Tutorial on the numerical modeling of edge diffracted waves by the ray method

Summary The concept of diffracted rays introduced by Keller (1962) opened the way for a ray approach in the numerical modeling of the diffraction phenomena frequently seen in the seismic field records. Unlike the computation of travel times, which has never caused any difficulties being governed by the same eikonal equation as are the rays of ordinary seismic body waves, the evaluation of the diffracted ray amplitude has been another story. In this paper we give a tutorial account of a highly promising technique for the computation of the ray amplitude of seismic waves diffracted by linear edges on seismic interfaces originally presented by Klem-Musatov (1980, 1995). We demonstrate the adequacy of this technique on a series of SH synthetic traces containing diffracted arrivals, some of them diffracted more than once. Our computer program is based on a successful combination of Klem-Musatov's approach with the zero order approximation of the Asymptotic Ray Theory (Červeny and Hron, 1980). We showed in the paper that both techniqúes are ideally suited for such a combination, since the ray amplitude evaluation in each of them is based on the same transport equation. In our tutorial review we present all formulae which are needed for a practical implementation of the method and provide their physical interpretation, wherver possible, by using the numerical examples presented in the paper.