Second-and higher-order traveltimes for seismic imaging

A computer-implemented three-dimensional seismic imaging method comprising:

• a) providing accepted traveltimes for an accepted grid region of a seismic exploration volume;
• b) providing tentative traveltimes for a set of close grid points situated one grid point away from the accepted grid region, the tentative traveltimes for the set of close grid points being arranged on a heap;
• c) selecting a minimum traveltime from the tentative traveltimes, the minimum traveltime corresponding to a minimum-traveltime grid point;
• d) saving the minimum traveltime as an accepted traveltime, thereby adding the minimum-traveltime grid point to the accepted grid region;
• e) adding neighbors of the minimum-traveltime grid point which are not in the accepted grid region to the set of close grid points;
• f) computing tentative traveltimes for the neighbors using a high-order finite-difference approximation to the eikonal equation if enough accepted traveltimes are available, or a first-order finite-difference approximation to the eikonal equation otherwise;
• g) putting the tentative traveltimes for the neighbors on the heap;
• and
• h) employing the accepted traveltimes to generate an image of the volume.

A computer-implemented three-dimensional seismic imaging method comprising:

• a) computing accepted traveltimes for grid points of a seismic exploration volume, by
• establishing a narrow band of grid points adjacent to a traveltime front at each of a plurality of positions of the traveltime front in the volume,
• establishing a heap of tentative traveltimes for the narrow band,
• saving a minimum traveltime from the heap as an accepted traveltime in a traveltime output grid, and
• advancing the front at a minimum traveltime grid point corresponding to the minimum traveltime using a high-order approximation to the eikonal equation if enough upwind accepted traveltimes are available, and using a first-order approximation otherwise;
• and
• b) imaging the volume using the accepted traveltimes.

A computer-implemented seismic data processing method comprising the steps of:

• a) providing a set of seismic signals for a target seismic exploration region;
• b) providing a velocity model for the target region;
• c) computing a set of traveltimes for the target region by providing traveltimes for grid points in an accepted grid region within the target region, and, for each target grid point for which an accepted traveltime is to be computed,
• determining whether enough neighboring traveltimes are available for a high-order traveltime computation operator,
• if enough traveltimes are available, computing a traveltime for the target grid point using the high-order operator, and
• if enough traveltimes are not available, computing the traveltime for the target grid point using a first-order traveltime computation operator;
• and
• d) processing the seismic signals using the set of traveltimes to characterize a propagation of the seismic signals through the target region.

A computer-implemented three-dimensional seismic data processing method comprising the steps of:

• a) providing a set of seismic signals for a seismic exploration volume;
• b) providing a velocity model for the volume;
• c) generating a set of accepted traveltimes for the volume by
• providing accepted traveltimes for an accepted grid region within the volume,
• providing tentative traveltimes for a set of trial grid points arranged in a narrow band around the accepted grid region,
• arranging the tentative traveltimes on a heap,
• selecting a minimum traveltime from the heap as an accepted traveltime, thereby adding to the accepted grid region a minimum-traveltime grid point corresponding to the minimum traveltime,
• adding a neighbor of the minimum-traveltime grid point which is not in the accepted grid region to the set of trial grid points,
• determining whether enough accepted traveltimes are available for a high-order traveltime computation for the neighbor,
• if enough accepted traveltimes are available, computing a tentative traveltime for the neighbor using a high-order traveltime computation operator,
• if enough accepted traveltimes are not available, computing the tentative traveltime for the neighbor using a first-order traveltime computation operator,
• putting the tentative traveltime for the neighbor on the heap, and
• advancing the accepted grid region to generate the set of accepted traveltimes;
• and
• d) processing the seismic signals using the set of accepted traveltimes to characterize a propagation of the seismic signals through the volume.

A computer system programmed to perform a seismic data processing method comprising the steps of:

• a) providing a set of seismic signals for a target seismic exploration region;
• b) providing a velocity model for the target region;
• c) computing a set of traveltimes for the target region by providing traveltimes for grid points in an accepted grid region within the target region, and, for each target grid point for which an accepted traveltime is to be computed,
• determining whether enough neighboring traveltimes are available for a high-order traveltime computation operator,
• if enough traveltimes are available, computing a traveltime for the target grid point using the high-order operator, and
• if enough traveltimes are not available, computing the traveltime for the target grid point using a first-order traveltime computation operator;
• and
• d) processing the seismic signals using the set of traveltimes to characterize a propagation of the seismic signals through the target region.

A computer-readable medium encoding instructions to perform a seismic data processing method comprising the steps of:

• a) providing a set of seismic signals for a target seismic exploration region;
• b) providing a velocity model for the target region;
• c) computing a set of traveltimes for the target region by providing traveltimes for grid points in an accepted grid region within the target region, and, for each target grid point for which an accepted traveltime is to be computed,
• determining whether enough neighboring traveltimes are available for a high-order traveltime computation operator,
• if enough traveltimes are available, computing a traveltime for the target grid point using the high-order operator, and
• if enough traveltimes are not available, computing the traveltime for the target grid point using a first-order traveltime computation operator;
• and
• d) processing the seismic signals using the set of traveltimes to characterize a propagation of the seismic signals through the target region.

A seismic imaging apparatus comprising:

• a) means for providing a set of seismic signals for a seismic exploration volume;
• b) means for providing a velocity model for the volume;
• c) means for computing a set of traveltimes for the volume by providing traveltimes for grid points in an accepted grid region within the volume, and, for each target grid point for which an accepted traveltime is to be computed,
• determining whether enough neighboring traveltimes are available for a high-order traveltime computation operator,
• computing a traveltime for the target grid point using the high-order operator if enough traveltimes are available, and
• computing the traveltime for the target grid point using a first-order traveltime computation operator if enough traveltimes are not available for the high-order operator;
• and
• d) means for processing the seismic signals using the set of traveltimes to characterize a propagation of the seismic signals through the volume.