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STRESS-SLIP-CONSTITUTIVE-LAW
FAULT MODELS
[c7, p201-202]]

A completely different class of large-scale-faulting models are now being developed to more realistically incorporate the fault-failure process into the earthquake deformation cycle (for example, Stuart, 1979; Tse and Rice, 1986). Instead of specifying slip on the platebounding fault, these models extrapolate from laboratory observations of the time-dependent frictional properties of rocks (for example, Dieterich, 1979; Tullis, 1988) to assign slip-stress-constitutive laws to the fault surface. As remotely applied stresses increase, each segment of the fault slips at a rate that depends on both the previous slip history and the current applied stress, and so the cycle of elastic-strain accumulation and release can be simulated. By specifying the depth dependence of fault frictional properties, a slip behavior nearly identical to that of the thick-lithosphere model ( Fig. 7.11A ) follows naturally. A sample calculation of this type (Tse and Rice, 1986) illustrates the method and shows typical results ( Fig. 7.13). After a large coseismic slip event in approxImately the upper 10 km of the model fault, transient postseismic slip occurs on both the coseismic fault plane and its downdip extension. As slip rates decline to near zero on the shallow segments of the fault, interseismic slip at greater depths approaches nearly steady-state values. Finally, near the end of the cycle, the constitutive model predicts an increase in slip rate on the shallow coseismic fault segment before the next large slip instability ("earthquake").

Although the appropriateness of this extrapolation of laboratory results to large-scale faulting is a matter of current debate and the scaling of laboratory parameters to the field is uncertain, Tse and Rice's calculations clearly demonstrate that the principal observed features of the earthquake deformation cycle on the San Andreas fault can be reproduced by such models. Ongoing laboratory studies should refine and modify the stressslip-constitutive laws, and geodetic and continuous strain-monitoring observations of preearthquake and postearthquake crustal deformation can test the applicability of these postulates to large-scale faulting processes.