Proper orthogonal decomposition based seismic source wavefield reconstruction for finite element reverse time migration

Abstract

The large storage requirement is a critical issue in cross-correlation imaging-condition based reverse time migration (RTM), because it requires the operation of the source and receiver wavefields at the same time. The boundary value method (BVM), based on the finite difference method (FDM), can be used to reconstruct the source wavefield in the reverse time propagation in the same way as the receiver wavefield, which can reduce the storage burden of the RTM data. Considering that the FDM cannot well handle models with discontinuous material properties and rough interfaces, we develop a source wavefield reconstruction strategy based on the finite element method (FEM), using proper orthogonal decomposition (POD) to enhance computational efficiency. In this method, we divide the whole time period into several segments, and construct the POD basis functions to get a reduced order model (ROM) for the source wavefield reconstruction in each segment. We show the corresponding quantitative analysis of the storage requirement of the POD-FEM. Numerical tests on the homogeneous model show the effectiveness of the proposed method, while the layered model and part of the Marmousi model tests indicate that the POD-FEM can keep an excellent balance between computational efficiency and memory usage compared with the full-stored method (FSM) and the BVM, and can be effectively applied in imaging.