(with fewer discontinuities) equivalent to the seismic structure for the
eastern Mojave Desert given in Table 1 of

Qu et al. \[1994\]. Parameters • c , • m1 , • m2 , and µ•are variable.

Figure 5. (left) Misfit with respect to several data subsets in • m1 ••
c ⁄• m1 space for µ•=12 GPa and

• m1 ⁄• m2 =3. (right) Corresponding misfit pattern for the case µ•=0
(Maxwell viscoelastic fluid lower crust).

Dashed lines indicate lowest two contours associated with each subset.
The Mojave Block model is indicated

by the solid circles in Figure 5 (left).

Figure 6. ΩF (defined in section 3.2) at probability levels P =0.95 and
P =0.99 through the model slices

µ•=12 GPa and µ•=0, for • m1 ⁄• m2 =3.

Figure 7a. Misfit with respect to several data subsets in • m1 •• c ⁄•
m1 space for µ•=12 GPa and- 28 -

m1 ⁄• m2 =1. The best isoviscous mantle model is indicated by the solid
circles.

Figure 7b. ΩF (defined in section 3.2) at probability levels P =0.95 and
P =0.99 through the model slice

µ•=12 GPa, for the isoviscous mantle model.

Figure 8. Observed uplift with respect to GOLD and corresponding
calculated uplift on the Mojave Block

model and the high • m1 model discussed in the text at the 10 GPS sites
on the Emerson transect (Plates 4a and

4b). Error bars denote ±standard deviation in measurement.

Figure 9. Possible temperature structure beneath the east central Mojave
Desert based on the crustal geotherm

of Williams \[1996\], the mantle temperature structure implied by the
Mojave Block model (section 5.1), and geo-chemical

evidence for a shallow asthenosphere. Two crustal geotherms of Williams
\[1996\] correspond to the

range of heat flow values observed in the Landers region. A thermal
boundary layer between 30 and 60 km

depth is envisioned to accommodate a 500-600°C vertical temperature
difference at the top of the mantle. The

thin subcrustal domain at temperature below 975°C may exhibit
quasi-rigid behavior, but the upper 30 km of the

mantle as a whole has an average temperature consistent with a viscosity
of •5 •10 18 Pa s. An adiabatic tem-perature

gradient of 0.5°C/km is assumed for the temperature in the asthenosphere
below 60 km. Ranges of

sub-Mojave mantle viscosity from depth 30-50 km (m1 ) and \>50 km (m2 )
determined in this study are indi-cated.

The dry and wet peridotite solidus are from Basaltic Volcanism Study
Project \[1981\]. Viscosity of the

mantle and crust as a function of temperature are indicated by the upper
tick lines. They are calculated from

equation (12) with flow parameters of wet dunite \[Hirth and Kohnstedt,
1996\], and wet and dry Westerly granite

\[Freed and Lin, 1998, Table 3\], respectively, assuming 3 MPa
differential stress. The pressure dependence is

included only for the mantle viscosity calculation.

Plate 1. (a) Observed range change from September 1992 to January 1996
\[Peltzer et al., 1998\]. (b) Calculated

range change (equation (4)) on Mojave Block model (see section 3.2). (c)
Observed average horizontal velocity

with respect to fixed Goldstone from November 1992 to December 1995 and
corresponding 1 error ellipses

\[Savage and Svarc, 1997; Southern California Earthquake Center (SCEC)
Release 2, 1998, available at

http://www.scecdc.scec.org/group e/ release.v2\]. Calculated horizontal
velocity vectors (equation (3)) on Mojave

Block model are shown as black arrows. The seven SCEC GPS sites lying
outside of the boxed region are

referred to as \"far field\"; all remaining GPS sites are considered
\"near field\" (Table 1).

Plate 2. Surface displacement predicted by (a) Savage and Svarc \[1997\]
afterslip model, (b) poroelastic model,

and (c) the combination of Plates 2a and 2b. One color cycle represents
5.6 cm of surface displacement towards

the radar. Black arrows depict horizontal displacement vectors. White
lines show fault geometry of Savage and

Svarc \[1997\] afterslip model (Plate 2a) and of Wald and Heaton's
\[1994\] coseismic model (Plates 2b and 2c).

After Peltzer et al. \[1998\].

Plate 3. (a) Calculated range change and (b) horizontal displacements on
a model with an isoviscous mantle:

• m1 =• m2 =6.0 •10 18 Pa s, • c ⁄• m1 =2.0, µ•=12 GPa. (c and d):
Corrsponding calculated range change and

horizontal displacement field on a model with a factor of 10 contrast in
mantle viscosity at 50 km depth:

• m1 =1.1 •10 19 Pa s, • m1 =1.1 •10 18 Pa s, • c ⁄• m1 =2.0, µ•=12 GPa.
Superimposed in Plates 3b and 3d

are the observed horizontal velocity vectors from Figure 1c.

Plate 4. (a) Range change contributed from vertical postseismic velocity
field on the Mojave Block model. (b)

Corresponding range change on a thin channel model parameterized by • c
=5 •10 18 Pa s, • m1 =• m2 =•, and

µ•=0 (c chosen to duplicate observed near-field fault-parallel
postseismic velocities). The pattern in Plate 4a

is negatively correlated with the coseismic uplift pattern and
positively correlated with the observed postseismic

range change (Plate 1a), whereas the pattern in Plate 4b is positively
correlated with the coseismic uplift pattern

and negatively correlated with the observed postseismic range change. (c
and d) Range change contributed from

horizontal postseismic velocity field on the Mojave Block and thin
channel models, respectively. (e and f) Total

range change patterns, equal to the sum of Plates 4a and 4c or Plates 4b
and 4d, respectively. In Plates 4a and

4b, lighter dashed lines and triangles denote the USGS sites on the
Emerson transect.