Seismic wave fields in continuously inhomogeneous media with variable wave velocity profiles

Abstract

In this work, elastic wave motion in a continuously inhomogeneous geological medium under anti-plane strain conditions is numerically investigated using the boundary integral equation method (BIEM). More specifically, the geological medium possesses a variable velocity profile, in addition to the presence of either parallel or non-parallel graded layers, of surface relief, and of buried cavities and tunnels. This complex continuum is swept either by time-harmonic, free-traveling horizontally polarized shear waves or by incoming waves radiating from an embedded seismic source. The BIEM employs a novel type of analytically derived fundamental solution to the equation of motion defined in the frequency domain, by assuming a position-dependent shear modulus and a density of arbitrary variation in terms of the depth coordinate. This fundamental solution, and its spatial derivatives and asymptotic forms, are all derived in a closed-form by using an appropriate algebraic transformation for the displacement vector. The accuracy of the present BIEM numerical implementation is gauged by comparison with available results drawn from examples that appear in the literature. Following that, a series of parametric studies are conducted and numerical results are generated in the form of synthetic seismic signals for a number of geological deposits. This allows for an investigation of the seismic wave field sensitivity to the material gradient and the wave velocity variation in the medium, to the presence of layers, canyons and cavities, and to the frequency content of the incoming signal.