一种优化的频率域三维声波有限差分模拟方法  

An optimal method for frequency-domain finite-difference solution of 3D scalar wave equation

作　　者：范娜 成景旺[1,3] 秦雷 赵连锋[5] 谢小碧[6] 姚振兴[5] FAN Na1,2,3, CHENG JingWang1,3 , QIN Lei4 , ZHAO LianFeng5 , XIE XiaoBi6 , YAO ZhenXing5 1 Key Laboratory of Exploration Technologies for Oil and Gas Resources(Yangtze University）, Ministry of Education, Wuhan 430100, China 2 Hubei Cooperative Innovation Center of Unconventional Oil and Gas, Wuhan 430100, China 3 School of Geophysics and Oil Resources, Yangtze University, Wuhan 430100, China 4 Sinopec Geophysical Corporation Huadong Branch, Nanjing 211112, China 5 Key Laboratory of Earth and Planetary Physics, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing 100029, China 6 Institute of Geophysics and Planetary Physics, University of California at Santa Cruz 95064, California, US)

机构地区：[1]油气资源与勘探技术教育部重点实验室(长江大学),武汉430100 [2]非常规油气湖北协同创新中心,武汉430100 [3]长江大学地球物理与石油资源学院,武汉430100 [4]中石化地球物理公司华东分公司,南京211112 [5]中国科学院地质与地球物理研究所,中国科学院地球与行星物理重点实验室,北京100029 [6]美国加州大学圣克鲁兹分校地球物理与行星物理研究所,圣克鲁兹95064

出　　处：《地球物理学报》2018年第3期1095-1108,共14页Chinese Journal of Geophysics

基　　金：国家自然科学基金(41604037,41504102,41674107,41504077)和油气资源与勘探技术教育部重点实验室(长江大学)开放基金(K2016-02)联合资助.

摘　　要：为提高频率域有限差分(FD,finite-difference)正演模拟技术的计算精度和效率,基于旋转坐标系统的优化差分格式被广泛应用,但是只应用于正方形网格的情况.基于平均导数法(ADM)的优化差分格式,应用于正方形和长方形网格模拟.这些频率域有限差分算子,各自具有不同的差分格式和对应的优化系数求解表达式.本文基于三维声波方程发展了一种新的优化方法,只要给定FD模板形式,可直接构造频散方程,求取FD模板上各节点的优化系数.此方法的优点在于频率域FD算子的优化系数对应各个节点,可扩展优化其他格式.运用此优化方法,计算得到了不同空间采样间距比情况下27点和7点格式的优化系数.数值实验表明,优化27点格式与ADM 27点格式具有相同的精度,优化7点格式比经典的7点格式具有更小的数值频散.To increase the computational accuracy and efficiency of frequency-domain finite- difference （FD） modeling method, the optimal FD scheme with rotated coordinate system were widely used. It requires the same spatial sampling intervals in horizontal and vertical directions, which limited their applications in practice. Later the average-derivative method （ADM） was proposed to work with the rectangular-grid modeling. However, these frequency-domain FD operators, unlike the time-domain FD operators of which the coefficients can be determined by a general optimal method even with different stencils, usually have their own forms of differential equations with different distributions of optimized coefficients. In this paper, we develop a general optimal method for frequency-domain FD modeling based on 3D acoustic wave equation. For a given finite-difference stencil, this method can generate the dispersion equation and optimize the expansion coefficients. The advantage of this method is that the optimized coefficients correspond to the grid nodes of FD stencil and it is very easy to expand to other FD schemes. We computed the optimized coefficients of 27- and 7- point schemes with different aspect ratios. Numerical experiments demonstrate that our optimal 27-point scheme have the same accuracy with ADM 27- point scheme and our optimal 7-point scheme have higher accuracy than the classical 7-point scheme.

关 键 词：三维声波方程 频率域 有限差分 优化系数 

分 类 号：P631[天文地球—地质矿产勘探]