Seismic data processing including variable water velocity estimation and compensation therefor

A computer system programmed to correct input seismic data for time-variable water velocities comprising:

• at least one memory device configured to store the input seismic data and computer program instructions;
• and
• at least one processor for executing the computer program instructions to:
• determine traveltime discontinuities in the input seismic data which are associated with the time-variable water velocities;
• transform the input seismic data from a data space that contains the traveltime discontinuities into a model space which does not contain the traveltime discontinuities;
• and
• reverse transform the transformed seismic data from the model space back into the data space,
• wherein the processor transforms the seismic data by using a conjugate gradients solver and an equation which includes operators based on the traveltime discontinuities to estimate the model-domain signal which reverse transforms to give the input seismic data.

A method, stored in a memory and executing on a processor, for correcting input seismic data for time-variable water velocities, the method comprising:

• transforming input seismic data from a data acquisition space to a model space depending on slant coordinates and enabling decomposition into plane waves, the transforming incorporating travel-time discontinuities;
• compensating for water-column velocity variations by phase-shifting the plane waves to eliminate the travel-time discontinuities;
• reverse transforming recombined phase-shifted plane waves back into the data acquisition domain to obtain seismic data corrected for time-variable water velocities;
• and
• generating an image of a formation under the seafloor using the seismic data corrected for time-variable water velocities.