Analysis of a dislocation model for earthquakes

TL;DR

This paper develops a simplified model for earthquake ground motion by approximating thin fault regions with surface representations, enabling more efficient numerical simulations of seismic events.

Contribution

It introduces a limit problem approximation for elasticity problems with thin fault regions, reducing computational complexity in earthquake modeling.

Findings

The limit problem accurately approximates the original elasticity problem.

Numerical examples demonstrate the efficiency of the surface representation approach.

The method simplifies simulations without significant loss of accuracy.

Abstract

Approximation of problems in linear elasticity having small shear modulus in a thin region is considered. Problems of this type arise when modeling ground motion due to earthquakes where rupture occurs in a thin fault. It is shown that, under appropriate scaling, solutions of these problems can be approximated by solutions of a limit problem where the fault region is represented by a surface. In a numerical context this eliminates the need to resolve the large deformations in the fault; a numerical example is presented to illustrate efficacy of this strategy.