3D elastic reverse time migration based on P- and S-wave decoupling

Elastic reverse time migration contains information of not only reflected P-wave but also converted S-waves. Converted S-waves have more information of underground, higher resolution, and wider offset. While to get clean PP and PS images, we need to separate P- and S-waves. The traditional P- and S-wave separation method is based on Helmholtz decomposition. It supposes P-waves are no rotation wavefield and S-waves are no divergence wavefield. So, P-waves are calculated by a gradient operator and S-waves calculated by a curl operator. The phase and amplitude information of decomposed waves are changed, because of a space difference operator. We adopt the P- and S-wave decoupled method to separate P- and S-waves. We extend this decoupled method to 3D media and compare with the Helmholtz decomposition method. We find this decoupled method can maintain the phase and amplitude information of separated P- and S-waves. By this decoupled method, the separated P- and S-waves both are vectors. We need to get scalar images from these vector wavefields if we want to use the decoupled method in elastic reverse time migration. We introduce Poynting vector of P- and S-waves to scalarize vector P- and S-waves. Then we use a traditional acoustic reverse time migration imaging condition to get scalar PP and PS images. These images can maintain phase and amplitude information, because we use P- and S-wave decoupled method to separate them. And the imaging results have no polarity inversal problem. But we find the Poynting vector of S-waves are inaccurate because the S-wave stress are interfered by P-waves. So, we use the S-wave quasi-stress tensor to calculate the S-wave Poynting vector. The S-wave quasi-stress are not interfered by P-waves. Finally, the S-wave Poynting vector calculated by S-wave quasi-stress will be more accurate. Numerical examples illustrate the validity of 3D P- and S-wave decoupled separation method and the accuracy of elastic reverse time migration by the Poynting vector.