Cagniard–De Hoop method

Summary

The Cagniard–De Hoop method is a technique to find exact closed-form solutions of transient wave problems in media made of homogeneous layers or half-spaces. It combines a Laplace transform in time with a transform in the horizontal coordinates, and then deforms the integration contour in the complex plane. On the deformed path the solution is visibly the Laplace transform of an explicit function of time, which can then be read off. It is a standard tool of elastodynamics and of seismology, for example for pulses in an elastic half-space.