Poynting and polarization vectors based wavefield decomposition and their application on elastic reverse time migration in 2D transversely isotropic media

Abstract

A B S T R A C TWith the progress in computational power and seismic acquisition, elastic reverse time migration is becoming increasingly feasible and helpful in characterizing the physical properties of subsurface structures. To achieve high-resolution seismic imaging using elastic reverse time migration, it is necessary to separate the compressional (P-wave) and shear (S-wave) waves for both isotropic and anisotropic media. In elastic isotropic media, the conventional method for wave-mode separation is to use the divergence and curl operators. However, in anisotropic media, the polarization direction of P waves is not exactly parallel to the direction of wave propagation. Also, the polarization direction of S-waves is not totally perpendicular to the direction of wave propagation. For this reason, the conventional divergence and curl operators show poor performance in anisotropic media. Moreover, conventional methods only perform well in the space domain of regular grids, and they are not suitable for elastic numerical simulation algorithms based on non-regular grids. Besides, these methods distort the original wavefield by taking spatial derivatives. In this case, a new anisotropic wave-mode separation scheme is developed using Poynting vectors. This scheme can be performed in the angle domain by constructing the relationship between group and polarization angles of different wave modes. Also, it is performed pointwise, independent of adjacent space points, suitable for parallel computing. Moreover, there is no need to correct the changes in phase and amplitude caused by the derivative operators. By using this scheme, the anisotropic elastic reverse time migration is more efficiently performed on the unstructured mesh. The effectiveness of our scheme is verified by several numerical examples.

Elastic wave‐mode separation in 2D transversely isotropic media using optical flow

“…Many studies have proved the feasibility of the space domain wave‐mode separation in elastic reverse time migration (Liu et al ., 2019; Lu et al ., 2019). Here, we also experiment on the Hess model to discuss the influence of the crosstalk artifacts.…”

“…As described by equation (), the determining factor of separation is the polarization angle; other factors distort the waveforms of the qP‐ and qSV‐waves. If we omit the entire deformation term (3a) and apply the inverse Fourier transform to equation (), we derive the wave‐mode separation formula in the space domain (Lu et al ., 2019): where , are separated qP‐ and qSV‐waves, respectively. This separation formula is not related to the spatial derivative operations.…”

“…As described by equation 1, the determining factor of separation is the polarization angle; other factors distort the waveforms of the qP-and qSV-waves. If we omit the entire deformation term (3a) and apply the inverse Fourier transform to equation (1), we derive the wave-mode separation formula in the space domain (Lu et al, 2019):…”

“…Advancements in seismic acquisition and high‐performance computing have enabled subsurface structures to be imaged using the elastic equation to obtain more physical information from the migrated images. In recent studies, elastic reverse time migration (ERTM) has been applied to produce satisfactory images of subsurface structures (Yan and Sava, 2008; Duan and Sava, 2015; Wang and McMechan, 2015; Du et al ., 2017; Li et al ., 2018; Lu et al ., 2019; Liu, 2019; Yang et al ., 2019). Widespread anisotropy occurs in the earth in three main categories: intrinsic anisotropy, fissure‐induced anisotropy and long‐wavelength, or effective, anisotropy (Wu, 2006).…”

“…However, this approach also requires amplitude and phase correction owing to spatial derivatives. Lu et al (2019) established a relationship between group and polarization angles using the phase angle as a link and then achieved anisotropic wave-mode separation in the space domain. They established a table of polarization angles relative to group angles and anisotropic parameters before elastic wave extrapolation.…”