频率—空间域非均质声波有限差分模拟  

A finite-difference scheme in frequency-space domain to solve heterogeneous acoustic wave equation

作　　者：吴悠 吴国忱[1,2] 李青阳 杨凌云 贾宗锋 WU You;WU Guochen;LI Qingyang;YANG Lingyun;JIA Zongfeng(School of Geosciences,China University of Petroleum(East China),Qingdao,Shandong 266580,China;Laboratory for Marine Mineral Resources,Qingdao National Laboratory for Marine Science and Technology,Qingdao,Shandong 266071,China)

机构地区：[1]中国石油大学(华东)地球科学与技术学院,山东青岛266580 [2]海洋国家实验室海洋矿产资源评价与探测技术功能实验室,山东青岛266071

出　　处：《石油地球物理勘探》2022年第2期342-356,I0004,共16页Oil Geophysical Prospecting

基　　金：国家自然科学基金重点项目“裂缝型储层五维地震解释理论与方法研究”(42030103)资助。

摘　　要：为准确高效地模拟声波在非均匀介质中的传播,文中构建了利用交错网格和混合网格进行频率—空间域非均质声波方程有限差分模拟的一般框架。分别推导了交错网格和混合网格有限差分格式并推广到高阶形式,采用加权平均思想对质量加速度项进行近似,运用最佳匹配层(PML)吸收边界条件有效压制人工边界反射。通过层状模型验证了所提方法的准确性,利用Marmousi模型证明了所提方法的稳定性。数值试验结果表明相同空间剖分精度下,混合网格和四阶交错网格数值模拟精度远高于二阶交错网格,混合网格模拟精度虽略低于四阶交错网格,但计算效率却明显高于四阶交错网格,因此混合网格法可作为频率域非均质声波正演模拟的首选方法。To accurately and efficiently simulate the propagation of acoustic wave in heterogeneous media,this paper constructed a general framework of finite-difference simulation of heterogeneous acoustic wave equations in frequency-space domain using a staggered grid and a hybrid grid.The finite-difference schemes of the staggered grid and the hybrid grid were respectively derived and extended to higher-order forms.The weighted average method was employed to approximate the mass acceleration term,and the perfectly matched layer(PML)absorbing boundary condition was used to effectively suppress the artificial boundary reflection.The accuracy of the method was verified by a layered model,and its stability was examined by the Marmousi model.Numerical experiments show that under the same space subdivision precision,the simulation accuracy of the hybrid grid and the fourth-order staggered grid is much higher than that of the second-order staggered grid.Although the simulation accuracy of the hybrid grid is slightly lower than that of the fourth-order staggered grid,it has higher computational efficiency.Thus,the hybrid grid method can be the first choice for the forward modeling of acoustic wave in heterogeneous media in a frequency domain.

关 键 词：非均匀声波方程 频率—空间域 有限差分 数值模拟 交错网格 

分 类 号：P631[天文地球—地质矿产勘探]