Hybrid Green's function for SH motion in a low velocity layer

Abstract

Wave motion in an elastic layer has been analyzed conventionally either in terms of normal (discrete and continuous) mode spectra or in terms of ordinary or generalized ray fields. Either of these representations is inconvenient for describing the motion over the entire range of observations from early to late arrivals. A recently developed hybrid formulation, wherein modal fields, ray fields and a remainder are combined according to specified criteria within a single rigorous framework, overcomes these difficulties, Combinations may be chosen that ensure smooth passage from the ray phase at early times to the modal phase at later times. The method is illustrated here on the two-dimensional time-dependent SH Green's function for a homogeneous sediment layer above a higher velocity homogeneous semi-infinite bedrock, with the source located in the sediment. The hybrid fields may include various combinations of trapped modes, leaky modes, trapped rays, leaky rays, and lateral rays (head waves). This study complements an earlier investigation wherein the source was located in the bedrock.