基于一阶速度-应力方程的起伏地表最小二乘逆时偏移  

Least-squares reverse time migration based on first-order velocity-stress wave equation with surface topography

作　　者：李振春[1,2] 卫二祥 黄建平[1,2] 王九拴[3] 杨静[3] LI Zhenchun;WEI Erxiang;HUANG Jianping;WANG Jiushuan;YANG Jing(State Key Laboratory of Deep Oil and Gas,China University of Petroleum(East China),Qingdao 266580,China;School of Geosciences,China University of Petroleum(East China),Qingdao 266580,China;Data Processing Center,GRI,BGP Inc,CNPC,Zhuozhou 072751,China)

机构地区：[1]深层油气全国重点实验室(中国石油大学(华东)),山东青岛266580 [2]中国石油大学(华东)地球科学与技术学院,山东青岛266580 [3]中国石油集团东方地球物理勘探有限责任公司研究院资料处理中心,河北涿州072751

出　　处：《中国石油大学学报(自然科学版)》2025年第2期108-117,共10页Journal of China University of Petroleum(Edition of Natural Science)

基　　金：“十四五”重大项目(2021QNLM020001);国家创新群体项目(41821002);国家自然科学基金项目(42074133);长庆油田公司复杂油田地震波成像技术的基础理论研究(2023-10502);中石油BGP项目(2023DJ8307)。

摘　　要：最小二乘逆时偏移(least-squares reverse time migration,LSRTM)具有更高的成像分辨率、振幅保真性及均衡性等优势。然而,目前的LSRTM算法大多基于水平地表假设,在面对复杂地形时无法很好地适应剧烈的起伏地表。基于二阶常密度声波方程的LSRTM算法忽略了密度变化对振幅的影响,很难在变密度介质中取得保真的成像结果。为此,从一阶速度-应力方程出发,在曲线坐标系下推导相应的扰动方程和伴随方程,并通过伴随状态法给出梯度更新公式,最终实现基于贴体网格的起伏地表LSRTM算法。模型试算验证了算法的有效性和对复杂地表的适应性。结果表明,提出的算法能够消除起伏地表的影响、压制低频噪声、恢复高频成分、均衡成像振幅,实现地下变密度介质的高分辨率和高保真度成像。Least-squares reverse time migration(LSRTM)offers advantages such as higher imaging resolution,amplitude fidelity,and amplitude balancing.However,most existing LSRTM algorithms assume a horizontal surface and struggle to handle complex topographic variations.Additionally,LSRTM based on the second-order constant-density acoustic wave equation neglects the impact of density variations on amplitude,making it challenging to achieve high-fidelity imaging in variable-density media.To address these limitations,we derive the perturbation and adjoint equations from the first-order velocity-stress equation under a curvilinear coordinate system.Using the adjoint-state method,we formulate the gradient update equation and implement an LSRTM algorithm based on a body-fitted grid to accommodate undulating surfaces.The results confirm the effectiveness of the proposed algorithm and its adaptability to complex topographies.Specifically,the algorithm successfully mitigates the effects of irregular terrain,suppresses low-frequency noise,recovers high-frequency components,and balances imaging amplitudes,thereby achieving high-resolution,high-fidelity imaging of subsurface variable-density media.

关 键 词：贴体网格 起伏地表 一阶速度-应力方程 最小二乘逆时偏移 

分 类 号：P631.4[天文地球—地质矿产勘探]