Elastic Wavefield Decomposition Using the Physical-Constrained Neural Network and Its Application on Reverse-Time Migration

By using multicomponent and multiwave seismic data, elastic reverse time migration (ERTM) can produce accurate PP and PS images for complex structures. One key of ERTM is to decompose the source- and receiver-side wavefields into pure P- and S-waves with correct amplitudes and phases. Conventional wavefield decomposition methods require to solve either a Poisson’s equation or an additional P-wave equation, increasing the computational cost. To mitigate this issue, we present a novel framework of physical constrained neural network (PCNN) to efficiently implement P- and S-wave separation. The new network includes both fully connected and convolutional blocks for data fitting and takes into account the properties of curl-free P-wave and divergence-free S-wave as a physical constraint. After the training, the proposed PCNN can accurately decompose elastic wavefield and produce pure P- and S-waves with correct phases, amplitudes and physical unit. We then apply the PCNN-based method to multicomponent reverse-time migration, in which a modified dot-product imaging condition is used to calculate PP and PS images. Numerical experiments demonstrate that the proposed PCNN-based workflow can produce accurate PP and PS images while improving the computational efficiency by three orders of magnitude compared to traditional Helmholtz-based decomposition methods.