Quasi-static and Quasi-dynamic Modeling of Earthquake Failure at Intermediate Scales

Abstract

We present a model for earthquake failure at intermediate scales (space: 100 m-100 km, time: 100 m/vshear 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.