基于L_(p)拟范数稀疏约束和交替方向乘子算法的波阻抗反演  

Seismic acoustic impedance inversion using L_(p) quasi-norm sparse constraint and alternating direction multiplier algorithm

作　　者：张雨强 文晓涛[1,2] 吴昊 刘军 刘炀[1,2] ZHANG Yuqiang;WEN Xiaotao;WU Hao;LIU Jun;LIU Yang(College of Geophysics,Chengdu University of Technology,Chengdu 610059,China;State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation,Chengdu University of Technology,Chengdu 610059,China;Key Laboratory of Tectonics and Petroleum Resources(China University of Geosciences),Ministry of Education,Wuhan 430074,China)

机构地区：[1]成都理工大学地球物理学院,四川成都610059 [2]成都理工大学油气藏地质及开发工程重点实验室,四川成都610059 [3]中国地质大学构造与油气资源教育部重点实验室,湖北武汉430074

出　　处：《石油物探》2022年第5期856-864,共9页Geophysical Prospecting For Petroleum

基　　金：国家自然科学基金项目(41774142);“构造与油气资源”教育部重点实验室开放研究基金课题(TPR-2020-16)共同资助。

摘　　要：波阻抗是反映岩性的重要参数之一,该参数可通过叠后反演获得。基于L_(1)范数稀疏约束的正则化方法是目前常用的叠后波阻抗反演算法,但该方法获得的先验信息有限。为了挖掘更多的稀疏先验信息,进一步提高反演结果的精度,引入了基于L_(p)拟范数(0<p<1)稀疏约束和交替方向乘子算法两项关键技术。前者针对稀疏先验信息挖掘不足问题,采用了比L_(1)范数更为稀疏的L_(p)拟范数(0<p<1)作为稀疏约束,并加入了初始模型约束构成目标函数;后者针对L_(p)拟范数无法直接求解问题,采用交替方向乘子算法将目标函数分解为多个可以直接求解的子函数,然后交替求解。将提出的反演方法用于理论模型及实际数据的反演,与传统L_(1)范数稀疏约束的基追踪反演算法相比,新方法得到的反演结果精度更高,并具有一定的抗噪性。Seismic impedance is an important parameter reflecting lithology and can be obtained via post-stack seismic inversion.The regularization method based on the L_(1)norm sparse constraint is a typically used post-stack inversion algorithm;nonetheless,the prior information yielded by this method is limited.Two key technologies based on the L_(p)quasi-norm(0<p<1)sparse constraint and an alternating direction multiplier are introduced to mine more prior information and further improve the inversion accuracy.To address the insufficient mining of sparse prior information,the former technology uses the L_(p)quasi-norm(0<p<1),which is sparser than the L_(1)norm as a sparse constraint and adds the initial model constraint to form the objective function.As the L_(p)quasi-norm cannot be solved,the alternating direction multiplier is used to decompose the objective function into multiple sub-objective functions that can be solved directly and then alternately.The proposed inversion method is applied to a theoretical model and actual data.Compared with the conventional basis pursuit inversion algorithm using the L_(1)norm sparse constraint,the proposed method yields more accurate inversion results and exhibits anti-noise properties.

关 键 词：交替方向乘子算法 波阻抗反演 稀疏正则化 L_(p)拟范数 

分 类 号：P631[天文地球—地质矿产勘探]