Ray‐reflectivity method for SH‐waves in stacks of thin and thick layers

Abstract

Summary Reflectivity and ray theories are united to produce a hybrid technique of computing synthetic seismograms for a plane layered medium in subcritical regions. Numerical experiments have indicated that this technique is useful when the depth structure is one composed of thick layers separated by finely layered zones. As the theory for wave propagation in a plane layered medium is well known, the simple SH case is investigated so that the basic idea of the method may be conveyed without an excess of mathematics that would be necessitated if the P‐SV problem were considered. In computing the ray‐reflectivity seismogram, the thick layers are treated using asymptotic ray theory while the thin‐layered zones are treated as quasiinterfaces where analogues of reflection and transmission coefficients called reflectivities and transmittivities are calculated utilizing a Thomson‐Haskell formulation. A stationary phase approximation is employed when evaluating the integral which gives the displacement due to an arbitrary ray propagating in the thick layers of the above‐mentioned medium, and the validity of this approximation is discussed. A comparison of ray, numerical integration (reflectivity) and ray‐reflectivity synthetic sections indicates that this method yields quite acceptable results for subcritical reflection work and is suitable for application in seismic interpretation as individual arrivals associated with ray‐paths in the thick layers may be identified. Furthermore, the method is quite cost efficient and may be extended to a medium where the thick layers are non‐planar using asymptotic ray theory in these layers. Copyright © 1982, Wiley Blackwell. All rights reserved