A deeper explanation: Mechanism of strain accumulation and release around a strike-slip fault zone

The mechanics of stress accumulation around a strike-slip fault zone depends on the effective thickness of the lithosphere as well as whether the lower lithosphere fails progressively with time or not. This is illustrated by the "thick-lithosphere" and "thin-lithosphere" models of Figure 1. In the thick-lithosphere case, loading is accomplished not only by the situation of the fault zone within a broad lateral shear zone but also by steady aseismic slip of a deep creeping zone beneath a shallow locked zone where stress is accumulating. In the thin-lithosphere case, no such slip at depth takes place, but stress concentration around the fault zone can still take place because of accelerated reloading of the fault zone following a cycle of previous earthquakes, as in the viscoelastic coupling model of Savage and Prescott (1978).

Complementing these two stress accumulation models are two possible postseismic mechanisms -- afterslip and viscoelastic flow (Figure 2). In the afterslip case the plastosphere directly beneath the seismic rupture undergoes aseismic slip and produces transient deformation of the upper lithosphere such that after sufficient time has elapsed the net displacement pattern will appear as two rigid blocks which have slid past one another. In the viscoelastic case, postseismic readjustment beneath the upper lithosphere involves continous flow in the plastosphere, leading to a different and continually-evolving state of deformation in the upper lithosphere.

In principle, geodetic data could distinguish between the two mechanisms using the horizontal deformation field alone provided that the strike-slip sources are finite length. We can gain an understanding of the behavior of the flowing regions beneath the seimogenic crust by analysis of GPS and InSAR data collected after large crustal earthquakes. Such data record the evolution of horizontal and vertical surface ground motion and can detect the effects of possible deep flow by recording just a few years of measurements. Analysis of triangulation data following historic large earthquakes such as the 1952 Kern County earthquake and 1857 Fort Tejon earthquake show quite large postseismic displacements accumulated over periods of 20 to 40 years, in these cases reaching >10 cm over and above that expected from steady background tectonic loading. Viscoelastic flow in the lower crust and mantle is capable of producing these transient displacements by coupling of the upper crust with these ductile regions.

An example of postseismic relaxation

Figure 3 shows the hypothetical normal fault event rupturing the top half of the upper crust. The grey and colored regions are purely elastic and viscoelastic portions of a coupled elastic-viscoelastic system. The arrows and color contours track cumulative displacement and strain (in the viscoelastic region) at the time of the earthquake and at 20 or 100 years after the earthquake in a profile bisecting the 200-km long fault. It is clear that vigorous flow deep below the rupture persists for a long time after the earthquake and that the surface deformation pattern evolves considerably from the coseismic state. The character of the transient surface displacement depends on the details of the viscoelastic stratification. This suggests that observations of GPS and InSAR data collected in the years after the earthquake hold the potential for elucidating the details of this stratification.

Postseismic strain in southern California

The 1992 M=7.3 Landers earthquake involved 3-4 meters of right-lateral strike slip on NNW-trending right-lateral faults with total length of about 80 km (Figure 4 ). The 1999 M=7.1 Hector Mine earthquake occurred about 30 to the east of the Landers rupture and had a similar amount of slip, with a fault length of about 50 km (Figure 4 ). A rich set of GPS data (Figure 5 ) and InSAR data (Figure 6 ) is available to study the postseismic deformation from the Hector Mine earthquake. These data exhibit deformation rates of 20-40 mm/yr in both horizontal and vertical velocity for 4 months following the earthquake. Elevated velocities up to 20 mm/yr persist for more than 2 years after the earthquake. All postseismic deformation rates are much larger than preseismic rates (as measured by the USGS Emerson transect) in the years prior to the earthquake.

A salient feature of the InSAR pattern is the long wavelength quadrant pattern of uplift and depression: uplift of the SW and NE quadrants and depression of the NW and SE quadrants. Such a vertical deformation pattern is opposite to that expected for any kind of deep afterslip mechanism. The long wavelength signal also suggests a deep source. Another key pattern in observed postseismic deformation is the large magnitude of horizontal postseismic velocities during the early (first 4 months) postseismic period.

Implications for mantle rheology

Pollitz, Wicks and Thatcher (2001) proposed that the postseismic uplift pattern measured by InSAR was caused by mantle relaxation of the coseismic stresses imparted by the Hector Mine earthquake. The found that a weak mantle of effective Maxwellian viscosity of 4 x 10^17 Pa s could explain the pattern and amplitude of vertical uplift for the first 8 months following the earthquake. Consideration of the time dependence of uplift revealed that the effective viscosity was larger the later the considered time period, e.g., interferograms spanning just the first few months after the earthquake suggested much smaller effective viscosities than later periods. Pollitz (2003) carried this result further with a detailed interpretation of the available GPS time series. He proposed that a mantle rheology defined by a Burgers body could explain the detailed spatial and temporal pattern of measured postseismic deformation. This rheology (Figure 7) is an analogue for combined transient and steady-state creep, the Kelvin element of the analogue corresponding to transient creep and the Maxwell element corresponding to steady state creep; the viscosity associated with the Kelvin element is much smaller than that of the Maxwell element, and the associated relaxation produces the relatively rapid postseismic motions observed in the first few months. Pollitz (2003) obtained viscosity values of 1.6 x 10^17 Pa s (corresponding to a material relaxation time of 0.07 years) for the Kelvin element and 4.6 x 10^18 Pa s (corresponding to a material relaxation time of 2 years) for the Maxwell element. The crust rheology, which was assumed to be Maxwellian in these studies, is invariably found to be several times larger than the larger (Maxwellian) viscosity of the mantle. This result echoes other geophysical evidence of a relatively weak mantle in tectonically active areas of continents. (See Jackson et al., 2002.) The estimated mantle viscosities in the Mojave Desert are compatible with a hydrous olivine mantle (e.g., Dixon et al., 2004).

In summary, the results of analysis of postseismic deformation data for several earthquakes point to a broadscale relaxation as the dominant postseismic process. This suggests that the thin lithosphere model (Figure 1) may be appropriate for describing the earthquake cycle at least within this part of the eastern California shear zone.