Tomographic velocity inversion constitutes a nonlinear inversion problem because both the velocity and ray paths are unknown. To solve such a nonlinear problem, we use a bootstrap approach. First, starting with an initial guess and the operator based on it, we measure the traveltime errors by comparing observed traveltimes with the computed traveltimes obtained through the assumed model. Next, the error in the assumed model is solved by inverting the measured traveltime errors. We then iterate this linear inversion with the updated velocity model and hope that it converges.
If we choose the residual moveout (RMO) velocity analysis for traveltime error measure, a model-dependent RMO velocity analysis is required to compute accurate traveltime error. However, the measuring of the RMO velocity for a nonflat reflector is often difficult and is not practical to implement because it requires a line search in a prestack-migrated image cube Zhang (1990). To avoid such exhaustive searching, Etgen 1990 applied residual dip moveout (RDMO) before RMO velocity analysis so that the common reflection events could be lined up on the common surface location plane in the image cube.
Chapter 4 describes a way of measuring RMO velocity that reflects traveltime errors along the ray paths where the event has moved, with the help of plane-wave synthesis imaging along irregular reflectors.