Dynamic rupture on a planar fault in three-dimensional half space - I. Theory

Abstract

In this study, we extended the boundary integral equation method (BIEM) to include the effect of free surface, which is crucial for the interpretation of near-field observations of large earthquakes on dipping faults, which are buried shallower or rupture to the ground. On the basis of the Green's function in 3-D half space, the boundary integral equations (BIEs) for dynamic rupture propagation on a planar fault embedded in 3-D elastic half space are derived. Since the Green's function can only be expressed as double integration, rather than analytic closed form as in full space, computation of the BIEs for rupture dynamics in half space is rather complicated. Consequently, serious difficulties arise, including the existence of hypersingularities in the kernels and the computation of rapid oscillatory multiple integrals. To resolve them, we first systematically presented the effective regularization procedures, which consists of the generalized Apsel-Luco correction and the regularization algorithm proposed by Karami & Derakhshan to remove the hypersingularities, then proposed a simple while efficient algorithm to speed up the computation of integrals involved in the kernels of BIEs. Finally, the BIEM algorithm proposed in this study for modelling rupture dynamics of a fault with arbitrary dip angle in 3-D half space becomes exercisable, and provides a powerful tool for investigating the physics of earthquake dynamics.