The ray reflectivity method with critically refracted waves

Abstract The hybrid ray reflectivity technique which employs a combination of asymptotic ray theory and matrix methods for computing synthetic seismograms in a medium composed of thick layers separated by thin layered transition zones is reexamined. The original theoretical development had no provisions for critically refracted waves. Consequently, it was useful only at small source-receiver offsets. Using an asymptotic formulation, which employs matrix methods, a system is devised here to compute critically refracted wave amplitudes which originate from the top of the thick layer underlying a thin layered zone. This is done for all source-receiver offsets where a critically refracted wave may exist. It is usual practice to employ a less complicated form of the solution for critically refracted wave amplitudes than is used in this article. The solution presented here utilizes parabolic cylinder functions. However, the above mentioned solution is finite everywhere the critically refracted wave theoretically exists, even at the critical distance. This is deemed to compensate for the extra computing time required. In addition, a correction term to the reflected ray near the critical distance, both post- and precritical is presented. It is in this region where the critically refracted wave and the reflected wave interfere. The zero-order asymptotic ray theory amplitude, which is equivalent to the zero-order saddle point amplitude, is not accurate here. The usefulness of this approach is evidenced by the improved match between synthetic traces computed using the ray reflectivity and the Alekseev-Mikhailenko techniques. In particular, the existence of what have been termed “screened head waves” predicted by the ray reflectivity method and confirmed numerically using the highly Alekseev-Mikhailenko method, is of significance.