Shortest Path Raytracing on Tetrahedral Meshes

An algorithm to perform raytracing on tetrahedral meshes with the shortest path method is presented. Parameterization in terms of unstructured meshes allows better fitting of the discrete model to structures with arbitrary geometries. To build the raytracing graph, the discretization scheme employs primary nodes at the vertexes and secondary nodes on the edges and faces of the tetrahedra. Improvement of the raytracing accuracy is achieved when compared to results obtained with rectilinear grid of comparable (and to some extent larger) cell size. Compared to rectilinear grids, an increased computational effort must however be deployed to generate the graph needed for raytracing. Besides, tests revealed that increasing the number of secondary nodes rather than refining the mesh appears to be the best approach to improve accuracy. The proposed algorithm appears appropriate for traveltime tomography schemes because it allows using meshes coarser than rectilinear grids for the same level of accuracy, thus reducing the size of the inverse system to solve.