基于柯西分布约束和快速近端目标函数优化的三维重力反演方法  

3Dgravity inversion based on Cauchy distribution constraint and fast proximal objective function optimization

作　　者：彭国民 刘展[1,2] 于会臻 徐凯军[1,2] 陈晓红[1,2] PENG GuoMin;LIU Zhan;YU HuiZhen;XU KaiJun;CHEN XiaoHong(School of Geosciences,China University of Petroleum(East China),Qingdao 266580,China;Laboratory for Marine Mineral Resources,Qingdao National Laboratory for Marine Science and Technology,Qingdao 266071,China;Research Institute of Exploration and Development,Shengli Oilfield,SINOPEC,Dongying Shandong 257000,China)

机构地区：[1]中国石油大学(华东)地球科学与技术学院,青岛266580 [2]海洋国家实验室海洋矿产资源评价与探测技术功能实验室,青岛266071 [3]中国石化胜利油田分公司勘探开发研究院,山东东营257000

出　　处：《地球物理学报》2018年第12期4934-4941,共8页Chinese Journal of Geophysics

基　　金：国家高技术研究发展计划(863计划)(2012AA09A201);国家青年自然科学基金(41304094)联合资助

摘　　要：优化算法的选取在很大程度上影响着三维重力反演的计算效率,从而制约着三维重力反演的实用性.在复杂地质构造背景下,不同岩性单元之间可能会发生物性突变,产生尖锐边界.为此,本文提出了一种新的基于柯西分布约束和快速近端目标函数(Fast Proximal Objective Function,FPOF)优化的三维重力反演方法.FPOF优化方法的一个突出特点是在每一步迭代过程中逐一计算剖分网格内的未知密度参数,因此,有较低的计算复杂度和较高的计算效率.此外,目标函数中柯西范数(Cauchy norm)的引入会对反演结果施加稀疏性,有助于产生块状效果.理论模型测试表明,本文方法不仅能产生更加聚焦的反演效果,而且反演所需的时间也比传统的共轭梯度优化方法少.最后将本文方法应用于我国西部某地区实际重力数据,反演结果与已知的地质信息有较好的一致性.The choice of an optimization algorithm affects computational efficiency of 3D gravity data inversion to a great extent and thereby constrains its application in the industry.In the context of complex subsurface geological settings,sharp boundaries may exist between different rock units that have large physical property contrasts.To this end,we propose a novel 3D gravity inversion method based on Cauchy distribution constraint and fast proximal objective function(FPOF)optimization.A salient characteristic of FPOF optimization is to calculate the unknown density in each subdivided unit of the inversion domain one by one at each iteration,thus reducing computational complexity and improving computational efficiency.In addition,the inclusion of Cauchy norm into objective function imposes sparseness on model parameters to be inverted and consequently facilitates a blocky density distribution.The test of synthetic data demonstrates that the proposed inversion method not only recovers more focused anomalous density bodies but also costs less run time than conventional CG optimization method.At last,the application of the proposed inversion method to real gravity data in the Western China shows that the recovered 3D density model agrees well with the known geological knowledge.

关 键 词：三维反演 重力数据 快速近端目标函数优化 柯西分布 

分 类 号：P631[天文地球—地质矿产勘探]