Computing first-arrival seismic traveltimes on unstructured 3-D tetrahedral grids using the Fast Marching Method

Abstract

SUMMARY The Fast Marching Method is an efficient numerical algorithm for propagating interfaces such as first-arrival seismic wave fronts travelling through a velocity distribution. Fast Marching solutions have been developed for use on rectilinear grids in 2-D and 3-D. We are interested in unstructured grids as they provide some computational advantages when dealing with complicated shapes that are difficult to represent with rectilinear grids. Fast Marching solutions have also been developed for unstructured 2-D triangular grids but this has yet to be extended to unstructured 3-D tetrahedral grids. In this paper, we extend the Fast Marching Method to unstructured 3-D tetrahedral grids using a derivation that follows the 2-D case. The resulting equations are discussed in intuitive terms and an error analysis is performed. Our method is applied to a simple synthetic example and to a more complicated model based on the Voisey's Bay massive sulphide deposit in Labrador, Canada.