一种基于Nesterov加速梯度法的最小二乘逆时偏移成像研究  

Research on least square inverse time migration imaging based on Nesterov accelerated gradient method

作　　者：张晓丹[1] 苟海洋 刘东晓 崔琳[1] 刘贵忠[2] 张志禹[3] 王舒仪 白子彤 ZHANG XiaoDan;GOU HaiYang;LIU DongXiao;CUI Lin;LIU GuiZhong;ZHANG ZhiYu;WANG ShuYi;BAI ZiTong(School of Electronic Information,Xi'an Polytechnic University,Xi'an 710600,China;School of Information and Communications Engineering,Xi'an JiaoTong University,Xi'an 710049,China;School of Automation and Information Engineering,Xi'an University of Technology,Xi'an 710048,China)

机构地区：[1]西安工程大学电子信息学院,西安710600 [2]西安交通大学信息与通信工程学院,西安710049 [3]西安理工大学自动化与信息工程学院,西安710048

出　　处：《地球物理学进展》2022年第6期2498-2507,共10页Progress in Geophysics

基　　金：国家自然科学基金(61901347);陕西省自然科学基金(2022JM-146)资助。

摘　　要：传统梯度类迭代算法在最小二乘偏移成像过程中存在生成上升的搜索方向和成像分辨率不足的问题,为最小二乘逆时偏移应用于实际工作带来诸多不便.针对该问题本文提出一种基于Nesterov加速梯度法(Nesterov Accelerated Gradient,NAG)的最小二乘逆时偏移成像方法.首先,基于最速下降法在每次梯度迭代方向上引入历史积累梯度因子,将历史积累梯度因子作为校正因子加入下一次迭代的梯度方向中;其次,根据优化的校正因子更新本次迭代的梯度方向和步长,使最速下降法相邻次迭代的梯度下降方向不在正交,避免了最速下降法生成上升搜索方向造成的振荡问题;最后,判断归一化数据残差是否达到阈值,并输出偏移成像结果.通过文中实验可见:本文提出的方法在偏移成像剖面的连续性和地层细节刻画方面均得到较好提高,同时改善了梯度迭代算法的归一化残差收敛精度,加快了目标函数的收敛速度,文中实验数据结果显示最小二乘逆时偏移归一化残差值平均降低8%,残差收敛效率平均提升约12.71%.该方法有效改善了最小二乘逆时偏移成像的收敛困难问题,为复杂构造地下介质高效高分辨率成像提供了一种新手段.In the process of the Least Square Reverse Time Migration(LSRTM),the traditional gradient iteration algorithm has two problems in generating ascending search direction and insufficient image resolution ratio,which brings a lot inconvenience to the application of the Least Square Reverse Time Migration in practical work.In order to solve this problem,this paper proposes the Least Square Reverse Time Migration imaging method based on Nesterov Accelerated Gradient(NAG).Firstly,the historical accumulation gradient factor was introduced in each gradient iteration direction based on the fastest descending method,and the historical accumulation gradient factor was added into the gradient direction of the next iteration as a correction factor.Secondly,the latest iteration gradient direction and step size were updated according to the optimized correction factor,so that the gradient descending direction of the next iteration of the fastest descending method was not orthogonal,and the oscillation problem caused by the rise search direction generated by the fastest descent method was avoided.Finally,determining if the normalized data residuals reach the threshold and output the migration imaging results.According to the experiments in the paper:The method proposed by this paper in the continuity of migration imaging profiles and detailed description was improved better.At the same time,the gradient iteration algorithm of normalized residual convergence accuracy was improved and the convergence rate of the objective function was accelerated.The experiment data results in this paper show that the Least Square Reverse Time Migration normalized residual values was reduced by an average 8%,and residual error convergence efficiency was increased by an average about 12.71%.This method effectively optimises the convergence difficulty of the least square reverse-time migration imaging and provides a new method for the efficient high-resolution imaging of complex underground media.

关 键 词：最小二乘逆时偏移 Nesterov加速梯度 历史积累梯度因子 校正因子 

分 类 号：P631[天文地球—地质矿产勘探]