From Cagniard's method for solving seismic pulse problems to the method of the differential transform

AbstractCagniard's method is well-known in mathematical geophysics. The integral transform method of Cagniard involves path deformations in the complex plane, residue calculus and, in some cases, branch cuts. The technique of the differential transform, which evolved from that of Cagniard, involves an integral-free transform and avoids the integral considerations associated with Cagniard's technique. These two techniques are examined here by considering their application to Garvin's problem, a classical pulse-propagation problem in geophysics. This examination demonstrates the superiority of the technique of the differential transform over that of Cagniard, thus confounding the belief that the intricate integral considerations involved in Cagniard's technique are unavoidable