Kirchhoff–Helmholtz reflection seismograms in a laterally inhomogeneous multi‐layered elastic medium – II. Computations

Abstract

Summary. High‐frequency reflection and refraction seismograms for laterally variable multi‐layered elastic media are computed by using the frequency domain elastic Kirchhoff–Helmholtz (KH) theory of Frazer and Sen. Both source and receiver wavefields are expanded in series of generalized rays and then elastic (KH) theory is applied to determine the coupling between each source ray and each receiver ray at each interface. The motion at the receiver is given as a series of integrals, one for each generalized ray. We use geometrical optics and plane wave reflection and transmission coefficients for rapid evaluation of the integrand. When the source or the receiver ray field has caustics on the surface of integration geometrical ray theory breaks down and this gives rise to singularities in the KH integrand. We repair this using methods suggested by Frazer and Sen. Examples of reflection seismograms for 2‐D structures computed by elastic KH theory are shown. Those for a vertical fault scarp structure are compared with the seismograms obtained by physical modelling. Then OBS data obtained from the mid‐America trench offshore Guatemala area are analysed by computing KH synthetics for a velocity model that has been proposed for that area. Our analysis indicates the existence of a small low‐velocity zone off the trench axis. No head wave arrivals are obtained in our KH synthetics since we do not consider multiple interactions of a ray with an interface. The nearly discontinuous behaviour of elastic R/T coefficients near the critical angle causes small spurious phases which arrive later than the correct arrivals. Copyright © 1985, Wiley Blackwell. All rights reserved