Complex-valued adaptive-coefficient finite difference frequency domain method for wavefield modeling based on diffusive-viscous wave equation

IF 3 2区地球科学 Q1 GEOCHEMISTRY & GEOPHYSICS

Geophysics Pub Date : 2023-11-20 DOI:10.1190/geo2023-0271.1

Haixia Zhao, Shaoru Wang, Wenhao Xu, Jinghuai Gao

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引用次数: 0

Abstract

The diffusive-viscous wave (DVW) equation is an effective model for analyzing seismic low-frequency anomalies and attenuation in porous media. To effectively simulate DVW wavefields, the finite-difference or finite-element method in the time domain is favored, but the time-domain approach proves less efficient with multiple shots or a few frequency components. The finite-difference frequency-domain (FDFD) method, featuring optimal or adaptive coefficients is favored in seismic simulations due to its high efficiency. Initially, we develop a real-valued adaptive-coefficient (RVAC) FDFD method for the DVW equation, which ignores the numerical attenuation error and is a generalization of the acoustic adaptive-coefficient FDFD method. To reduce the numerical attenuation error of the RVAC FDFD method, we introduce a complex-valued adaptive-coefficient (CVAC) FDFD method for the DVW equation. The CVAC FDFD method is constructed by incorporating correction terms into the conventional second-order FDFD method. The adaptive coefficients are related to the spatial sampling ratio, number of spatial grid points per wavelength, and diffusive and viscous attenuation coefficients in the DVW equation. Numerical dispersion and attenuation analysis confirm that, with a maximum dispersion error of 1% and a maximum attenuation error of 10%, the CVAC FDFD method only necessitates 2.5 spatial grid points per wavelength. Compared with the RVAC FDFD method, the CVAC FDFD method exhibits enhanced capability in suppressing the numerical attenuation during anelastic wavefield modeling. To validate the accuracy of our proposed method, we propose an analytical solution for the DVW equation in a homogeneous medium. Three numerical examples substantiate the high accuracy of the CVAC FDFD method when employing a small number of spatial grid points per wavelength, but this method demands computational time and computer memory similar to those required by the conventional second-order FDFD method. A fluid-saturated model featuring various layer thicknesses is used to characterize the propagation characteristics of DVW.

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基于扩散粘性波方程的波场建模复值自适应系数有限差分频域法

扩散粘性波（DVW）方程是分析多孔介质中地震低频异常和衰减的有效模型。为有效模拟 DVW 波场，时域有限差分法或有限元法受到青睐，但时域方法在处理多拍或少数频率成分时效率较低。有限差分频域法（FDFD）具有优化或自适应系数的特点，因其高效率而在地震模拟中受到青睐。最初，我们为 DVW 方程开发了一种实值自适应系数 (RVAC) FDFD 方法，该方法忽略了数值衰减误差，是声学自适应系数 FDFD 方法的一般化。为了减少 RVAC FDFD 方法的数值衰减误差，我们为 DVW 方程引入了复值自适应系数 (CVAC) FDFD 方法。CVAC FDFD 方法是通过在传统的二阶 FDFD 方法中加入修正项而构建的。自适应系数与空间采样率、每个波长的空间网格点数以及 DVW 方程中的扩散和粘性衰减系数有关。数值弥散和衰减分析表明，在最大弥散误差为 1%、最大衰减误差为 10%的情况下，CVAC FDFD 方法每个波长只需要 2.5 个空间网格点。与 RVAC FDFD 方法相比，CVAC FDFD 方法在抑制无弹性波场建模过程中的数值衰减方面表现出更强的能力。为了验证我们提出的方法的准确性，我们提出了均质介质中 DVW 方程的解析解。三个数值示例证实了 CVAC FDFD 方法在每个波长采用少量空间网格点时的高精度，但该方法所需的计算时间和计算机内存与传统二阶 FDFD 方法类似。利用具有不同层厚的流体饱和模型来描述 DVW 的传播特性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Geophysics 地学-地球化学与地球物理

CiteScore

6.90

自引率

18.20%

发文量

354

审稿时长

3 months

期刊介绍： Geophysics, published by the Society of Exploration Geophysicists since 1936, is an archival journal encompassing all aspects of research, exploration, and education in applied geophysics. Geophysics articles, generally more than 275 per year in six issues, cover the entire spectrum of geophysical methods, including seismology, potential fields, electromagnetics, and borehole measurements. Geophysics, a bimonthly, provides theoretical and mathematical tools needed to reproduce depicted work, encouraging further development and research. Geophysics papers, drawn from industry and academia, undergo a rigorous peer-review process to validate the described methods and conclusions and ensure the highest editorial and production quality. Geophysics editors strongly encourage the use of real data, including actual case histories, to highlight current technology and tutorials to stimulate ideas. Some issues feature a section of solicited papers on a particular subject of current interest. Recent special sections focused on seismic anisotropy, subsalt exploration and development, and microseismic monitoring. The PDF format of each Geophysics paper is the official version of record.