Deriving the eikonal approximation: a scattering diagram tutorial
Kristopher A. Innanen
"Diagram analysis" is a way of parsing, classifying, and manipulating the non-linear terms of inverse scattering, ultimately aiding in the derivation of new seismic processing algorithms. Scattering diagrams originate in forward as opposed to inverse scattering, and so an introduction to these topological organizational devices is best accomplished by considering the forward problem. We will use them to help derive a familiar expression in wave theory. The eikonal approximation, a relative of the WKBJ approximation, can be arrived at in several ways, for instance by direct integration of the Lippmann-Schwinger equation. In this paper we will demonstrate that, by retaining only Born series terms that correspond to a certain class of scattering diagrams, the same approximation can be recovered. In fact the diagram derivation could be argued to achieve its goal in a less roundabout way than the older approach.