Thematic Set: Depth migration velocity model building with wave equation imaging

In spite of impressive advances in the application of wave equation imaging technology to generate images of complex structures, ray-based tools are generally used for the equally important step of velocity determination. Closing the experimental loop, by using the same wave equation imaging algorithm to measure velocity and to obtain a final image, is more than just philosophically pleasing. In strata exhibiting complex velocity structure, wave equation migration algorithms may be the only tools able to image some reflectors, so it stands to reason in such cases that only a wave equation velocity update can reliably measure velocity errors near these reflectors. In this article, we present a wave equation velocity update scheme, similar to depth focusing analysis, utilizing the time-shift imaging condition. We demonstrate the robustness of this approach under salt and in a land fault shadow example with limited acquisition effort. A common criticism levied against wave equation migration is the difficulty in efficiently obtaining 3D angle gathers (incidence, azimuth, and dip angle). We also present an efficient Fourier-domain angle decomposition technology for wave equation migration and demonstrate efficacy on synthetic and field data examples.