Incorporating topography into wave-equation imaging through conformal mapping

Jeff Shragge and Paul Sava

jeff@sep.stanford.edu, paul@sep.stanford.edu

ABSTRACT

Conformal mapping is a technique used widely in applied physics and engineering fields to facilitate numerical solution of boundary value problems involving solution domains characterized by complex geometry. The predominant reason for applying a conformal mapping procedure is to transform an irregular solution domain to one of symmetric geometry. The conformal map transform has the property that the angle between neighboring arc segments is (locally) conserved under the mapping. Accordingly, in the context of wave-equation imaging under topography, conformal mapping can transform an irregular, topographically-influenced solution domain to a regular computational mesh. In this paper, we demonstrate that the use of the conformal mapping transform coupled with Riemannian wavefield extrapolation generates an orthogonal coordinate system and the governing wavefield contination equation required for wave-equation migration directly from a topographic surface. We illustrate the potential of this approach by migrating a 2-D prestack data set acquired on a geologic model of thrust belt.