Second-and higher-order traveltimes for seismic imaging

Abstract

Seismic traveltimes are computed using a conditional high-order method: the traveltime computation operator is second- or higher-order if enough suitable upwind traveltimes are available, and first-order otherwise. Typically, a first-order operator is employed only around singularities, e.g. corners and cusps; a high-order operator is employed for the vast majority of grid points in the target volume. Selectively switching to first-order makes the method relatively simple and computationally efficient, as compared to a pure high-order method. At the same time, most traveltimes are computed to high-order accuracy. In the preferred embodiment, the traveltime front is selectively advanced at its minimum traveltime grid point, using a finite-difference approximation to the eikonal equation. A narrow band propagation zone is used to advance the finite-difference stencil. Tentative traveltimes for the narrow band adjacent to the traveltime front are computed using the eikonal equation and arranged on a heap. The minimum traveltime (top of the heap) is selected as an accepted traveltime, saved in the output table, and removed from the heap. Tentative traveltimes for all non-accepted grid points neighboring the selected point are then computed/recomputed and put on the heap.