Seismic source wavefield reconstruction based on proper orthogonal decomposition for finite element modeling

Abstract

The cross-correlation imaging condition based reverse time migration (RTM) requires the source and receiver wavefields correlating at the same time. The boundary value method (BVM) can be used to reconstruct the source wavefield in the reverse time propagation same as the receiver wavefield, which can reduce the storage burden of RTM. However, it increases one more computation to solve the wave equation for each shot. In this work, we present a proper orthogonal decomposition (POD) based finite element method (FEM) that can approximately reconstruct the source wavefield with high efficiency. We derive the POD basis functions and give the detailed steps of reconstructing the source wavefield in reverse time by POD-FEM. Numerical tests on part of Marmousi model are given to verify the effectiveness of our method. With comparable accuracy, our method can keep a good balance between memory usage and computation time.