Double Plane Wave Least Squares Reverse Time Migration with Approximate Diagonal Hessian

Abstract

We propose a least squares reverse time migration (RTM) strategy using double plane wave (DPW) data. We derive a DPW Born modelling operator that predicts the DPW data with the reflectivity models. The adjoint of the proposed modelling operator is recognized as the frequency domain DPW RTM operator. Both the modelling and the RTM operator utilize plane wave Green’s function. The DPW Born modelling operator together with its adjoint leads to an efficient DPW least squares RTM. To improve the convergence rate and obtain images with balanced amplitude, we derive a pre-conditioner, which is the diagonal matrix of the approximate Hessian matrix for the misfit function of the DPW data. We show that same plane wave Green’s functions can be used for the modelling operator, the RTM operator and the pre-conditioner throughout the iterative updating process. As a result, wavefield propagations are not required for the DPW least squares RTM during model updating processes, which significantly improves the efficiency of the least squares RTM.