基于弹性反射波正演表达的转换波逆时偏移与反偏移  

Converted wave reverse time migration and demigration based on forward expression of elastic reflected waves

作　　者：丁超[1] 马坚伟[1,2] DING Chao;MA JianWei(Department of Mathematics,Harbin Institute of Technology,Harbin 150000,China;Department of Earth and Space Sciences,Peking University,Beijing 100871,China)

机构地区：[1]哈尔滨工业大学数学学院,哈尔滨150000 [2]北京大学地球与空间科学学院,北京100871

出　　处：《地球物理学报》2024年第9期3496-3509,共14页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(42230806,U23B6010);中国石油天然气集团有限公司-北京大学基础研究项目资助。

摘　　要：针对线性化弹性反射波方程无法直接用于弹性转换波反偏移模拟的问题,本文提出基于高频近似的一次反射波模拟新方法.该方法基于地震波传播的散射理论,先对地下速度扰动的空间变化进行高频近似,再基于散射波传播方程推导得到线性化一次反射波传播方程.基于弹性反射地震数据表达,本文采用线性算子的伴随估计反射系数,实现反射波逆时偏移.根据该线性表达,联合背景速度和成像值来模拟一次反射横波传播,实现了弹性波角度域反偏移,并进一步导出成像值关于波速的梯度.数值实验表明,基于弹性反射地震数据表达的偏移成像方法,既克服了极性反转效应,又使成像结果包含了更为丰富的反射角信息;一次反射波模拟方法获得的弹性地震数据具有较高的精度和稳定性,得到的弹性波场的振幅和相位信息与理论解析解吻合较好,有效保证了成像域层析速度反演梯度的稳定求解.A primary reflected wave equation with the subsurfaces reflectivity function was proposed to solve the problem that conventional mathematical and physical formula can't simulate the linear elastic reflected wave propagation very well.Under the scattering wave propagation theory,the linear simulation method is used to refine the reflectivity function by approximating the spatial change of velocity perturbation with the high-frequency approximation.Then the primary reflected wave equation was extracted from scattering wave equation.Based on the linear expression of elastic reflection seismic data,reflection coefficient of the converted S wave can be approximately estimated by the adjoint of the linear operator and realize reflected converted wave reverse time migration.According to this linear expression,the paper realizes angle domain demigration and reconstructs the upward converted S wave.And then derives the gradient of image with respect to velocity by adjoint state method.Numerical test results show that the reverse time migration imaging based on elastic reflected seismic data could overcome polarity reversal and the imaging results contain reflected angle information.The primary reflected wave simulation method is precise and stable,and the reflected wave's amplitude and phase information are close to theoretical results,which effectively ensures the stability of solution of gradients of the migrated image with respect to velocity.

关 键 词：弹性波动方程 反射波 转换波逆时偏移 逆散射成像条件 高频近似 角度域反偏移 

分 类 号：P631[天文地球—地质矿产勘探]