Seismic modeling: A frequency‐domain/finite‐element approach

Abstract

One of the most important applications in seismic modeling is to determine the effects of topography, weathering zones, and complicated structure on seismic data in designing data acquisition techniques and in evaluating seismic processing techniques including ground roll removal, static analysis, velocity analysis, migration, and seismic stratigraphy. To mimic seismic field data, one must be able to simulate efficiently roll-along seismic data acquisition, where the source locations are progressively moved along the Earth’s surface or down a borehole. Conventional timedomain finite-difference, finite-element, and spectral techniques accurately model scalar and elastic wave equations, but their costs increase linearly with the number of source locations. In addition, since these methods are implemented as explicit time marching schemes, it is not clear how to model seismic attenuation (l/Q) which depends upon the strain rate. Instead of solving the equation of motion in the time domain, this paper shows how one can solve them in the temporal frequency (w) domain using a Petrov-Galerkin finite-element technique. The advantages of the frequency-domain finite-element technique are (1) efficient multiple source modeling, (2) accurate inclusion of attenuation (l/Q) effects, (3) no stability limitations, and (4) ease of coupling to boundary integral and other nonlocal boundary conditions. Examples illustrating the application of this method include surface seismic, offset VSP, and sonic wave train logging techniques.