Seismic Wave Field Generation in Heterogeneous Geological Media Containing Multiple Cavities

Abstract

We develop a boundary integral equation (BIE) method for the numerical simulation of seismic motions in geological media containing multiple cavities under anti-plane strain conditions. We consider a half-plane of heterogeneous structure subjected to either time-harmonic incident shear waves or to body waves radiating from a seismic point source. Three different types of material heterogeneity are considered: (a) The density and shear modulus vary proportionally as quadratic functions of depth, but the wave speed remains constant; (b) the material is viscoelastic, with a shear modulus and density that vary with respect to the spatial coordinates in an arbitrary fashion, with a wave velocity is frequency and position–dependent; (c) the material has a depth-dependent shear modulus and constant density, yielding a linear wave velocity profile. This necessitates the development of three frequency-dependent integral equation schemes based on: (a) A Green’s function for a quadratically-graded elastic half-plane; (b) a fundamental solution for a viscoelastic full-plane with position–dependent wave speeds; and (c) a fundamental solution for an elastic full-plane with a linearly varying wave speed. Numerical examples are presented for inhomogeneous geological media containing any number of cavities of arbitrary geometry and position.