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Helmholtz decomposition with a scalar Poisson equation in elastic anisotropic media

Petroleum Science 2024年第3期21卷 1597-1610页

作者： Xin-Yu Fang Gang Yao Qing-Qing Zheng Ping-Min Zhang Di Wu Feng-Lin Niu State Key Laboratory of Petroleum Resources and Engineering China University of Petroleum (Beijing) Unconventional Petroleum Research Institute China University of Petroleum (Beijing) Department of Mathematics College of Science China University of Petroleum (Beijing) College of Geophysics China University of Petroleum (Beijing) Department of Earth Environmental and Planetary Sciences Rice University

P-and S-wave separation plays an important role in elastic reverse-time migration. It can reduce the artifacts caused by crosstalk between different modes and improve image quality. In addition, P-and Swave separation can also be used to better understand and distinguish wave types in complex media. At present, the methods for separating wave modes in anisotropic media mainly include spatial nonstationary filtering, low-rank approximation, and vector Poisson equation. Most of these methods require multiple Fourier transforms or the calculation of large matrices, which require high computational costs for problems with large scale. In this paper, an efficient method is proposed to separate the wave mode for anisotropic media by using a scalar anisotropic Poisson operator in the spatial *** 2D problems, the computational complexity required by this method is 1/2 of the methods based on solving a vector Poisson equation. Therefore, compared with existing methods based on pseudoHelmholtz decomposition operators, this method can significantly reduce the computational cost. Numerical examples also show that the P and S waves decomposed by this method not only have the correct amplitude and phase relative to the input wavefield but also can reduce the computational complexity significantly.

关键词： Anisotropic media Scalar anisotropic Poisson equation improved elastic wavefield decomposition

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