基于MC-PML的二维Rayleigh波正演模拟及频散特征分析  

2D Rayleigh wave modeling based on MC-PML and its dispersion characteristics analysis

作　　者：杜兴忠 黄金强 胡昌荣 宋绍飞 高国超 金宗玮 DU XingZhong;HUANG JinQiang;HU ChangRong;SONG ShaoFei;GAO GuoChao;JIN ZongWei(Power China Guiyang Engineering Corporation Limited,Guiyang 550081,China;College of Resources and Environmental Engineering,Key Laboratory of Karst Georesources and Environment(Guizhou University),Ministry of Education,Guiyang 550025,China;Guizhou Natural Gas Pipeline Network Corporation Limited,Guiyang 550081,China;Frontiers Science Center for Deep Ocean Multispheres and Earth System,Key Lab of Submarine Geosciences and Prospecting Techniques,Ministry of Education and College of Marine Geosciences,Ocean University of China,Qingdao 266100,China)

机构地区：[1]中国电建集团贵阳勘测设计研究院有限公司,贵阳550081 [2]贵州大学资源与环境工程学院,喀斯特地质资源与环境教育部重点实验室(贵州大学),贵阳550025 [3]贵州天然气管网有限责任公司,贵阳550081 [4]深海圈层与地球系统教育部前沿科学中心,海底科学与探测技术教育部重点实验室和中国海洋大学海洋地球科学学院,青岛266100

出　　处：《地球物理学进展》2024年第2期542-560,共19页Progress in Geophysics

基　　金：国家自然科学基金地区项目“基于最优传输目标泛函的VTI介质多参数全波形反演方法研究”(42364008);贵州省科技计划项目“面向喀斯特岩溶探区的井间地震波全波形反演方法研究”(黔科合基础-ZK[2022]一般060);“贵州长输油气管道反井钻机小角度钻井关键技术研究”(黔科合支撑[2022]一般009);中国电建集团贵阳勘测设计研究院有限公司重大研究专项“岩溶洼地建库开发利用关键技术研究”(YJZD2020-02)联合资助。

摘　　要：Rayleigh波正演模拟是认识Rayleigh波传播规律的重要手段,也是Rayleigh波反演的基础.然而,在浅地表高泊松比地质体的Rayleigh波正演模拟中,应力镜像与二阶速度展开的自由表面处理方法配合传统的C-PML技术会产生严重的数值不稳定问题.为此,本文首先从弹性波动方程出发,基于应力镜像与二阶速度展开法,推导了自由边界条件下应力分量与速度分量的更新公式;然后再借助MC-PML边界条件处理模型左右两边和底部的人工截断边界,以确保自由边界与吸收边界耦合区域的计算稳定;最终采用GPU并行编程架构,实现了基于MC-PML的Rayleigh波正演模拟技术.通过四组典型模型试验及频散分析结果表明:应力镜像与二阶速度展开的自由表面处理方法结合MC-PML技术能够准确刻画Rayleigh波传播规律,MC-PML技术不受自由表面影响,未见数值不稳定,频散能量谱的峰值连线与理论频散曲线的高度一致性进一步证实本文Rayleigh波正演模拟所采用的关键处理技术是正确的.Rayleigh wave modeling is an important tool to understand the law of Rayleigh wave propagation,and it is also the basis of Rayleigh wave inversion.However,in the near-surface high Poisson's ratio seismic modeling,the free-surface boundary method of stress image and second-order velocity evolving case numerical instability when combining the traditional C-PML technology.To overcome this issue,this paper starting from the elastic wave equation,derived the updating formulas of stress component and velocity component under the free-surface boundary condition based on the stress image and second-order velocity expansion method,then,the artificial truncated boundaries at the left and right sides and the bottom of the model are processed by using MC-PML boundary conditions to ensure the computational stability of the coupling region between free boundary and absorbing boundary,finally,Rayleigh wave modeling based on MC-PML is realized by using GPU parallel programming architecture.The results of four typical numerical experiments and dispersion analysis shown that the free-surface treatment scheme of stress image method and second-order velocity expansion combined with MC-PML technology can accurately describe the law of Rayleigh wave propagation,and the MC-PML technology is not affected by the free surface and does not appear numerical instability.The correctness of the key techniques used in the Rayleigh wave modeling is further verified from the high consistency between the peak line of the dispersion energy diagram and analytical solutions of dispersion curves.

关 键 词：RAYLEIGH波 正演模拟 高泊松比 C-PML MC-PML 频散 

分 类 号：P631[天文地球—地质矿产勘探]