Orthogonal mesh generation for Riemannian wavefield extrapolation

Jeff Shragge

jeff@sep.stanford.edu

ABSTRACT

This paper presents a general method for generating 2D or 3D orthogonal coordinate systems. Developed coordinate systems are triplication free and appropriate for use in Riemannian wavefield extrapolation. This method exploits properties of potential function solutions of Laplace's equation. I show that certain specifications of a potential function's boundary conditions lead to a physical representation of equipotential surfaces where there are equivalent to extrapolation steps. Potential function solutions, obtained through conjugate gradient solvers, are used subsequently in a phase-ray-tracing procedure that generates geometric rays orthogonal to the equipotential surfaces. These rays collectively define an orthogonal coordinate system linked to the underlying Cartesian mesh through definable one-to-one mappings. The utility of this approach in generating coordinate systems is tested on a 2D model of rugged topography from the Canadian Foothills, and on 3D topography of the San Francisco Bay area.