Cagniard Method in Complex Time Revisited.

摘要

The Cagniard-de Hoop method is ideally suited to the analysis of wave propagation problems in stratified media. The method applies to the integral transform representation of the solution in the transform variables (s,p) dual of the time and transverse distance. The objective of the method is to make the p-integral take the form of a forward Laplace transform, so that the cascade of the two integrals can be identified as a forward and inverse transform, thereby making the actual integration unnecessary. Typically, the method is applied to an integral that represents one body wave plus other types of waves. In this approach, the saddle point of w(p) that produces the body wave plays a crucial role because it is always a branch point of the integrand. Furthermore, the paths of steepest ascent from the saddlepoint are always the tails of the Cagniard path.