Elastic waves in periodically stratified media with interfacial slip

Abstract

A periodically stratified elastic media can be replaced by an equivalent homogeneous transverse isotropic medium in the long wavelength limit. The case of a homogeneous medium with equally spaced parallel interfaces along which there is imperfect bonding [M. Schoenberg, J. Acoust. Soc. Am. 68, 1516–1521 (1980)] is a special case of such a medium. Slowness surfaces are derived for all plane-wave modes through the equivalent medium and reflection coefficients for a half-space of such a medium are found. The slowness surface for the SH mode is an ellipsoid. The exact solution for waves in a medium with parallel slip interfaces is found using the matrix method for periodic media [K. Gilbert, J. Acoust. Soc. Am. Suppl. 1 66, S73 (1979)] applied to elastic waves. Explicit results are derived and in the long wavelength limit, shown to approach the results for waves in the equivalent homogeneous medium. Under certain conditions, a half-space of a medium with parallel slip interfaces has a reflection coefficient independent of the angle of incidence and thus acts like an acoustic reducing mirror.