An exact adjoint operation pair in time extrapolation and its application in least-squares reverse-time migration

摘要

To reduce the migration artifacts arising from incompletedata or inaccurate operators instead of migrating data withthe adjoint of the forward-modeling operator, a least-squaresmigration often is considered. Least-squares migration re-quires a forward-modeling operator and its adjoint. In a deri-vation of the mathematically correct adjoint operator to a giv-en forward-time-extrapolation modeling operator, the exactadjoint of the derived operator is obtained by formulating anexplicit matrix equation for the forward operation and trans-posing it. The programs that implement the exact adjoint op-erator pair are verified by the dot-product test. The derivedexact adjoint operator turns out to differ from the convention-al reverse-time-migration (RTM) operator, an implementa-tion of wavefield extrapolation backward in time. Exampleswith synthetic data show that migration using the exact ad-joint operator gives similar results for a conventional RTMoperator and that least-squares RTM is quite successful in re-ducing most migration artifacts. The least-squares solutionusing the exact adjoint pair produces a model that fits the databetter than one using a conventional RTM operator pair.