Improving prestack time migration by least-squares equivalent offset method

Abstract

Time migration is an important tool to provide a subsurface image because it is faster and less sensitive to velocity errors than depth migration. However, a reliable and focused time migration image is achievable only with well-determined time-migration velocities. As an alternative of prestack time migration, equivalent offset migration (EOM) provides intermediate common scatterpoint (CSP) gathers that have higher fold and larger offset range than common midpoint (CMP) gathers, which enables precise focusing of the velocity semblance and accurate velocity analysis. However, direct implementation of EOM might introduce coherent mapping noise, which smears the velocity spectra and decreases the resolution of the final stacked image. We reformulate the EOM as a linear operator that maps CMP gathers to CSP gathers and then propose least-squares equivalent offset migration (LS-EOM) method that inverts for optimal CSP gathers by minimising the misfit between simulated and observed CMP gathers. Compared with the EOM method, LS-EOM provides noise-free CSP gathers, leading to better focusing of the velocity semblance and higher resolution of the final stacked image. Both synthetic and field data tests demonstrate the effectiveness of our proposed method.