Formulations of Solutions for Earthquake Source Models and Some Related Problems

Abstract

Expressions for displacement potentials due to a dip-slip fault and a strike-slip fault model with arbitrary dip angle are presented in Cartesian coordinates, cylindrical coordinates and spherical coordinates. From these results, displacements and stresses when the time variation of the source is a step function type are also derived.
It is shown that the solutions obtained above can easily be expanded to those for moving dislocation models.
In the last part of this paper, the solutions in polar coordinates are expressed in another polar coordinates with different origin. The expressions can immediately be applied to the problems of generation of seismic waves and excitation of the free oscillations of the earth due to a dislocation in a spherical earth.