Stationary Phase Approach To True Amplitude Migration

True amplitude migration is a di raction stack with a properly chosen weight function in its migration kernel. Many papers claim that with a carefully chosen weight function, di raction stack migration will yield an image with its amplitudes proportional to the angular-dependent re ection coe cients at the re ector positions. Bleistein used the stationary phase method to give a proof of this claim. By evaluating his proof and numerical examples I show that even with a properly chosen weight function, the di raction stack may not give an image with its amplitudes proportional to the re ection coe cients at the re ector positions, especially in case of multiple relectors and multiple shots. I found that a better true amplitude image may be obtained by reducing the weighted di raction stack to an evaluation of the migration kernel at the stationary points, or by a partial integration over the vicinity of the stationary points. I also propose a new approach, denoted as re ector-based remigration, in implementing the stationary phase approximation to weighted di raction stack migration.