Regularized least-squares theory is the fundamental basis for solving the geometry regularization problem in this work. To preserve the resolution of dipping events in the final image, the regularization term includes a transformation by Azimuth Moveout Biondi and Vlad (2001). Additionally, Biondi and Vlad's method is computationally efficient because they apply the AMO operator in the Fourier domain and precondition the least-squares problem.
For this work, we use an AMO operator designed for converted waves Rosales and Biondi (2001). Regularization with this operator intends to: 1) preserve the resolution of the dipping events, 2) correct for the spatial lateral shift of the common conversion point, and 3) handle the amplitudes properly.
We present a general overview of the AMO regularization theory and discuss special considerations for converted waves regularization. We present an iterative methodology to regularize the PS data due to the dependency of the PSAMO operator on the ratio between the P and the S velocities.