Quasi-static and quasi-dynamic modeling of earthquake failure at intermediate scales

We present a model for earthquake failure at intermediate scales (space: 100 m-100 km, time: 100 m/nu(shear)- 1000's of years). The model consists of a segmented strike-slip fault embedded in a 3-D elastic solid as in the framework of BEN-ZION and RICE (1993). The model dynamics is governed by realistic boundary conditions consisting of constant velocity motion of the regions around the fault, static/ kinetic friction laws with possible gradual healing, and stress transfer based on the solution Of CHINNERY (1963) for static dislocations in an elastic half-space. As a new ingredient, we approximate the dynamic rupture on a continuous time scale using a finite stress propagation velocity (quasi-dynamic model) instead of instantaneous stress transfer (quasi-static model). We compare the quasi-dynamic model with the quasi-static version and its mean field approximation, and discuss the conditions for the occurrence of frequency-size statistics of the Gutenberg-Richter type, the characteristic earthquake type, and the possibility of a spontaneous mode switching from one distribution to the other. We find that the ability of the system to undergo a spontaneous mode switching depends on the range of stress transfer interaction, the cell size, and the level of strength heterogeneities. We also introduce time-dependent log (t) healing and show that the results can be interpreted in the phase diagram framework. To have a flexible computational environment, we have implemented the model in a modular C++ class library.