In this project we have made two attempts to derive and model crustal deformation in southern California. One is study the postseismic deformation in the Landers area, and the other is to model long term deformation across the plate boundary.
1. Post-Landers relaxation constant estimation
In order to decimate the postseismic deformation signals of the Landers earthquake, we have done extensive processing and reprocessing of the GPS data collected from June 1992 to September 1995 in the Landers region. This effort is related to our velocity map endeavor, and has produced new solutions for the 1992, 1993, and 1995 post-Landers measurements.
Our next step is to combine 4-10 days daily solutions into experimental solutions. PGGA and IGS solutions are also included for the days which had no local sites surveyed. We then model the experimental solutions to obtain station position time series, using ITRF94 positions and velocities to constrain fiducial sites at Algonquin, Westford, Richmond, Yellowknife, Penticton, and Fairbank to 5, 5, 5 mm and 0, 0, 0 mm/yr for their N, E, U components, respectively.
In the vicinity of the coseismic rupture, their north components generally demonstrate stronger postseismic deformation signal than the east components. This observation is consistent with the sense of the coseismic motions at those sites. We use the north components of sites GOLD, PIN1, 7000, LAZY, and WIDE for relaxation constant estimation. Their station positions are modeled as a function of time by:
P_i(t) = P_i(t0) + V_i*(t-t0) + D_i*exp(-(t-t0)/tau)
where i denotes the i-th site, V_i is its long term velocity component, D_i is the amplitude of exponential relation, t0 the time of the earthquake, and tau the relaxation constant. A nonlinear inversion of the data yields tau = 33 days, 23 < t < 53 days at 95% confidence level.
Another attempt is made to search for the second relaxation component, if it exists. This is done by a 2-D grid search. Values of tau1 and tau2 are assigned each time, the data are inverted to estimate P_i(t0), V_i, D_i1, and D_i2. Result from the grid search reveals that the second relaxation term correlates highly with the long term deformation rate, and if exists, it should have a very large (years) relaxation constant. An F-test shows that this term is not significant at the 95% confidence level. This result indicates that our data support only one relaxation term at the time range from several days to one year. It however, cannot rule out the possibility that another relaxation term at the range of several years, also exists. In fact, the long term deformation rate in the region has sped up significantly since the earthquake (conclusion achieved by comparing geodetic estimates obtained from analyzing data measured before and after the earthquake), suggesting that such a long term relaxation is significant.
2. Long term deformation modeling using Finite Element Method.
In this study we have used a finite element code for a 2.5 D faulted medium that Kong and Bird wrote to model long term crustal deformation in California (Bird, 1989; Bird and Kong, 1994). The lithosphere is cut into blocks by faults with finite strength, and the deformation is driven by steady motion at remote boundaries. A nonlinear viscous "thin plate" is integrated in the vertical dimension of the lithospheric properties, which is also controlled by the in situ topography and heat flow.
The code was previously run on an IBM main frame. The first task we have performed is to convert the code and make it run on a Sun Ultra II workstation. This step is involved with rewriting some subroutines and doing case tests, we now have got the code running fine. We then make a series of forward modeling to fit the geodetic data (SCEC velocity map v.1.0, Shen et al., 1997) and the geological measurements (Kong and Bird, 1994). Fig. 1 shows the FEM grid, which is composed of 314 elements and 147 fault sections. Faults are denoted by solid curves; those without ticks are dipping 90 degrees, straight ticks dipping 65 degrees, square ticks 45 degrees, and triangle ticks 25 degrees, respectively. Fault locking depth is controlled by the local temperature profile, we define 410 degrees celsius isotherm as the boundary of brittle/ductile transition. We have adjusted 3 parameters: the fault strength of the San Andreas, the fault strength of the rest of the faults, and the activation energy in the nonlinear viscosity function. We have not finished the parameter searching yet; however, some preliminary conclusions can be made. First, the model seems to fit geological data better than geodetic data. Discrepancies with the geodetic data are largest at the Landers area and the Imperial fault zone, where deformation may reflect significant postseismic deformation rather than long term deformation. Such discrepancies can be seen in Fig. 2, which shows the strike slip components of fault slip rates predicted by the best fit model we have got so far. The geodetic data require centimeter level shear motion across the Mojave shear zone, whereas the model predicts only 1 mm/yr shear there. Second, the model seems favoring lower fault strength, as Bird and Kong (1994) found out. The San Andreas fault seems to favor fault strength of 0.10 to 0.20, lower than that for the rest of the faults.
Because we had only relatively short time to work on the modeling work, parameter searching and testing are far from finished. Other parameters should be considered in the searching list are the fault locking depth and the fault dip angles. Data selection may also be necessary, we need to screen out the geodetic data which are strongly influenced by postseismic deformation.
References
Bird, P., New finite element techniques for modeling deformation histories of continents with stratified temperature-dependent rheologies, J. Geophys. Res., 94, 3967-3990, 1989.
Bird, P., and X. Kong, Computer simulations of California tectonics confirm very low strength of major faults, Geol. Soc. Am. Bull., 106, 159-174, 1994.
Shen, Z.-k., D. Dong, T. Herring, K. Hudnut, D. Jackson, R. King, S. McClusky, L.-y. Sung, Crustal deformation measured in Southern California, EOS, 78, (43), 1997.
