Raytracing in topological tetrahedral models

We examine 3-D seismic raytracing in tetrahedral models in which triangularly-tiled horizon surfaces have been embedded. The faceted nature of these surfaces introduces discontinuities in the ray parameter direction when surface normals are used to raytrace across the boundaries via Snell’s law. Since the ray parameter direction is a critical aspect of raytracing, some smoothing of the surface normals is required. The first method we examine is a simple averaging of normals around a vertex, similar to the Gouraud method (Glassner 1990) used for rendering faceted surfaces. We show, however, that significant improvements in raytracing accuracy can be achieved by defining a local radius of curvature for each triangle in the surface, and using it to precondition the normals at triangle vertices prior to averaging.