Head and Reflected Waves from an SH Line Source in a Dipping Layer Overlying an Elastic Medium

Abstract

The displacements due to a periodic and impulsive line source of SH waves in a dipping layer overlying an elastic solid are theoretically investigated using a reflected wave formulation. A formal solution is found by which the contributions due to head and reflected waves are determined by evaluation of the integrals by the method of steepest descent. Although the individual waveforms are similar for the wedge and the horizontally layered case, the synthetic seismograms are markedly different due to the difference in travel times.
Using ray paths, the contributions of the integrals have been interpreted. The range of existence of head waves has been examined and the discontinuities in the wedge associated with diffracted waves studied. In the case of a free or rigid lower boundary of the wedge, the dispersion relation has been determined.