Inverse methods for elastic waves in stratified media

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Abstract
Two methods of solving the inverse problem for elastic waves at normal incidence on horizontally stratified media are discussed: Goupillaud’s equal-travel-time-layer approach, and Ware and Aki’s inverse-scattering method. The scattering method is simplified by showing that the impedance is proportional to the square of the Jost solution at zero frequency. The scattering method is discretized and a recursion relation is found for the impedance. In the continuum limit, the two methods are equivalent where the impedance is continuous but nonequivalent at points of discontinuity. The scattering method assigns the arithmetic average across the jump to the jump point.