Evelyn J. Price and David T. Sandwell

Cecil H. and Ida M. Green Institute of Geophysics and Planetary Physics, Scripps Institution of Oceanography, La Jolla, CA 92093-0225

We use the technique of Interferometric Synthetic Aperture Radar (InSAR) to examine small-scale features in the deformation field associated with the Landers earthquake and Big Bear aftershock . Our study is spatially limited to a 100x100 km SAR data frame surrounding the northern portion of the surface rupture (Plate 1) and is limited by data availability to temporally integrate all deformations occurring between April 24 and August 7, 1992. While the coseismic and postseismic deformations associated with this earthquake have been studied by other workers using the InSAR technique [Massonnet et al., 1993; Massonnet et al., 1994; Zebker et al., 1994; Peltzer et al., 1994; Feigl et al., 1995; Peltzer et al., 1996], our processing methods , which entail computation of phase gradients, bring out short wavelength features to reveal previously unrecognized strain patterns.

Like the phase of an interferogram, the gradient of the phase depends on the topography and deformation of the Earth's surface, and differences in the atmosphere at the two times of imaging. In an attempt to isolate the phase gradient due to deformation, the topographic contribution to the phase gradient can be computed using a digital elevation model or additional interferometric pairs and subsequently removed. Because we can not yet remove atmospheric variations from an interferogram, we use ancillary geologic information in our interpretations of the phase and phase gradient. One of the many advantages of the phase gradient map is that it can be used as to interpret large-scale interferogram phase variations by highlighting small-scale deformations on fractures and faults.

Phase gradients attributable to deformation show small-scale variations in deformation gradient with near total coverage of the area imaged. Strain concentrations along pre-existing faults and structural features are observed allowing us to study spatial heterogeneity in the deformation field of a large earthquake. This heterogeneity has been suggested by other workers to explain deviations of geodetic measurements from those predicted by elastic models [e.g. Hudnut et al., 1994; Murray et al., 1993]. In this paper, this heterogeneity is mapped in a SAR data frame over part of the region affected by the Landers earthquake.

The Landers earthquake sequence is conventionally characterized by three events; the 4/23/92, 04:51 UTC, 33.94° N, 116.33° W Joshua Tree earthquake (Mw 6.1); the 6/28/92, 11:58 UTC, 34.22° N, 116.43° W Landers event (Mw 7.3); and the 6/28/92, 15:07 UTC, 34.21° N, 116.83° W Big Bear event (Mw 6.2). The data discussed in this study (Table 1) contain deformation occurring between April 24 and August 7, 1992 in an area surrounding the northern part of the rupture of the Landers event (Plate 1).

The Landers earthquake has been modeled teleseismically as a two-event phenomenon with the conventionally placed hypocenter 30-40 km north of Joshua Tree as a small, shallow (3-6 km deep) Mw 6.8 Earthquake with strike 359° rupturing unilaterally to the north and provoking a larger magnitude (Mw 7.15) second event about 30 km to the north having a strike of 333° [Kanamori et al., 1992]. The rupture, which was initially oriented nearly due north on the Johnson Valley fault, changed its orientation as it propagated by stepping right onto progressively more north-westwardly oriented major faults. The earthquake ruptured nearly 20 mapped and unmapped faults; the main 5 of which are (from South to North) the Johnson Valley Fault, the Kickapoo Fault (sometimes called the Landers fault), the Homestead Valley Fault, the Emerson Fault, and the Camp Rock fault (Plate 1). The maximum measured surface displacement was 5.1 m on the Emerson fault near Bessemer Mine Road [Hart et. al, 1993]. In addition to the main rupture slip, triggered slip was reported on several faults within a 100 km radius including the Pisgah, Calico-West Calico (including fractures NE of Newberry Springs), Johnson Valley, Upper Johnson Valley, Lenwood, Old Woman, and Pinto Mountain faults [Hart et al, 1993].

The Landers Earthquake ruptured deeper and stronger than any earthquakes previously recorded in the area. It had more than 60,000 shocks including fore-shocks, co-shocks and after-shocks [Hauksson et al., 1994]. Shock patterns pertinent to this study include clusters of aftershocks not on the main fault rupture. In particular, aftershock clusters in our area include the Barstow sequence, a cluster near the Calico fault North of the Mojave Valley, a cluster on the Calico fault just east of the rupture on the Camp Rock fault, and seismicity associated with the Newberry Fractures which are northeast of the Calico fault in the Mojave Valley [Unruh et al., 1994] (Plate 1).

The faults of the western Mojave Desert (Plate 1) define an 80 km wide region of N-NW right-lateral shear and lie within the Eastern California Shear Zone (ECSZ) [Dokka and Travis, 1990a; Dokka and Travis, 1990b; Savage et al., 1990; Sauber et al., 1986]. These faults have been active since about 10.6 Ma and have accommodated 9-14 % of total plate motion [Dokka and Travis, 1990a] at this latitude on the Pacific-North American plate boundary. The faults of the Mojave Block are characterized as discontinuous with the only fault traversing the entire length of the Mojave from the Pinto Mountain Fault to the Garlock fault being the Calico-Blackwater system. Faults tend to end in structurally complex zones of extension or shortening with zones of extension characteristically marked by triangular shaped lakes and zones of shortening marked by mountains and hills [Dokka and Travis, 1990a]. Geologically determined fault offsets show greater than 40 km of cumulative offset throughout the region south of Barstow [Dokka and Travis, 1990a] while geodetic results show most of the deformation in this region accommodated between the Helendale and Calico faults south of Barstow (6.7 mm/yr) with negligible deformation to the east [Sauber et al., 1986]. This contrast between geologic and geodetic results points to a recent westward migration of strain [Sauber et al., 1986].

In spite of the surface rupture and shock characteristics of large earthquake swarms ( April 10, 1947 Manix [Richter, 1947; Doser, 1990]; June 1, 1975 Galway Lake [Hill and Beeby, 1977; Fuis and Lindh, 1979]; and March 15, 1979 Homestead Valley [Hill et al., 1980]) which have implied significant fault interactions, geologic results have led to block models of faulting in the Mojave with faults accommodating motion independently of each other in time and space [Garfunkel, 1974; Carter et al., 1987; Dokka and Travis, 1990a]. These presumptions about the nature of faulting in the Mojave have led to underestimation of the earthquake magnitude potential in the area [e.g. Wesnousky, 1986; Hart et al., 1993] and confusion as to the link between the San Andreas Fault (SAF) and the more Northern parts of the ECSZ. The Landers earthquake changed these presumptions by rupturing along several faults across areas previously modeled as coherent blocks [Hart et al., 1993].

SAR and InSAR

We use radar imagery data (Table 1) collected by the C-band (5.2 GHz) SAR instruments aboard the ERS-1 and ERS-2 satellites. The raw signal data are processed using a JPL-heritage SAR processor whose output consists of a complex signal that is a measure of the complex backscatter of a patch on the ground delayed by the travel time of the signal from sensor to target and back (see Curlander and McDonough, [1991] and McDonough et al., [1985]). After processing, the phase of a SAR image resolution element is the sum of several components: 1) the phase delay due to the two-way travel time between sensor and target (location of a SAR pixel on the ground), 2) a random phase component due to the complicated interference pattern produced by radar signal interaction with multiple ground scatterers within an image resolution element, and 3) additive noise.

InSAR is a method by which the phase differences of two SAR images are used to calculate the differences in range from two SAR antennae having slightly different viewing geometries to targets on the ground [Graham, 1974; Zebker and Goldstein, 1986] (Figures A1 and A2). The ERS radar interferometer is composed of either the same antenna on one platform "repeating" its orbit (e.g. ERS-1 ), or two antennae on different platforms having nearly the same orbit (e.g. ERS-1/ERS-2 tandem mission ). The antennae are separated in both space and time (repeat-pass interferometry) and range differences can be due to a number of sources including topography, surface deformation, and atmospheric differences at the two times of imaging. The line that connects the two antennae in space is called the interferometer baseline (Figures A1 and A2).

In repeat-pass interferometry, spatial coverage limitations are imposed by phase decorrelation and the geometry of imaging. Three sources of phase decorrelation have been identified as temporal decorrelation due to motion of scatterers between imaging times, spatial (or baseline) decorrelation that is more influential when the interferometric baseline is longer, and thermal noise in the system electronics [Goldstein et al., 1988; Zebker and Villasenor, 1992]. In areas of complete spatial or temporal decorrelation (very steep topography or the area surrounding the Landers surface rupture, respectively), the phase can not be recovered. The sensor’s ability to image the terrain with geometric fidelity depends on the slope of the terrain and the look angle of the radar. "Robust" imaging of the terrain can occur only if the slope does not satisfy the criteria for geometric layover or shadowing. Because ERS1/2 have a steep average look angle of 21°, geometric layover is a common phenomenon in mountainous areas. The black patches in Figure 2 and Plates 2, 3, 4, and 5 occur in areas where the topographic interferogram could not be unwrapped using a "tree" algorithm (e.g. Goldstein et al., [1988]). They exist in the phase gradient map (which should show total coverage) because we used the topography computed from the topographic interferogram to perform orthorectification on our images.

Because we can not yet remove the atmospheric signal from the topographic phase-corrected interferograms, it is important to be able to recognize atmospheric artifacts in interferograms so they are not confused with tectonic deformations. Short-wavelength atmospheric artifacts (which could be confused with small-scale tectonic deformations) typically have length scales on the order of 5-10 km and can cause as much as 10 cm of excess two-way path length (3 interferogram fringes). Examples can be found in Massonnet and Feigl, [1995]; Rosen et. al, [1996]; and Zebker et. al, [1997].

Regional atmospheric effects corresponding to long-wavelength ionospheric perturbations and differences in the hydrostatic component of the troposphere manifest themselves as a planar phase trend in an interferogram [Tarayre and Massonnet, 1996]. This phase trend makes it necessary either to compute an "artificial baseline" [Tarayre and Massonnet, 1996] or to remove the long-wavelength atmospheric effect from the interferogram at some point in the data processing. If these regional effects are not removed, they will produce a constant offset in the phase gradient map which could be interpreted as a regional tilt.

Despite variations in the refractivity of the atmosphere and ionosphere, repeat-pass InSAR has proved valuable for applications involving deformation of the surface of the earth. Several studies [Zebker et al, 1994; Massonnet et al, 1993] have compared coseismic deformation signatures obtained from INSAR with those measured by GPS. Zebker et al., [1994] found the correlation of GPS displacements with those obtained from his interferometric method to be 0.958 while Massonnet et al., [1993] found interferometric displacement estimates to agree with GPS measurements of displacement within 3.4 cm RMS. Also, the results of forward modeling of the large-scale ground displacement field near earthquakes agree qualitatively with INSAR fringe maps [Massonnet et al. 1993; Peltzer et al., 1994]. In this study, we differentiate between small, localized tectonic deformations and atmospheric artifacts using proximity to pre-existing geologic structures as a discriminative criterion.

The basic steps of our InSAR data processing are quite standard. We process the raw radar echoes to SAR images and match the images to a sub-pixel level. We then form an interferogram by multiplying each complex pixel in one image by the complex conjugate of the matching pixel in the other image. Interferograms computed in this fashion have a corrugated appearance [Li and Goldstein, 1990, their fig. 7] resulting from a high phase rate in range due to imaging geometry. The flat earth correction (Appendix A) [Zebker et al., 1994] removes those fringes due to earth curvature and imaging geometry.

There are some data processing steps that are either done differently here than in previous studies or should be elaborated upon for the sake of explaining the resolution and interpretation of our results. These include estimation of baselines from orbital knowledge, image filtering, and phase gradient computation and combination.

In contrast to previous studies, which estimated baseline parameters from imagery and topography data, we computed baselines from ERS-1/2 precise orbits provided by Scharroo et al., [1997] (Table 1). These orbits have radial accuracies of 50 mm and cross-over repeatability within 70 mm giving an overall baseline accuracy better than 70 mm. The advantage of this approach is that surface displacements and long-wavelength atmospheric artifacts are not absorbed into the baseline estimate. Repeat orbits are usually not parallel necessitating the computation of a new baseline at several points in azimuth within an image frame [e.g. Gabriel and Goldstein, 1988].

(1)

(3a)

(3b)

The sign of the horizontal component is positive in the direction of radar look.

Methods of filtering interferograms range from simple averaging over pixels (taking looks) [e.g. Gabriel et al., 1989] to spatially variable filters whose power spectra are matched to that of the local phase [Goldstein et al., 1988; Werner et al., 1992]. We filtered the real and imaginary parts of the complex interferogram (with pixel spacing as sampled by the radar) separately using a low-pass Gaussian 5 point by 17 point filter whose characteristics are discussed in Appendix B. Because none of the baselines of the interferograms examined in this study are longer than 150 m, we do not find in necessary to use an adaptive filter.

(4)

(5)

In this study, we averaged two pairs from the ERS1-ERS2 tandem mission to obtain an estimate for the topographic phase gradient. We then scaled and subtracted this topographic phase gradient from the interferogram phase gradient for the ERS-1 pair which includes the earthquake (Table 1) to obtain an estimate of the phase gradient (Figure 2) related to the deformation which occurred between April 24 and August 7, 1992.

(6)

(7)

When the topographic and geometric phase contributions are removed, the residual phase can be assumed to be due to deformation and is:

(8)

The geometric relationship between an earth-based rectangular coordinate system and a satellite referenced system is illustrated in Figure 1. Assuming that the radar line-of-site (LOS) and satellite ground-track directions are orthogonal, we define a right-handed rectangular coordinate system in the satellite reference frame in which the directions of the first, second, and third rectangular vector components are, respectively, in the satellite LOS direction, the satellite along-track direction, and the direction perpendicular to the plane of imaging (z). We then find the rotation matrix (A) that transforms earth-based rectangular coordinates (East (E), North (N), Up (U)) into the satellite coordinate system. The rotation matrix, A, is fully determined (for a descending pass geometry) by defining the along-track axis to lie in the earth-referenced E-N plane and to make an angle of 180°-y with the N axis (where y is the angle between the satellite ground-track and South) , the LOS axis to make an angle 180°-q with the U direction (where q is the radar look angle), and the base vector perpendicular to the plane of imaging to make an angle 90°-q with the U direction (Figure 1). The assumption that the LOS and along-track directions are orthogonal is reasonable in our case since the angle between them (in the imaging plane) is 90° ± s where s , the squint angle, is less than 0.03° for the ERS imaging radars.

If u is the displacement in the satellite coordinate system and u is the displacement in the earth-based coordinate system,

u = Au (9)

and the displacement measured by the radar interferometer is the LOS component of u which is u₁.

The gradient of the displacement in the earth-based coordinate system can be transformed using the same rotation matrix to yield tensor components proportional to the phase gradient of deformation. If the deformation gradient tensor (e.g. Malvern, [1969]) in the earth-based coordinate system is J and the deformation gradient tensor in the satellite coordinate system is J then,

J = AJA^T (10)

The two components of phase gradient due to deformation that we can measure using InSAR are proportional to two components of J: J₁₁ is the derivative of u₁ in the LOS direction, and J₁₂ is the derivative of u₁ in the along-track direction. Our phase gradient maps plot only the deformation gradient component that is in the LOS direction because this component highlights the predominantly N-S structures. Note that the deformation gradient tensor includes both strain and rotation.

As is evident from this analysis, the LOS component of deformation is a linear combination of all the components of the earth-referenced deformation as are the two phase gradient components a linear combination of all the deformation gradient components in an earth-based coordinate system. Because of this, other information including geologic mapping, GPS measurements, earthquake orientations, and/or assumptions about the nature of the deformation is necessary to interpret radar interferometric measurements. Even in the case where ascending and descending passes of the satellite are available for a given deformation event, information about the magnitude of the horizontal displacement vector or its orientation is necessary to determine its three components.

The phase gradient presented in Figure 2, and Plates 3a, 4a, and 5a is capable of both adding to the knowledge about the earthquake rupture pattern and mapping extensions of faults difficult to trace geologically by highlighting strain concentrations on secondary fractures and triggered or sympathetic slip on major faults. The larger scale deformation patterns are best observed as variations in the wrapped phase since their contribution to the phase gradient measurements is that of a regional constant shift.

The stacked LOS phase gradient (Eqn. 5) of two ERS1/2 tandem mission interferograms was scaled and subtracted from the phase gradient of the ERS1 April 24-August 7, 1992 interferogram to produce the gradients shown in Figure 2, and Plates 3a, 4a, and 5a. The unwrapped phase of the Dec. 3-4, 1995 tandem interferogram was scaled and subtracted from the phase of the Apr.-Aug., 1992 interferogram to produce the fringes in Plates 2, 3b, 4b, and 5b. Because each image was collected during a descending pass of the right-looking ERS satellite, the nearest range to the satellite is on the right-hand side of the figures.

Plate 2 and Figure 2 show the relationship of the deformation phase gradient to the deformation fringe phase for the entire area of the study (100 km by 100 km) defined by an ERS data frame. The deformation fringe phase is comparable to maps shown in other studies [Massonnet et al., 1993; Zebker et al., 1994]. The most obvious feature in the map is the region of phase decorrelation around the main rupture. Ground scatterers in this region underwent random motions between the two imaging times with length scales greater than the wavelength of the SAR. The phase cannot be recovered here. Three areas outside the decorrelated rupture signature show remarkable deformation fringe and phase gradient signatures. Area A (Plates 3a, 3b, and 3c) surrounds the end of the rupture and includes the Camp Rock (CRF), Emerson (EmF), Johnson Valley (JVF), and Lenwood (LF) faults and small parts of the Calico fault (CF). Area B (Plates 4a, 4b, and 4c) includes the Calico and Pisgah (PF) faults as they traverse the latitude of the Mojave Valley (MV) as well as deformation related to structures which have been dubbed the Newberry Fractures [Unruh et al., 1994]. Area C (Plates 5a, 5b, and 5c) includes Coyote Dry Lake (CDL) and the Barstow earthquake cluster [Hauksson et al., 1993].

The fringe pattern between the Johnson Valley Fault and the main rupture is dense and elongated parallel to the azimuth of the rupture (Plate 3b). The density of fringes decreases logarithmically across the Johnson Valley from east to west as is expected from elastic half-space modeling of the lithosphere (see Massonnet et al., [1993]). Because of the viewing geometry mentioned above, this pattern is indicative of either a left-lateral shear in the direction of earthquake rupture or a tilt of the region between the Camp Rock-Emerson and Johnson Valley faults. Between the Camp Rock-Emerson and Johnson Valley faults, negative phase gradients occur in linear patterns striking N-NE (Plate 3a). It is likely that these correspond to secondary fault rupture at depth. The fringes across these secondary faults ramp downward with increasing range indicating relative ground movement away from the satellite on the western sides of the faults. If no vertical deformation is assumed, this evidence, combined with the observation of negative phase gradients, indicates right-lateral displacements across these secondary structures. Offsets along each of the secondary faults between the Johnson Valley Fault and the main rupture are typically 2 radians which is equivalent to 9 mm of LOS displacement.

The elongated fringe pattern in the Upper Johnson Valley is limited to the north by an arcuate feature seen in the phase gradient map (Plate 3a) which defines the transition of the surface morphology from alluvial fill to mountainous. This feature demarcates the northern extension of the Fry Mountains (Area marked B in Plate 3a) and is one of the bounds on a zone a complex deformation [Zebker et al., 1994 (their Plate 6, area B)] that extends west to the Ord Mountains, north to the rupture on the Camp Rock Fault, and south to the Fry Mountains. Although previous workers have interpreted this region to contain "cracking" [Zebker et al., 1994], analysis of the azimuth and range gradient maps indicate drainage patterns intersecting a fracturing pattern consistent with the style of deformation in the Upper Johnson Valley. While geologic maps [Dibblee, 1964] of the area show the termination of the Johnson Valley fault near its intersection with the Fry Mountains, the interferometric phase gradient shows an offset along a fracture connecting the mapped terminus of the Johnson Valley Fault with the Camp Rock Fault near the terminus of the earthquake rupture (Plates 3a and 3c). This linkage is not obvious in the fringe map (Plate 3b). This extension of the Johnson Valley Fault is the only coherent feature within the zone of complex deformation. Geologic mapping results show an east-side down offset along a short fracture intersecting the end of the rupture on the Camp Rock fault near GPS site 7000 (Plate 3c) that may correspond to this northward extension of the Johnson Valley Fault [Ken LaJoie, Personal Communication].

While the northern end of the Fry Mountains intersects the main rupture trace, from the west, at the north end of the step-over region linking the Emerson Fault and the Camp Rock Fault, the south end of the step-over region is flanked to the east by a north-eastwardly trending Mesozoic structure called Iron Ridge (Plate 3c). After the earthquake, two NE to E striking zones of aftershocks bordered Iron Ridge to the north and south (Plate 1) [Hauksson et al., 1993]. The northern zone of aftershocks is associated with triggered slip on left-lateral, NE striking fractures [Hart et al., 1993; Ken LaJoie, Personal Comm.].

Iron Ridge corresponds directly to a region of rounded, nearly circularly enclosed fringes in the interferogram (Plate 3b, label C). Fringes ramp upward to the west with positive phase gradient on the satellite side of Iron Ridge and ramp downward to the west with negative phase gradient on the opposite side. The semi-circular fringes are most likely indicative of uplift during the time period surrounding the earthquake with the central fringe representing maximum displacement toward the satellite. The phase variation across this feature is 37.5 radians representing 16.8 cm of LOS displacement. The zone of semi-circular fringes is cut to the northeast by the West Calico Fault (WCF) (Figure 1) and bounded further to the east by a south-eastward extension of the Calico Fault as evidenced in the interferometric phase gradient map (Plate 3a) and previously mapped fault locations (Plate 3c).

The phase gradient is positive along linear features (Plate 3a, label D) located south-west of the Johnson Valley which correspond to the Lenwood Fault, a northern extension of the Old Woman Fault, and an unidentified fault west of the Old Woman Fault (Plate 3c). The fringe map exhibits upward ramping of fringes across these structures from east to west indicating relative displacement towards the satellite on the west sides of the faults. LOS displacements across the faults are typically 15 mm. If the displacement across these faults was purely horizontal, the phase gradient features and fringe patterns indicate left-lateral sympathetic slip. If the displacement is vertical, there was uplift on the west sides of these faults relative to the east sides.

The Calico fault (Plates 1 and 4) runs beneath the Mojave Valley in the left half of Plate 4. The phase gradient is negative along this fault while the deformation fringe phase shows down-ramping from east to west indicating relative displacement away from the satellite on the west side of the fault. A strain concentration on this fault is not obvious in the fringe map. The LOS displacement across this fault is 8-9 mm. Assuming only horizontal offset, the interferometric evidence suggests that the offset was right-lateral. This agrees with mapping results reported in Hart et al., [1993].

The fractures in the center of Plate 4 have been mapped and named the Newberry fractures [Unruh et al., 1994; Ken LaJoie, Personal Communication]. Geologic mapping shows that they are purely extensional in a NE-SW direction. LOS displacements across the fractures range from 5-22 mm. Associated with these fractures, the interferometry results show two regions of enclosed fringe patterns. A relative LOS displacement of 13 mm is present across the northern fringe pattern while a relative LOS displacement of 44 mm is present across the southern fringe pattern. The interferogram fringes ramp down towards the centers of the patterns and the phase gradients are negative on the satellite sides of the fringe patterns and positive on the sides further from the satellite. Because of their association with the extensional Newberry fractures and their location near Troy Dry Lake, the ground features are here interpreted as subsidence basins.

The Barstow earthquake cluster trended north to northwest (Plates 1 and 5b) and did not occur on known surface faults. The maximum magnitude earthquake in the cluster occurred on August 5, 1992 [Hauksson et al., 1993] with magnitude 4.7 [CNSS earthquake database]. The fringe pattern in the left-hand portion of Plate 5 consisting of two, coupled, bulls-eyes (one positive LOS displacement and one negative LOS displacement) straddles the intersection of the Barstow cluster, the Calico fault and the Coyote Lake fault (Plate 5c). Several earthquakes with magnitude greater than 3.5 occurred at or near this location during the time period between April 24 and August 7, 1992 (Plates 1 and 5b; stars). The phase gradient image shows little indication of a surface fault rupture. The fringes indicate right-lateral offset across the Calico fault with vertical uplift of the Calico Mountains, or left-lateral offset across the conjugate Coyote Lake fault. The shocks in the Barstow cluster had a predominantly right-lateral, strike-slip focal mechanism [Hauksson et al., 1993]. The relative LOS displacement measured across the enclosed fringes is 5.3 cm.

Flanking the east side of the Calico Mountains, a structure which may be a north-eastern branch of the Calico Fault is apparent in the phase gradient map (Plate 5a, label C; Plate 5c). The fault appears to include a series of right-lateral strike-slip offsets connected by extensional cracks. This is evidenced by the change in phase gradient signature from negative to a negative-positive double as the fracture changes orientation. Typical LOS displacements of 5mm are associated with right-lateral offsets across this fault.

North-east of this apparent north-eastern branch of the Calico Fault is Coyote Dry Lake (Plate 5a, label D; Plate 5c). The deformation fringe phase and phase gradient maps shows deformation of the lake shore between the time period April 24-August 7, 1992 and a small amount of what can be interpreted as subsidence within the lake bed itself. Subsidence in the interior of the lake bed was 9-10 mm LOS while deformation along the shoreline reached 13 mm LOS across some features. This deformation could be either earthquake related or indicate a seasonal change of the lake-bed between spring and summer.

The interferometric results presented here indicate that small-scale LOS deformations associated with the Landers earthquake occurred within 75-100 km of the main rupture. These small-scale deformations are superimposed on a deformation field such as might be expected from the response of an elastic lithosphere to the Landers earthquake [e.g. Massonnet et al., 1993, their Fig. 3b]. These small-scale deformations are associated with secondary fractures, pre-existing faults, dry lake beds, and mountainous regions; they provide insight into the formation of such geomorphic features and help define the role of these features in fault interactions. Furthermore, interferometric maps showing small- scale deformations could be used as a reconnaissance tool for mapping faults and coseismic displacements and for decisions involving GPS receiver location or GPS data exclusion from inversions that assume elastic behavior.

The long, linear secondary faults superimposed on the dense, elongated fringe pattern between the Johnson Valley Fault and the main rupture (Plate 3) indicates a shear zone between the main rupture trace and the Johnson Valley Fault with probable faulting of the basement rock. Faulting is believed to extend to the basement because it is unlikely that the overlying alluvium is cohesive enough to sustain fractures with lengths of 10 km. Geologic mapping of surface ruptures indicative of shear zones in alluvium due to the Landers earthquake shows a maximum length of shear fractures to be on the order of 500 m (e.g. Johnson et al., [1994]; Sowers et al., [1994]).

The fractures between the rupture on the Camp Rock -Emerson faults and the Johnson Valley fault are similar in style to fracture patterns seen in much smaller versions of shear zones associated with the Landers earthquake (e.g. Johnson et al., [1994]). As the orientation of a fracture changes with respect to the look direction of the radar, the sense of slip on a fracture with the same phase gradient sign changes. Hence, the smaller fractures close to the Johnson Valley Fault (Plate 3c) most likely have left-lateral offsets across them while the larger fractures that traverse the entire valley floor to intersect with the main rupture most likely accomodate left-lateral offsets near the Johnson Valley fault which change to right-lateral offsets as the fractures near the main rupture. This behavior is similar to that of a curved fracture in the Happy Trail shear zone observed by Johnson et al., [1994]. The fracture flanking the eastern side of the Fry Mountains (Plate 3c) probably also accommodated some east side up motion similar to some fractures seen in the Happy Trail shear zone. Because of their regular spacing between mountain ranges, the long fractures in the Johnson Valley and between the Lenwood fault and the north-westward continuation of the earthquake rupture may be related to and/or facilitate the uplift of the Fry and Ord Mountains (Plate 3c).

The fractures in the Upper Johnson Valley may have collectively accommodated some significant portion of right-lateral shear. Murray et al., [1993] require ~0.5 m of right-lateral slip on a northwest trending fault between stations Boulder and Means on the east and Old Woman, Fry, and Rock on the West (Plate 3c) to fit their trilateration data to an elastic half-space model. The tie-lines between the above stations span the Upper Johnson Valley. Because displacement on the Upper Johnson Valley Fault (which runs through the Upper Johnson Valley between the Johnson Valley Fault and the Camp Rock-Emerson Faults) was on the order of centimeters [Ken LaJoie, Personal Communication], offset on another fault or over a region is necessary to fit the geodetic data. This discrepancy could be resolved with further modeling of the displacement expected from an elastically responding lithosphere and comparison of models to interferometric results.

Stress changes on faults not involved in the main rupture are indicated by published and preliminary modeling of the stress field induced by the earthquake in an elastic half-space [Harris and Simpson, 1992; Stein et al., 1992; Bob Simpson, Personal Communication]. Two lines of evidence suggest that InSAR observed displacements on the Lenwood and Old Woman Faults were vertical, west-side up rather than left-lateral and sympathetic. First, Coulomb failure stress is predicted to have decreased by only as much as 17 bars across the Lenwood and northern portion of the Old Woman Fault [Harris and Simpson, 1992], while the calculated stress drop on the Landers earthquake surface rupture was approximately 85 bars; assuming that the level of stress on other faults in the Mojave Desert before the earthquake was similar to that on the faults involved in the Landers earthquake, a 17 bar stress drop would not be enough to induce sympathetic slip. Second, preliminary modeling results show vertical displacements across these faults, if present, should be west-side up [Bob Simpson, internet communication]. Thus, while the Lenwood and northern Old Woman faults probably relaxed subsequent to the Landers earthquake, the stress drop was not enough to induce left-lateral, sympathetic slip. Instead, the displacements measured in the SAR interferogram were probably vertical, west-side up which is consistent with the geomorphology (Plate 1).

Geologic field mapping and tectonic modeling suggest that the offset observed by InSAR on the Calico fault was right-lateral. The Calico fault (Plate 4) lies in a region of the model of Stein et al., [1992] in which faults on optimally oriented planes were brought closer to failure by the Landers earthquake induced stress field. Geologic mapping indicates right-lateral slip on the Calico Fault [Hart et al., 1993]. Also, there are no geomorphic structures directly related to the Calico fault that would indicate that it accommodates vertical motions (Plate 4c).

The Newberry Fractures were mapped by geologists [Unruh et al., 1994; Ken LaJoie, Personal communication] immediately after the Landers earthquake. The Unruh et al. study shows a series of parallel, linear fractures trending N-NE while more detailed mapping by Ken LaJoie in the field and using air photos also shows curved fractures similar to those seen in the SAR interferogram (Plate 4a and 4c). These fractures opened pre-existing structures and exhibited normal dip-slip separation of as much as 12 cm and lateral offsets of 5 cm or less [Unruh et al., 1994]. These structures are interpreted by Unruh et al., [1994] as evidence of pure northwest-southeast extension. The collocation of these fractures with extensional basins may show how, incrementally, the Troy Dry Lake bed was formed or may be related to internal deformation of the lake bed itself. The region surrounding the Newberry fractures and Calico fault shows a deviation from the fringe pattern expected from modeling an elastic lithosphere’s response to the earthquake [e. g. Massonnet et al., 1993]. This deviation could be due to inhomogeneities in the crust and may account for some of the anomalous motion at Mojave GPS network station TROY (Plate 4c) where motion was 150% of that expected from elastic half-space models [Miller et al., 1993].

Deformation near the Calico fault related to the Barstow earthquake cluster is a further example of small-scale deformation associated with the Landers earthquake induced stress field. Earthquakes of the Barstow cluster were confined to depths less than 10 km and occurred along a linear trend not related to any geologically mapped fault. The Barstow shocks began six to eight hours after the Landers main shock [Hauksson et al., 1993]. In the interferogram (Plate 5b), the only clear fringe pattern associated with the Barstow cluster occurs where its trend intersects the Calico and Coyote faults. However, there is negative shading in the phase gradient map aligned with the cluster (Plate 5a) that indicates diffuse right-lateral shear likely related to faulting at depth. The enclosed fringe patterns at the intersection of the Calico and Coyote Lake Faults (Plate 5b) are probably indicative of uplift of the Calico Mountains on the south-east side of the Coyote Lake Fault and subsidence on the north-west side of the Coyote Lake Fault as the Calico Fault accommodated a right-lateral offset.

Because GPS results adequately fit far-field coseismic displacements as predicted by an elastic half-space model [Bock et al., 1993; Blewitt et al., 1993], such a model can be presumed a good one for the large-scale displacement pattern associated with the earthquake rupture. Small-scale anomalies in the displacement field are most likely confined to the region within 100 km of the earthquake rupture and are likely due to interaction of crustal and surficial structures with the earthquake induced stress field. These small-scale anomalies could account for some of the deviation from an elastic half-space model in the near-field such as noted by Miller et al., [1993], Murray et al., [1993], and Hudnut et al., [1994].

It is unfortunate that more detailed field observations of the Landers earthquake rupture are not available to ground-truth InSAR observations. Air photos show offsets along some fractures that corroborate InSAR observations (Newberry fractures) but do not exhibit fine details such as seen in the Upper Johnson Valley region of the interferogram [Ken LaJoie, personal communication]. If InSAR observations including the displacement field and displacement phase gradient were made available within a few months of the earthquake, it might have been possible to plan field surveys to study features seen in the interferogram. Our own expedition into the field (January, 1997) indicated that much of the millimeter and centimeter scale deformation has been eroded by natural processes and recreational vehicles.

SAR interferometry allows near total spatial coverage of the radar LOS deformation and the gradient of the radar LOS deformation in the region of a major earthquake. This spatial coverage allows us to study heterogeneity in the deformation field. This heterogeneity can be investigated using the phase gradient map which highlights offsets on major faults, secondary fractures, and geologic structures that aren’t apparent in interferogram fringe maps. Interpretations of these interferogram fringe and phase gradient maps depend on ancillary information including geological field mapping, GPS measurements, and lithospheric modeling to determine meaningful displacements on and across geological structures.

Our observations show that there is localized heterogeneity in the deformation field of the Landers earthquake within 80 - 100 km of the main rupture. Unmapped faults or questionable extensions of previously mapped faults which experienced triggered slip are highlighted by the phase gradient observations. Secondary fractures in the Upper Johnson Valley indicate a shear zone between the Johnson Valley fault and the main rupture that may include the region between the Lenwood fault and the Camp Rock fault occupied by the Fry and Ord mountains. Previously mapped fractures associated with extension in the Mojave Valley are apparent in the phase gradient map and corroborate field observations. Also, there are correlations between fringe patterns and geomorphology indicating incremental deformation of extensional and compressional structures including Iron Ridge, the Calico Mountains, Coyote Dry Lake, and Troy Dry Lake.

(A2a)

The range difference due to a spheroidal earth with no topography is equal to the parallel component of the baseline.

(A3)

(A4)

(A5)

To isolate the range change due to deformation, we remove the flat earth range change (see above) and the topographic range change estimated from other interferograms (see below).

(A6)

(A7)

Interferograms formed from full-resolution, SAR images contain significant phase noise. The gradient operation amplifies the shortest wavelength noise resulting in a noisy estimate of phase gradient. To suppress a portion of this noise, we filter the data before computing the gradient by forming a multi-look average using a Gaussian-shaped filter. We have designed a convolution filter that is nearly isotropic in ground-range/azimuth space consistent with the sampling frequency of the radar.

We thank Howard Zebker for help developing an InSAR processing system and for providing us with some of the algorithms used to process our data. Duncan Agnew suggested we formalize the relationship between the phase gradient and the deformation gradient tensor and pointed us towards important geodetic observations pertinent to this work. We thank Ken LaJoie and Bob Simpson for discussions aiding in the interpretation of the data. We thank Bernard Minster for a careful and constructive internal review. Finally, we thank Paul Rosen and Howard Zebker for helpful external reviews. This work was supported by NSF and NASA.

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