全波形反演中非精确线性搜索方法研究  

Inexact line search method in full waveform inversion

作　　者：马晓娜 徐善辉 柯沛 张洪涛 Ma Xiaona;Xu Shanhui;Ke Pei;Zhang Hongtao(Institute of Geophysics,China Earthquake Administration,Beijing 100081;BGP Inc.,China National Petroleum Corporation,Hebei Zhuozhou 072751;Liaoning No.1 Hydrogeological Engineering Geology Group Co.,Ltd,Liaoning Jinzhou 121000)

机构地区：[1]中国地震局地球物理研究所,北京100081 [2]中国石油集团东方地球物理勘探有限责任公司新兴物探开发处,涿州072751 [3]辽宁工程勘察设计院,辽宁锦州121000

出　　处：《Applied Geophysics》2023年第4期374-384,668,共12页应用地球物理（英文版）

基　　金：supported by the Special Fund of the Institute of Geophysics,China Earthquake Administration(Grant Number DQJB19B25 and Grant Number DQJB21K31).

摘　　要：全波形反演是一个非线性数据拟合过程,以反演迭代的方式来获取地下高精度模型参数。其中,更新步长的选取影响整个反演过程的计算效率和反演结果的精度。非精确线性搜索方法是求取更新步长的有效方法,其不要求目标函数达到精确最小,利用判断条件和初始步长得到合适的更新量即可,不依赖目标函数的形式,具有较大发展潜力。本文首先对数学上求解最优化问题中经典的Armijo判断条件、Wolfe判断条件以及Goldstein判断条件在地震数据全波形反演中的应用效果展开研究。Overthrust模型测试证明Armijo判断条件和Goldstein判断条件收敛性相似,计算效率高,对全波形反演具有更好的适用性。同时,在全波形反演中使用Adaptive Barzilai-Borwein(ABB)方法,充分利用模型参数变化量和梯度变化量自适应地计算初始步长。此外,本文对ABB初始步长计算方法中的阈值展开研究,探索适用于全波形反演方法的阈值范围。模型测试验证了ABB初始步长计算方法的有效性,且其阈值小于0.5时全波形反演效果最好。Full waveform inversion(FWI)is a nonlinear data ftting process that can derive high-resolution model parameters through iteration.In this process,step length is related to inversion accuracy and computational effciency.It can be calculated effciently with the inexact line search method,which does not require a misfit function to achieve the exact minimum.This method is aimed toward obtaining the appropriate descent using evaluation conditions and initial step length.Moreover,it does not depend on the form of the misfit function.In the inexact line search method,the evaluation condition and initial step length are obviously important factors.In this work,the classical Armijo,Wolfe,and Goldstein evaluation conditions in solving optimization problems in mathematics are studied and compared in detail.Numerical examples from the synthetic data of the overthrust model show that the convergence characteristics of Armijo and Goldstein are similar and that the computational efficiency is high and conducive to seismic FWI.In addition,the adaptive Barzilai–Borwein(ABB)method is adopted in FWI.The ABB method maximizes the changes in model parameters and gradients to adaptively calculate the initial step length.The threshold value of the ABB method for the initial step length estimation is also studied to explore a suitable threshold value that can ensure that large and small step lengths are frequently adopted in FWI.Numerical examples from the synthetic data of the overthrust model demonstrate the validity of the ABB method.Moreover,the inversion is superior when the threshold value is less than 0.5.

关 键 词：全波形反演 非精确线性搜索 判断条件 ABB初始步长 阈值 

分 类 号：P631.4[天文地球—地质矿产勘探]