| This thesis examines the problem of designing least-squares Kirchhoff migration algorithms for imaging the subsurface. In particular, the imaging problem is posed as an inverse problem. The forward operator is constructed via a Kirchhoff de-migration operator. Smoothing constraints are used to find a stable solution to the inversion of the de-migration operator.;Synthetic and real data examples are used to validate theoretical findings and test the performance of the proposed LS-PSTM algorithm.;Numerical strategies (based on semi-iterative solvers) are used to estimate seismic images that are consistent with measured wave fields. The algorithm, denoted Least-squares PreStack Time Migration (LS-PSTM), is used to estimate common image gathers (CIG) with reduced acquisition artifacts. The algorithm is also capable of regularizing the data, in other words, it can be used to reconstruct missing seismograms. |
