Interpolation of a seismic velocity model using a projections onto convex sets method

A non-transitory computer-readable memory having computer-executable instructions stored thereon that, when executed by a computer processor, perform steps comprising:

• receiving a sparse seismic velocity model for a subterranean region of interest,
• wherein the sparse seismic velocity model comprises a plurality of populated positions and a plurality of missing positions, and
• wherein each of the plurality of populated positions comprises a velocity;
• determining an interpolated seismic velocity model by determining the velocity at each of the plurality of missing positions using the velocity at populated positions within the plurality of populated positions and interpolation;
• determining an intermediate dense seismic velocity model by updating the velocity at each of the plurality of missing positions using the interpolated seismic velocity model and projections onto convex sets method;
• determining a dense seismic velocity model using the intermediate dense seismic velocity model;
• receiving time-domain seismic data for the subterranean region of interest;
• determining depth-domain seismic data using the time-domain seismic data and the dense seismic velocity model;
• and
• generating a seismic image using the depth-domain seismic data.

A system comprising:

• a seismic processing system configured to:
• receive a sparse seismic velocity model for a subterranean region of interest,
• wherein the sparse seismic velocity model comprises a plurality of populated positions and a plurality of missing positions;
• and
• wherein each of the plurality of populated positions comprises a velocity,
• determine an interpolated seismic velocity model by determining the velocity at each of the plurality of missing positions using the velocity at populated positions within the plurality of populated positions and interpolation,
• determine an intermediate dense seismic velocity model by updating the velocity at each of the plurality of missing positions using the interpolated seismic velocity model and projections onto convex sets method,
• determine a dense seismic velocity model using the intermediate dense seismic velocity model,
• receive time-domain seismic data for the subterranean region of interest, and
• determine depth-domain seismic data using the time-domain seismic data and the dense seismic velocity model;
• and
• a seismic interpretation workstation configured to:
• generate a seismic image using the depth-domain seismic data, and
• determine a depth of a hydrocarbon reservoir using the seismic image.