Joint P- and S-wave velocity reflection tomography using PP and PS data: An approach based on co-depthing and differential semblance in scattering angle optimization

The velocity-depth ambiguity in depth migration is a well known problem stemming from several factors, such as limited aperture, band-limitation of the source and the interplay between parameters of the background medium contributing to the nonuniqueness of the problem. In addition, the isotropic assumption can cause severe depth errors in the presence of anisotropy. These are severe issues when considering PP and PS images from depth migration where geologically equivalent horizons should be mapped to the same depths. The present method is based upon the differential semblance misfit function in angle to find fitting background models. This requires amplitude-compensated angle-domain common image-point gathers to be uniform. Depth consistency between the PP and PS depth image is enforced through a regularization approach penalizing mistie between key imaged reflectors in addition to the differential semblance misfit function. By migration/map demigration, time information is obtained on the key reflectors of the PP and PS image. This time information, which is independent of the velocity model, can be map-migrated to reconstruct the reflectors in depth for a given background model giving an automatic way to quantify the depth discrepancy in the tomographic approach. An approximative simplification uses the normal-incidence point rays in the map migration. The method is presented in a general 3-D framework allowing for the use of true depth information such as well markers and the inclusion of anisotropy. A strategy is presented to retrieve all parameters of a transversly isotropic medium with a known symmetry axis depending on the available information. This is employed on an ocean bottom seismic field data set from the North Sea.