Optical flow vector of elastic waves in transversely isotropic media

Abstract

The propagation direction of the wavefield is particularly important for migration imaging in the reverse-time migration (RTM) of elastic waves in transversely isotropic (TI) media. However, due to the problem of the computational instability of the Poynting vector, the wave field propagation direction estimated based on the Poynting vector method has errors and cannot accurately indicate the real propagation direction of the elastic wavefield. To solve this problem, a method for calculating the optical flow vector of elastic waves in TI media is developed to obtain the propagation direction. The optical flow vector of elastic waves in TI media is determined by applying the spatial and temporal derivatives of the wavefield at each time step under the assumption that the wavefields are almost the same at subsequent time steps and are smooth in the spatial direction. As the additional smoothing item is added and the multiple iterative algorithm is introduced in calculating the optical flow vector, the direction is calculated more accurately than the Poynting vector. Based on the optical flow vectors, we can separate the source wavefield and receiver wavefield into four directions: up-going, down-going, left-going, and right-going wavefields, respectively, and finally perform elastic reverse-time migration (ERTM) imaging based on the optical flow vector traveling-wave separation. We use a layered model and the BP model to test our method. The testing results demonstrate that the optical flow vector can overcome the Poynting vector limitations and obtain more accurate and reliable information regarding the direction of elastic wave propagation in TI media, as well as precisely separate the wavefields. The separated wavefields for migration effectively improve the quality of the ERTM.