应用稳定方向矢量的纯qP波方程有限差分波场数值模拟

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关键词：qP波，有限差分波场模拟，方向矢量，稳定的坡印廷矢量，光流矢量，强各向异性介质 中图分类号：P631 文献标识码：A DOI：10.13810/j.cnki.issn.1000-7210.20250244

Finite-difference wavefieldnumerical simulation of pure qP-wave equations usingstable direction vectors

Yang Weiye1， Yong Peng²，Huang Jianping1， Zhang Zixiao1.2 （1.School of Geoscience，China University of Petroleum （East China），Qingdao，Shandong 26658O，China; 2.Institute of Acoustics，Chinese Academy of Science，Beijing lOol9o，China）

Abstract： Pure qP-wave equations in transversely isotropic （TI） media involve complex spatial-wavenumber coupling terms，but solving them byadopting low-rank approximation and pseudo-spectral methods comes at：a high numerical simulation cost.Scalar operators are introduced to normalize the wavenumber vector into a unit vector aligned with the wavefield propagation direction，and the asymptotic approximation finite-difference method is combined for solution，which cantransform the spatial-wavenumber coupling terms into the spatial domain for processing，thereby improving numerical simulation efficiency. However，serving as a rough estimate ofthe Poynting vector，asymptotic approximation yields direction vectors with alternating orientations and singularities.Additionally，thePoynting vectorhas obvious null points，which willafect the stabilityof wavefield extrapolation processes. Especially for some media with partial strong anisotropic characteristics，the results of asymptotic approximation wavefield simulation will produce numerical noise and amplitude instability. To this end，this paper adopts the stabilized Poynting vector approximation and optical flow vector approximation to replace the traditional asymptotic approximation for obtaining more stable and accurate wavefield directions. Meanwhile，scalar operators are combined to solve the pure qP-wave equation in TI media. Numerical experiments demonstrate that in some media with strong anisotropic characteristics，the method based on stable direction vectors can beter suppress numerical noisein the wavefield，improve simulation accuracy，and yield higherresolution reverse time migration （RTM） images.This study expands the application scopeofthis eficient finitedifference wavefield simulation method in strongly anisotropic media.

Keywords： qP-wave，finite diference wavefield modeling，direction vector，stabilized Poynting vector，optical flow vector，strongly anisotropic medium

0 引言

各向异性12广泛存在于实际的岩层中，在油气勘探领域，面对层状的沉积岩以及裂隙发育较多的含油气带，采用传统的各向同性假设会错误描述地震波的传播过程，给地震成像等[3-5带来不利影响。（剩余16656字）