VTI介质改进声学近似qP波交错网格正演模拟

doi:10.13810/j.cnki.issn.1000-7210.2024.01.010

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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。

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	梁锴
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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

Abstract：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 with ε< δ （ε and δ are 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 first-order 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 both ε≥ δ and ε< δ and is applicable for complex VTI media.

Key words： improved acoustic approximation qP wave VTI media dispersion relation staggered grid spatial asymptotic approximation

收稿日期: 2023-04-27

PACS:

P631

基金资助:本项研究受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）和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。

通讯作者: 梁锴,山东省青岛市黄岛区长江西路66号中国石油大学(华东)地球科学与技术学院,266580。Email:liangkai@upc.edu.cn E-mail: liangkai@upc.edu.cn

作者简介: 梁锴讲师，1982年生； 2004年获石油大学（华东）勘查技术与工程专业学士学位，2006年获中国石油大学（华东）地球探测与信息技术专业硕士学位，2009年获该校地质资源与地质工程专业博士学位；现在中国石油大学（华东）从事复杂介质地震波传播理论和波场模拟方面的教研工作。

引用本文:

梁锴, 陈浩然, 孙上饶, 印兴耀. VTI介质改进声学近似qP波交错网格正演模拟[J]. 石油地球物理勘探, 2024, 59(1): 89-97. LIANG Kai, CHEN Haoran, SUN Shangrao, YIN Xingyao. Staggered-grid forward modeling of qP wave in VTI media with improved acoustic approximation. Oil Geophysical Prospecting, 2024, 59(1): 89-97.

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[1]	吴国忱.各向异性介质地震波传播与成像[M]. 山东东营: 中国石油大学出版社, 2006.
[2]	贾宗锋,吴国忱,李青阳,等.标量波方程广义有限差分正演模拟[J].石油地球物理勘探, 2022, 57(1):101-110.JIA Zongfeng,WU Guochen,LI Qingyang,et al.Forward modeling of scalar wave equation with generalized finite difference method[J].Oil Geophysical Prospecting, 2022, 57(1): 101-110.
[3]	王辉,何兵寿,邵祥奇.一阶速度—胀缩—旋转弹性波方程交错网格数值模拟[J].石油地球物理勘探,2022,57(6): 1352-1361.WANG Hui,HE Bingshou,SHAO Xiangqi.Numerical simulation of first-order velocity-dilatation-rotation elastic wave equation with staggered grid[J].Oil Geophysical Prospecting,2022,57(6):1352-1361.
[4]	陈亮,黄建平,王自颖,等.应用自适应变网格紧致差分的地震波数值模拟及逆时偏移[J].石油地球物理勘探,2023,58(3): 641-650,712.CHEN Liang,HUANG Jianping,WANG Ziying,et al.Seismic numerical simulation and reverse time migration with adaptive variable-grid and compact difference method[J].Oil Geophysical Prospecting,2023, 58(3):641-650,712.
[5]	ALKHALIFAH T.Acoustic approximations for processing in transversely isotropic media[J].Geophysics,1998,63(2): 623-631.
[6]	ALKHALIFAH T.An acoustic wave equation for anisotropic media[J].Geophysics,2000,65(4):1239-1250.
[7]	ALKHALIFAH T.An acoustic wave equation for orthorhombic anisotropy[J].Geophysics,2003,68(4):1169-1172.
[8]	梁锴,孙上饶,曹丹平,等.TTI介质弹性波近似解耦波动方程[J].地球物理学报, 2021, 64(12):4607-4617.LIANG Kai,SUN Shangrao,CAO Danping,et al.Approximate decoupled wave equations for elastic waves in TTI media[J].Chinese Journal of Geophysics,2021,64(12): 4607-4617.
[9]	孙上饶,梁锴,印兴耀,等.三维TTI介质弹性波相、群速度的近似配方表征法[J].石油地球物理勘探,2021,56(3): 496-504,518.SUN Shangrao,LIANG Kai,Yin Xingyao,et al.Approximate 3D phase and group velocities for elastic wave in TTI media based on an approximate match method[J].Oil Geophysical Prospecting,2021,56(3):496-504,518.
[10]	THOMSEN L.Weak elastic anisotropy[J].Geophysics,1986, 51(10):1954-1966.
[11]	FOWLER P J,DU X,FLETCHER R P. Coupled equations for reverse time migration in transversely isotropic media[J].Geophysics,2010,75(1):S11-S22.
[12]	CHU C,MACY B K,ANNO P D.Approximation of pure acoustic seismic wave propagation in TTI media[J].Geophysics, 2011,76(5):WB97-WB107.
[13]	DUVENECK E,BAKKER P M.Stable P-wave modeling for reverse time migration in tilted TI media[J].Geophysics, 2011,76(2):S65-S75.
[14]	ZHANG Y,ZHANG H,ZHANG G.A stable TTI reverse time migration and its implementation[J].Geophysics,2011, 76(3):WA3-WA11.
[15]	CHENG J,KANG W.Simulating propagation of separated wave modes in general anisotropic media,Part I:qP-wave propagators[J].Geophysics,2014,79(1):C1-C18.
[16]	CHENG J,KANG W.Simulating propagation of separated wave modes in general anisotropic media,Part II: qS-wave propagators[J].Geophysics, 2016,81(2): C39-C52.
[17]	郭成锋,杜启振,张明强,等.改进的TTI介质纯P波方程正演模拟与逆时偏移[J].地球物理学报,2017,60(1):258-270.GUO Chengfeng,DU Qizhen,ZHANG Mingqiang,et al. Numerical simulation and reverse time migration using an improved pure P-wave equation in tilted transversely isotropic media[J].Chinese Journal of Geophysics,2017,60(1):258-270.
[18]	XU S,ZHOU H.Accurate simulations of pure quasi-P-waves in complex anisotropic media[J].Geophysics, 2014,79(6):T341-T348.
[19]	杨鹏,李振春,谷丙洛.一种TI介质纯qP波正演方法及其在逆时偏移中的应用[J].地球物理学报,2017,60(11): 4447-4467.YANG Peng,LI Zhenchun,GU Bingluo.Pure quassi-P wave forward modeling method in TI media and its application to RTM[J].Chinese Journal of Geophysics,2017,60(11): 4447-4467.
[20]	胡书华,王宇超,刘文卿,等.复杂TTI介质稳定的纯qP波波场模拟方法[J].石油地球物理勘探,2018,53(2):280-287.HU Shuhua,WANG Yuchao,LIU Wenqin,et al.Pure quasi-P wave stable simulation in complex TTI media[J]. Oil Geophysical Prospecting, 2018, 53(2): 280-287.
[21]	张庆朝,朱国维,何登科,等.任意空间取向TI介质qP和qSV波解耦的波动方程[J].地球物理学报,2019,62(11): 4353-4366.ZHANG Qingchao,ZHU Guowei,HE Dengke,et al.A decoupled qP-wave and qSV-wave equation in TI media with arbitrary spatial oriented symmetry axis[J].Chinese Journal of Geophysics,2019,62(11):4353-4366.
[22]	徐世刚,包乾宗,任志明.简化的三维TTI介质黏滞纯声波方程及其数值模拟[J].石油地球物理勘探,2022,57(2): 331-341.XU Shigang,BAO Qianzong,REN Zhiming.A simplified pure visco-acoustic wave equation for 3D TTI media and its numerical simulation[J].Oil Geophysical Prospecting,2022, 57(2): 331-341.
[23]	XU S,STOVAS A,ALKHALIFAH T,et al.New acoustic approximation for transversely isotropic media with a vertical symmetry axis[J].Geophysics,2020,85(1):C1-C12.
[24]	STOVAS A,ALKHALIFAH T,WAHEED U B.Pure P-and S-wave equations in transversely isotropic media[J]. Geophysical Prospecting,2020,68(9):2762-2769.
[25]	LIANG K,CAO D,SUN S,et al.Decoupled wave equation and forward modeling of qP wave in VTI media with the new acoustic approximation[J].Geophysics,2023,88(1): WA335-WA344.
[26]	SHAN J,WU G,YANG S,et al.Simulation of improved pure P-wave equation in transversely isotropic media with a horizontal symmetry axis[J].Geophysical Prospecting,2023, 71(1):102-113.
[27]	董良国,马在田,曹景忠,等.一阶弹性波方程交错网格高阶差分解法[J].地球物理学报, 2000, 43(3):411-419.DONG Liangguo,MA Zaitian,CAO Jingzhong,et al.A staggered-grid high-order difference method of one-order elastic wave equation[J].Chinese Journal of Geophysics,2000, 43(3): 411-419.
[28]	刘洋,李承楚,牟永光.任意偶数阶精度有限差分法数值模拟[J].石油地球物理勘探,1998,33(1):1-10.LIU Yang,LI Chengchu,MOU Yongguang.Finite-difference numerical modeling of any even-order accuracy[J].Oil Geophysical Prospecting, 1998, 33(1):1-10.