VTI介质改进声学近似qP波交错网格正演模拟  

Staggered⁃grid forward modeling of qP wave in VTI media with improved acoustic approximation

作　　者：梁锴[1,2] 陈浩然 孙上饶 印兴耀 LIANG Kai;CHEN Haoran;SUN Shangrao;YIN Xingyao(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》2024年第1期89-97,共9页Oil Geophysical Prospecting

基　　金：国家自然科学基金项目“裂缝型储层五维地震解释理论与方法研究”(42030103);“基于全井段DAS观测的储层弹性特征跨尺度匹配方法研究”(42074162);山东省自然科学基金项目“强各向异性页岩裂缝储层地震波反射特征表征与模拟”(ZR202111200174);中海油有限公司项目“海底节点高精度成像技术研发及推广应用”(CNOOC-KJ GJHXJSGGYF 2022-01)联合资助。

摘　　要：Alkhalifah提出的声学假设近似令沿TI介质对称轴的qSV波速度近似为0,建立了相应的qP波波动方程并进行了数值模拟,但存在两个不足:一是方程中存在退化的qSV波解,不是纯qP波波动方程;二是方程不适用于ε<δ(ε和δ为Thomsen参数)的介质。为此,在Liang等的工作基础上,将改进声学近似方法的思想引入qP波频散关系和一阶波动方程推导。令qSV波的精确频散关系中的圆频率为0,同时结合椭圆分解,推导了VTI介质纯qP波解耦频散关系,利用改进标量算子的空间域渐近近似建立了VTI介质改进声学近似qP波一阶速度—应力波动方程,采用交错网格有限差分算法实现了基于改进声学近似的VTI介质纯qP波正演模拟。频散关系分析和数值示例表明,基于改进声学近似的qP波一阶波动方程不包含退化qSV波,是纯qP波方程,与弹性波波动方程模拟结果吻合较好,具有较高精度,并且该方程在ε≥δ和ε<δ的VTI介质中均是稳定的,同时也适用于复杂VTI介质。The acoustic approximation proposed by Alkhalifah assumed the qSV wave velocity along the symmetry axis of the TI media to 0,and he established the corresponding qP wave equation and realized numerical simulations.However,there are two shortcomings.Firstly,there is a degenerate qSV wave solution in the equation,which is not a pure qP wave equation.Secondly,the equation is not applicable in media withε<δ(εandδare the Thomsen parameter).Therefore,based on the work of Liang et al.,the idea of improved acoustic approximation methods is introduced into the derivation of the dispersion relation and first‑order wave equations for qP wave.The circular frequency in the accurate dispersion relation of the qSV wave is set to 0,and the elliptic decomposition is used to derive the decoupled dispersion relation of pure qP waves in VTI media.The spatial asymptotic approximation of the improved scalar operator is adopted to establish the qP wave firstorder velocity and stress wave equations in VTI media with improved acoustic approximation.The staggered grid finite difference algorithm is used to achieve the forward simulation of pure qP wave in VTI media based on improved acoustic approximation.The analysis of dispersion relation and numerical examples show that the qP wave first‑order equation with improved acoustic approximation does not include degenerate qSV waves and is a pure qP wave equation,which is in good agreement with the simulation results of the elastic wave equation and has high accuracy.The equation is stable in VTI media with bothε≥δandε<δand is applicable for complex VTI media.

关 键 词：改进声学近似 qP波 VTI介质 频散关系 交错网格 空间域渐近近似 

分 类 号：P631[天文地球—地质矿产勘探]