Building adjoint operators for least-squares migration using the acoustic wave equation

Seismic imaging can be solved as an inversion problem, which can be implemented as a least-squares migration (LSM). Compared with conventional migration algorithms, an LSM can produce imaging results with enhanced illumi-nation and resolution. However, solving an inversion problem faces difficulties in convergence, stability, and computational efficiency. To address these issues, efforts have been spent on examining the key elements in an LSM, including the mod-eling operators, the migration operators, the inversion solvers, etc. Advanced modeling operators are developed to accurately simulate the seismic data. Innovative migration algorithms are implemented to precisely compute the subsurface image. Fast inversion solvers are used to improve computation efficiency. Although all these techniques are robust to improve the LSMs, they often are studied independently. It is not often considered whether these elements are properly combined when used in an LSM. We have constructed LSMs with adjoint modeling and migration operators, and we develop algorithms to prepare input shot data for these LSMs.