Annular-sum transform of irregularly sampled seismic data

A computer-readable storage medium having stored thereon computer-executable instructions which, when executed by a computer, cause the computer to:

• receive seismic data acquired at irregularly spaced seismic sensors in a survey area;
• define a plurality of regularly spaced locations in the survey area;
• form a circle around one of the plurality of regularly spaced locations, wherein the circle has a radius such that a portion of the irregularly spaced seismic data is inside an annular ring;
• define an outer limit of the annular ring as the radius plus a half width of the annular ring such that the portion of the irregularly spaced seismic data is inside the annular ring;
• define an inner limit of the annular ring as the radius minus the half width of the annular ring;
• and
• interpolate the portion of the irregularly spaced seismic data inside the annular ring to estimate seismic data that would have been acquired at the one of the plurality of regularly spaced locations.

A computer system, comprising:

• a processor;
• and
• a memory comprising program instructions executable by the processor to:
• receive seismic data acquired at irregularly spaced seismic sensors in a survey area;
• define a plurality of regularly spaced locations in the survey area;
• form an annular ring around one of the plurality of regularly spaced locations;
• form two or more segments inside the annular ring, wherein the segments are equally sized;
• define two or more centers that correspond to the two or more segments;
• define a range for each center, wherein the range is defined as an area inside a first circle that contains the seismic data inside one of the segments;
• normalize the seismic data inside the range;
• compute a sum of the normalized seismic data inside the range;
• assign the sum of the normalized seismic data to the center;
• compute a sum of the centers;
• compute a product between the sum of the centers and a filter weight;
• and
• assign the product to the one of the plurality of regularly spaced locations.