Strain softening prior to two‐dimensional strike slip earthquakes

Abstract

A model for two‐dimensional strike slip faulting in which the fault friction is displacement softening is analyzed to estimate preearthquake crustal deformation and conditions for an earthquake instability. The friction law is initially displacement hardening but becomes softening after the peak stress is surpassed. The peak stress increases with depth to a maximum before decreasing again. The material surrounding the fault is represented by elastic plates. Several deformation histories are calculated by solving numerically the quasi‐static, nonlinear problem subject to displacement boundary conditions simulating relative plate motion. When the crust is compliant or the fault is rapidly softening, an inertia‐limited instability results. Prior to the instability the point of maximum fault slip rate moves upward toward the greatest peak stress position. The slip causes a rapid increase in shear strain rate at the free surface near the fault trace. Although fault slip is monotonic, the average fault stress reaches a maximum and then decreases before the instability. When instability is not possible, a similar but smoother deformation episode results. Qualitative extrapolation of the computed results suggests that crustal earthquakes may be preceded by accelerating fault slip near the focus, particularly below, and that the enhanced slip rate may cause recognizable strain and tilt anomalies at the free surface.

On the Deterministic Description of Earthquakes

“…We can also see that in this model the weakening phase is not linear, as in the idealized model given by , but exponential, as earlier postulated by Lachenbruch [1980], and it recalls the theoretical derivation of Matsu'ura et al [1992], e( u / d ′)e −( u / d ′) [see also Stuart , 1979; Stuart and Mavko , 1979]. We also mention that an exponential weakening was also introduced by Rice [2006, equations (16) and (23)], in describing two end‐member models for thermal pressurization.…”

Seismic quiescence precursors to two M7 earthquakes on Sakhalin Island, measured by two methods

“…The idea that precursory creep might cause a redistribution (with local reduction) of stress, and hence quiescence, is also old (e.g. Sobolev, 1995;Stuart, 1979). It is also not easy to accept the idea that strain softening might influence volumes at large distances.…”

Linear complementarity formulation for 3D frictional sliding problems

“…Alternatively, the non-linear and/or dynamic frictional sliding problem, albeit significantly more complicated owing to more complicated physical phenomena, avoids the complications of the quasi-static frictional sliding problem as not all elements that comprise a particular fault require consideration at each time step, but rather only those to which elastic waves have propagated at that particular time step. The associated non-linear friction treatments have been studied for some time and involve evolution of friction due to slip, velocity, and time, among other processes, e.g., [21,25,39,43]. In the quasi-static case, each sliding element imposes a contribution to tractions on all elements simultaneously, complicating the numerical problem.…”