Exact Ray Theory and its Application to the Reflection of Elastic Waves from Vertically Inhomogeneous Media

Abstract

Summary The possibilities and limitations of the theoretical investigation of elastic waves in horizontally layered media with the aid of the exact ray theory are studied. In order to simplify the problem as far as possible, it is restricted to the propagation of sound waves from a line source in a layered-liquid medium. Three different types of the transition between two homogeneous liquids are investigated: a first-order discontinuity, a transition consisting of a prescribed number of homogeneous layers, and a transition layer with linear variation of sound velocity and density with depth. Theoretical seismograms are computed by exact formulas and by wave front approximations for the reflected waves in these models. From these results, the main conclusions about the applicability of the exact ray theory to studies of wave propagation in more complicated media are as follows: (1) The exact ray theory is applicable to the investigation of vertical and near-vertical reflections from inhomogeneous media without difficulties; and (2) continuously refracted waves in such media can be investigated by an approximation which is sufficient for many practical cases. The final aim of this study was to test whether the exact ray theory can be used to compute theoretical seismograms for seismological applications. Therefore, some approximations were developed which are useful for computations for realistic models of the Earth's crust and upper mantle. An Earth-flattening approximation is given which accounts for the influence of the Earth's curvature on the propagation of body waves, and the approximate computation of point source seismograms from line source seismograms is described. An example of theoretical seismograms is presented for an upper mantle model, published by Julian & Anderson (1968).