COMPARISON OF NUMERICAL AND ASYMPTOTIC ESTIMATES OF ELASTIC WAVE FIELD

Abstract

Wave field theories derived from asymptotic methods, principally the ray method are the basis for interpretation of experimental and numerical results in seismic research. The zeroth-order term in the ray method, which has hitherto been used for quantitative interpretation, inherits the polarization and spectral properties of uniform plane waves and thus cannot explain certain phenomena that show up clearly in numerical modeling. We propose a method for the ray interpretation of nonsteady-state elastic wave fields found from numerical calculations, which does not rely on explicit formulas for higher-order approximations. We describe the method for the case of an anomalous PS wave. The proposed method for ray interpretation of the propagation of elastic waves is readily extended not only to P and S body waves in a smoothly varying inhomogeneous medium, but also to surface waves and to certain diffraction phenomena (e.g., the caustic, the penumbra and the like). The simplicity of the method means that it can be incorporated without any special difficulty into practically any algorithm for exact solution of the direct problem.