Elastic reverse time migration angle gathers using a stabilized Poynting vector without zero points within the wave propagation ranges

Generation of PP and PS angle gathers for elastic reverse time migration (ERTM) has important applications in velocity model updating and subsurface parameter inversion. The Poyntingvector-based method provides a cost-effective way to extract angle gathers from ERTM. However, the estimated propagation directions or angles based on Poynting vectors at or near zero points are unstable, and the reflection energy at these points is likely to be placed in an incorrect angle bin. This instability problem severely limits its use in the generation of high-quality angle gathers. To overcome this problem, we add the conventional Poynting vector with an ancillary one of the Hilbert transformed wavefield, a 90 degrees phase-shifted version of the original wavefield. The Poynting vector of the Hilbert transformed wavefield points in the same propagation direction as the conventional Poynting vector, but they have different zero-point distributions. Adding them together allows us to obtain a stabilized Poynting vector which thoroughly eliminates the zero points within the wave propagation range, and thus we obtain a stable algorithm to extract high-quality angle gathers from ERTM. The Hilbert transformed wavefield already exists in the P/S and up/down wavefield decomposition procedure, which has become a necessary step for ERTM to separate overlapping wavefields at reflectors before the computation of Poynting vectors. Results from two synthetic numerical examples indicate the effectiveness of our method in generating high quality angle gathers for ERTM.