全波形反演正则化方法对比  

Comparison of regularization methods for full-wave-form inversion

作　　者：李昕洁 王维红[1] 郭雪豹[1] 张庭俊 LI Xinjie;WANG Weihong;GUO Xuebao;ZHANG Tingjun(School of Earth Sciences,Northeast Petroleum University,Daqing,Heilongjiang 163318,China)

机构地区：[1]东北石油大学地球科学学院,黑龙江大庆163318

出　　处：《石油地球物理勘探》2022年第1期129-139,I0005,I0006,共13页Oil Geophysical Prospecting

基　　金：国家自然科学基金面上项目“基于数据驱动的逆散射级数层间多次波压制方法”(41974116);国家自然科学青年基金“基于近偏地震数据约束的全波形反演研究”(41904121);东北石油大学青年科学基金“去子波全波形反演方法研究”(2018QNL-03)联合资助。

摘　　要：正则化是缓解反演不适定性、约束解特征的重要方式。Tikhonov正则化、全变分(TV)正则化是全波形反演中常用的两种正则化方法,分别具有压制高波数和保护地层边缘的特点。双参数整形正则化、混合双参数正则化和稀疏结构约束正则化是在二者的基础上发展而来,并具备各自优势。为系统论证不同正则化方法特点,对五种正则化方法的全波形反演进行了对比分析。背斜—超覆模型、Marmousi模型测试表明,不同的正则化方法均对反演结果有不同程度的改进。双参数整形正则化兼具Tikhonov正则化和TV正则化的优势,并可有效提高深部反演精度。混合双参数正则化能进一步提高浅层反演精度。相较于其他方法,稀疏结构约束正则化无论在地层连续性,还是在边缘结构的刻画上均有明显优势。Regularization is an important way to alleviate the ill-posedness of inversion and the characteristics of constrained solutions.Tikhonov regularization and total variation(TV)regularization are two regularization methods commonly used in fullwaveform inversion.They can suppress high wavenumbers and protect the formation edge respectively.Two-parameter shaping regularization,hybrid two-parameter regularization,and sparse structure constraint regularization are developed on the basis of the former two and have their advantages.To systematically demonstrate the characteristics of different regularization methods,this paper makes a comparative analysis of the full-waveform inversion methods constrained by the five regularization methods.The anticline-overlap model and Marmousi model tests show that different regularization methods all improve the inversion results to various degrees.Two-parameter shaping regularization combines the advantages of Tikhonov regularization and TV regularization,which improves the deep accuracy.Hybrid twoparameter regularization further improves the accuracy of shallow inversion.Compared with other methods,sparse structure constraint regularization has obvious advantages in both stratigraphic continuity and the description of edge structure.

关 键 词：全波形反演 TIKHONOV正则化 全变分(TV)正则化 双参数正则化 稀疏结构约束正则化 

分 类 号：P631[天文地球—地质矿产勘探]