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F. F. Pollitz, C. Wicks, W. Thatcher

Mantle Flow Beneath a Continental Strike-Slip Fault: Postseismic Deformation After the 1999 Hector Mine Earthquake, Science, 293, pp. 1814-1818, 2001.

[Online Article][Printable Article (1.19 Mb)]

Fred F. Pollitz, Chuck Wicks, Wayne Thatcher
U.S. Geological Survey,
MS 977, 345 Middlefield Road Menlo Park, CA, USA

Abstract: Two recent large earthquakes in the Mojave Desert, California--the magnitude 7.3 1992 Landers and magnitude 7.1 1999 Hector Mine earthquakes--have each been followed by elevated crustal strain rates over periods of months and years. Geodetic data collected after the Hector Mine earthquake exhibit a temporally decaying horizontal velocity field and a quadrant uplift pattern opposite to that expected for localized shear beneath the earthquake rupture. We interpret the origin of this accelerated crustal deformation to be vigorous flow in the upper mantle in response to the stress changes generated by the earthquake. Our results suggest that transient flow in the upper mantle is a fundamental component of the earthquake cycle and that the lower crust is a coherent stress guide coupling the upper crust with the upper mantle.

Mineral physics dictates that beneath the continental upper crust, the temperature of rocks is sufficiently high that the underlying lower crust and mantle flow through various solid state creep mechanisms (1-4). The mechanics of stress evolution in Earth's continental crust remain to be resolved. Central issues are whether strain accumulation in continental shear zones is driven by thick bounding blocks or by localized shear beneath the faults, whether the lower crust flows more or less readily than the upper mantle, and whether faults penetrate to depths substantially greater than seismogenic depths (~15 km in the western United States). Postseismic readjustment of the crust after the 16 October 1999 Hector Mine earthquake (Fig. 1A) carries large signals from potentially deep flow processes, and observations of this readjustment can characterize its mechanism, as well as yield clues to the rheology of the lower crust and upper mantle.

We analyzed synthetic aperture radar (InSAR) and Global Positioning System (GPS) data collected during the first 9 months after the Hector Mine earthquake (Figs. 1, B, C, and E, and 2, A and B) to determine the postseismic surface velocity field. The Hector Mine earthquake involved about 2 m of right-lateral slip along a 40- to 50-km-long fault (5, 6), and the event altered the rate and pattern of regional aseismic crustal deformation. The InSAR data recorded range change, the change in distance between Earth's surface and an orbiting satellite (7, 8), during the 9-month postseismic epoch. The measured range change is attributed primarily to vertical movement of Earth's surface but is also affected by horizontal movements. A total of three image pairs, covering three different time periods over the first 9 months of the postseismic epoch, were used to construct the interferograms (Fig. 1, B, C, and E) (9). GPS data carry independent information about horizontal and vertical movements, but we restrict our analysis to the horizontal velocity field changes because of their relatively small errors.

Postseismic InSAR deformation exhibits local, near-fault motions, but here we focus on the long-wavelength signal (>~30 km), which exhibits a quadrant pattern. This pattern is similar for the three depicted time periods, as shown by the interferograms and a fault-parallel profile (Fig. 3). The two independent longer interferograms (Figs. 1, C and E, and 3, B and C), which have no scenes in common, show the strongest similarities, including range decrease lobes (predominantly uplift) centered on (35.1°N, -116.0°E) and (34.3°N, -116.3°E) and a range change increase lobe (subsidence) near (34.7°N, 116.8°E). The short, 1-month-long interferogram (Figs. 1B and 3A) has lower amplitudes, but it shares the same long-wavelength behavior west of the Hector Mine fault. Features near the eastern edge of the interferograms represent elevation-dependent noise (Fig. 1, B, C, and E). If interpreted in terms of vertical motions, the range change pattern would indicate ~15 to 20 mm of uplift in the north and south quadrants and a similar amount of subsidence in the east and west quadrants. The InSAR and GPS data sets contain about 30 to 40 mm/year of velocity signals; the horizontal postseismic velocity is about four times higher than the cumulative pre-1992 velocity across all of the central Mojave faults (10, 11). These features suggest a deep transient source for the postseismic deformation, and we consider two possible processes: (i) afterslip on discrete planes underlying the Hector Mine seismogenic ruptures and (ii) broadly distributed viscoelastic flow in the ductile lower crust and upper mantle (12). For purposes of modeling, we use the 20 October 1999 to 21 June 2000 time period for the InSAR and GPS data sets.

In our modeling approach, we consider three-dimensional displacement at point on Earth's surface between times t₁ and t₂ as

(1)

where u_def is afterslip-model or viscoelastic-model deformation, v_load is the secular tectonic-loading velocity field, u_trans represents uniform three-dimensional translation of all surface points, and u_tilt represents tilt about a horizontal axis. The corresponding range change is given by u(;t₁, t₂) · Î, where Î is the unit vector in the range direction.

The secular tectonic velocity field is constructed from a uniform engineering shear strain rate of 0.1 µstrain/year resolved on a N40°W-trending vertical plane, approximately the pre-Landers horizontal deformation field (11). The u_trans and u_tilt terms are determined by inversion of the data simultaneously with the deformation processes and remove the influence of errors in the reference frame of the data sets for that particular time interval. These arise mainly from imperfect knowledge of satellite orbits in the InSAR data as well as the motion of the Hector Mine epicentral area with respect to the regional International Terrestrial Reference Frame (ITRF97). Independent processing of the GPS data within the regional ITRF97 and rigid North America reference frames, respectively, shows that the former moves about 12 mm/year toward N10°E with respect to the latter. This differs somewhat from the ~8 mm/year toward N40°W motion of the central Mojave Desert with respect to stable North America determined from very long baseline interferometry data (13), and this difference is essentially absorbed by u_trans. The deformation component u_def(r; t) is calculated from appropriate dislocations imposed within the upper portion of a spherically layered viscoelastic Earth model, consisting of an elastic upper crust underlain by a viscoelastic lower crust and upper mantle of viscosity _c and _m, respectively (14).

Models are evaluated in terms of the L₁ or L₂ norm misfit, weighted by the data errors, with respect to the null model or a particular physical model (in the L₂ case, the initial and residual variance, respectively). In particular, variance reduction is defined as 100% × (1 - residual variance/initial variance).

To estimate an afterslip model, we invert in a least squares sense the GPS data set alone for distributed right-lateral afterslip at 16- to 36-km depth on hypothetical vertical planes beneath two representative Hector Mine rupture planes (15) (red segments of Fig. 2A) yielding ~100 mm/year of afterslip on these planes. Calculated horizontal velocity is in reasonable agreement with observed velocity (Fig. 2A), but the calculated range change (Fig. 1F) is anticorrelated with the observed range change (Fig. 1E), leading to a poor fit (variance reduction = -55%). This modeling does not include any contribution of post-Landers relaxation, but its inclusion can account for only a small fraction of the observed range change. The peak-to-peak variation in range change rate over the area from late 1992 to early 1996 was about 15 mm/year (16). Furthermore, the post-Landers range change rate based on a viscoelastic coupling model (16), projected forward to the early post-Hector Mine epoch, is only 6 mm/year, so that any contribution of post-Landers relaxation beyond the 1999 Hector Mine event will probably be much smaller than the ~40 mm/year signal in the post-Hector Mine interferograms. The InSAR mismatch cannot be remedied with any distribution of deep afterslip beneath the Hector Mine rupture along a right-lateral fault, involving either deeper or more laterally extensive dislocation surfaces, nor with inclusion of post-Landers relaxation effects, and for this reason joint inversion of the InSAR and GPS data sets cannot yield a physically plausible afterslip distribution.

A model of postseismic relaxation of the lower crust and upper mantle successfully explains these data. A grid search of residual misfit of the separate InSAR and GPS data sets with respect to the viscoelastic deformation model is obtained as a function of _c and _m (Fig. 4). The misfit patterns show that mantle viscosity is between ~3 and 8 × 10¹⁷ Pa s and that _{c m}; i.e., the mantle is more ductile than the lower crust (17). We consider a forward model with preferred values _m = ~4 × 10¹⁷ Pa s and _c = 1.1 × 10¹⁹ Pa s (Fig. 4). The calculated deformation patterns (Figs. 1D and 2B) fit the primary features of the observed postseismic range change and horizontal velocity fields. Variance reduction with respect to the InSAR data set is 67%. Fits of the postseismic model to GPS time series at representative sites (Fig. 2C) are in harmony with the exhibited time decay over the first 8 months.

Our results are consistent with the nonlinearity of upper mantle viscosity inferred from laboratory experiments of ductile olivine flow (2). The spatial pattern of deformation is unchanged from the earliest post-Hector Mine interval (Figs. 1 and 3), indicating that the same process is operative throughout the 9 months after the earthquake. Averaged over the first 8 months, deformation is matched best by _m ~ 3 to 8 × 10¹⁷ Pa s. In contrast, observations from 3 months to 3 years after the 1992 Landers earthquake, 30 km to the west, require _m ~ 6 to 8 × 10¹⁸ Pa s (16), an order of magnitude larger. Indeed, the Hector Mine interferograms suggest a factor of ~three increase in effective viscosity during the first 9 months after the Hector Mine earthquake, as demonstrated by the misfit patterns of the fault-parallel profiles as a function of viscosity (Fig. 3D). These and corresponding misfit patterns of two post-Landers interferograms (Fig. 3D) indicate that mantle viscosity is initially low after a large stress step, gradually increases with time, and converges to 1 to 3 × 10¹⁹ Pa s after 1 to 3 years of relaxation. Results obtained after the 1992 and 1999 earthquakes indicate stress dependence of the effective viscosity of the upper mantle.

Elsewhere in the western United States, mantle viscosity as inferred from lake drainage (18) and glacial unloading (19) sources is about 10¹⁹ Pa s, about the same as inferred for the 3-month to 3-year post-Landers period. The filling of Lake Mead, Nevada, about 250 km northeast of the central Mojave Desert in a similar tectonic environment, produced long-wavelength transient crustal deformation that requires the presence of a weak mantle of viscosity ~ 10¹⁸ Pa s (20). The high ductility of the sub-Mojave Desert mantle is further supported by isotopic studies (21, 22) that associate young (<1 million years ago) mantle-derived basalts with an asthenospheric source between about 50- and 70-km depth.

Extrapolation of laboratory-derived flow laws suggests that Earth's continental crust should flow under lower stresses than does the uppermost mantle (1-4) and that the relative strength of the mantle should persist to those depths where heat transport remains predominantly conductive, about 100-km depth for a moderate geothermal gradient. However, the documented inferences of high mantle ductility throughout the western United States demand a much thinner conductive layer, and Pollitz et al. (16) pointed out that the sub-Mojave viscosity profile is consistent with an upper mantle composed of hydrous olivine with temperature between the wet and dry basalt solidus reached within the top 30 km of the mantle. Furthermore, geochemical (23) evidence suggests a mafic composition for the lower crust beneath the central Mojave desert, which could enhance its strength (24). Modeling of isostatic rebound of Lake Bonneville (25) and loading of Lake Mead (20) require a strong elastic crust about 30 km thick, consistent with our results and again suggesting behavior that is more generally applicable to the western United States.

On the other hand, other evidence supports lower crustal flow in an actively deforming continental crust. However, these processes may result from unusual thermal conditions not found in many active regions. In strongly extended crust, the requirements of isostacy (26) and observations of crustal imaging (27) strongly suggest lower crustal flow beneath metamorphic core complexes. In active mountain belts, lower crustal flow has been proposed to explain both the characteristic topography and observed partitioning among thrust, strike slip, and extensional strains (28, 29). Detailed structural mapping and geochronology in a number of core complexes show that magmatism invariably precedes upper crustal extension (30) and proposed lower crustal flow, perhaps because of delamination of the lithospheric mantle. Such a thermal event would weaken lower crustal rocks (31), whereas subsequent flow and isostatic uplift would cool and restrengthen the lower crust. Lower crustal flow beneath mountain belts is documented in overthickened crust, with lower crustal rocks at more than twice their typical depths. At depths of ~50 km or more, these rocks would be at temperatures where their behavior is expected to be ductile, explaining their inferred flow in a way that is consistent with our results. Our inference of upper mantle postseismic flow suggests that during part of the seismic cycle, the lower crust acts as a stress guide coupling the upper crust to mantle motions.

References and Notes

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.	We thank D. Sandwell, W. Prescott, J. Svarc, K. Hudnut, N. King, and S. Kirby for helpful discussions; J. Savage and R. Stein for constructive reviews; D. Dreger for providing the Hector Mine coseismic model; and G. Bawden for assistance with graphics. We acknowledge the Southern California Integrated GPS Network and its sponsors, the W. M. Keck Foundation, NASA, NSF, the U.S. Geological Survey, and the Southern California Earthquake Center, for providing GPS data used in this study. This paper benefited from constructive criticisms by two anonymous reviewers.