Least-squares cross-well migration

The standard migration algorithm seeks to estimate the reflectivity field As by applying the transpose of the forward modeling operator L to the reflection data p^ref, i.e. the migrated section is given by As ˜ L^T p^ref. This, however, is an unnecessarily restricted definition that can promote artifacts in the migrated section. A more general definition is to recast the standard migration problem as a linear optimization problem. That is, find As that minimizes the cost function || L ?s - p ||²+ constraints. This provides a general framework to develop a variety of new migration algorithms which might reduce artifacts extant in standard migrated sections. As examples, we introduce several migration algorithms, such as SIRT migration and constrained Conjugate Gradient migration. The benefit might be a more accurate migration at the expense of much more CPU time.