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

Abstract To reduce the migration artifacts arising from incomplete data or inaccurate operators instead of migrating data with the adjoint of the forward-modeling operator, a least-squares migration often is considered. Least-squares migration requires a forward-modeling operator and its adjoint. In a derivation of the mathematically correct adjoint operator to a given forward-time-extrapolation modeling operator, the exact adjoint of the derived operator is obtained by formulating an explicit matrix equation for the forward operation and transposing it. The programs that implement the exact adjoint operator pair are verified by the dot-product test. The derived exact adjoint operator turns out to differ from the conventional reverse-time-migration (RTM) operator, an implementation of wavefield extrapolation backward in time. Examples with synthetic data show that migration using the exact adjoint operator gives similar results for a conventional RTM operator and that least-squares RTM is quite successful in reducing most migration artifacts. The least-squares solution using the exact adjoint pair produces a model that fits the data better than one using a conventional RTM operator pair.