应用保辛Stereo-modeling方法的振幅补偿逆时偏移成像  

Amplitude compensated reverse time migration by the symplectic stereo-modeling method

作　　者：李静爽[1] 张向佳 贺茜君 黄雪源 LI Jingshuang;ZHANG Xiangjia;HE Xijun;HUANG Xueyuan(School of Science,China University of Mining and Technology(Beijing),Beijing 100083,China;College of Geoexploration Science and Technology,Jilin University,Changchun,Jilin 130026,China;School of Mathematics and Statistics,Beijing Technology and Business University,Beijing 100048,China)

机构地区：[1]中国矿业大学(北京)理学院,北京100083 [2]吉林大学地球探测科学与技术学院,吉林长春130026 [3]北京工商大学数学与统计学院,北京100048

出　　处：《石油地球物理勘探》2024年第5期1037-1047,共11页Oil Geophysical Prospecting

基　　金：中央高校基本科研业务费专项资金重点领域交叉创新项目“深部储层高精度地震成像与储层参数智能化预测”(2023JCCXLX01);国家自然科学基金青年科学基金项目“分数阶粘滞波动方程及其数值模拟和Q补偿成像研究”(41604105)联合资助。

摘　　要：地震波数值模拟的精度很大程度上决定了逆时偏移结果的分辨率,文中采用保辛近似解析离散化方法,在Birkhoffian系统下求解黏滞声波方程,并进行振幅补偿的逆时偏移(RTM)。首先,将黏滞声波方程构造成一个Birkhoffian系统,对于该系统采用二阶保辛Runge-Kutta法进行时间推进,分别采用Stereo-modeling法(STEM)和传统有限差分法进行空间算子离散,相应得到SSM(Symplectic Stereo-modeling Method)和CSM(Conventional Symplectic Method)两种方法。之后,对SSM和CSM进行一系列数值性质分析,包括数值频散分析、与解析解比较、效率对比、稳定性测试等。结果显示,SSM的最大数值频散误差约为9%,而CSM约为26%;SSM的计算效率高且长时计算稳定,计算效率约为CSM的两倍。最后,应用三个模型进行了正演数值模拟和逆时偏移试验。对于衰减数据,与声波RTM相比,黏滞声波RTM成像振幅更高,能获得与无衰减数据声波RTM相近的成像振幅。对于油气藏模型,SSM比CSM的成像精度更高、数值频散更小。The resolution of reverse time migration(RTM)results highly depends on the accuracy of the seismic wave simulation.In this paper,the symplectic stereo-modeling method(SSM)is used to solve the visco-acoustic wave equation in the Birkhoffian system and RTM with amplitude compensation is conducted.First,a Birkhoffian system is constructed from the visco-acoustic wave equation.For the system,the second-order symplectic separable Runge-Kutta method is used to advance the time,the stereo-modeling method(STEM)and the conventional finite difference method are used to discrete the spatial operators,respectively,and two methods are obtained correspondingly:SSM and conventional symplectic method(CSM).Then a series of numerical properties of SSM and CSM are analyzed,including numerical dispersion analysis,comparison with analytical solution,efficiency comparison,and long-term calculation stability test,etc.The results show that the maximum numerical dispersion error of SSM is approximately 9%,while that of CSM method is approximately 26%.SSM exhibits high calculation efficiency and stability for long-time calculation,whose calculation efficiency is approximately twice that of CSM.Finally,the forward numerical simulation and RTM experiments are conducted through the application of three models.The results show that visco-acoustic RTM ima ging amplitude is higher than acoustic V-RTM(attenuated data),and it can obtain imaging amplitude similar to acoustic A-RTM(un-attenuated data).For reservoir model,SSM has higher imaging accuracy and smaller numerical dispersion than CSM.

关 键 词：黏滞声波方程 振幅补偿 保辛方法 逆时偏移 数值频散 

分 类 号：P631[天文地球—地质矿产勘探]