Helmholtz Decomposition for Elastic VTI Wavefield Based on Phase Direction

P- and S-waves are coupled in the process of elastic wave propagation. Wave mode separation is a key step to suppress crosstalk artifacts in elastic reverse-time migration. Pseudo-Helmholtz decomposition can separate P- and S-waves and keep their phase and amplitude correctly. However, because some partial derivatives act in the denominator, it is difficult to implement the first-order pseudo-Helmholtz decomposition efficiently and correctly. In this paper, we propose a new pseudo-Helmholtz decomposition operator based on the phase direction of the wavefront. There are three advantages of our proposed wavefield decomposition method: first, by making use of the phase direction, an approximated anisotropic Poisson equation is derived in the space domain. The new Poisson equation gives a more accurate auxiliary field than the Poisson equation in previous methods based on the assumption of kx=kz. Second, there are no mixed high-order derivatives in our proposed method. Therefore, it has a similar computational cost to the zero-order pseudo-Helmholtz decomposition method but has much less computational complexity than the existing first-order pseudo-Helmholtz decomposition operators. Third, we consider the generalized minimum residual (GMRES) algorithm, which is more efficient than LU decomposition, for solving the large sparse linear system after the anisotropic Poisson equation is discretized.