3dgeo Development, Inc.

James A Sethian

Alexander M Popovici

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.

Second-and higher-order traveltimes for seismic imaging

Accurate and reliable traveltimes for a seismic exploration volume having a complex velocity structure are generated by selectively advancing a traveltime front at its minimum traveltime grid point, using an entropy-satisfying 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. The traveltime computation is fast, unconditionally stable, resolves any overturning propagation wavefronts, and ensures that the eikonal equation is globally solved for each point of the 3-D grid. The traveltimes accurately characterize the propagation of seismic signals through the volume. The traveltimes are used for accurately imaging the volume.

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James A Sethian