Response of Layered Half-Space Obtained Directly in the Time Domain, Part I: SH Sources

Abstract

A rigorous method is presented to obtain—directly in the time domain and without the need for an integral transform over frequencies—the seismic response of horizontally layered, viscoelastic half-spaces due to arbitrarily distributed (or concentrated) sources. The method is based on exact expressions for the response of the underlying half-space cast in the wavenumber-time domain, and a complete modal solution in that domain for the layers. The proposed method is highly effective and avoids the problems of the usual propagator matrix method that arise when numerical integrations over both frequencies and wavenumbers are carried out, especially the waviness of the kernels due to resonances and reverberations in the layers when damping is light or even absent. Part I presents the basic methodology for the relatively simple case of antiplane SH sources in two-dimensional space, while Part II generalizes the concept to two-dimensional SV - P line sources and to three- dimensional point sources, including seismic couples.