Three-dimensional gravity inversion based on sparse recovery iteration using approximate zero norm  

基于近似零范数稀疏恢复的迭代解法的三维重力反演（英文）

作　　者：Meng Zhao-Hai Xu Xue-Chun Huang Da-Nian 孟兆海;徐学纯;黄大年

机构地区：[1]天津航海仪器研究所 [2]中国科学院地质与地球物理研究所中国科学院油气资源研究重点实验室,北京100029 [3]吉林大学地球科学学院,吉林长春130012 [4]吉林大学地球探测科学与技术学院,吉林长春130012

出　　处：《Applied Geophysics》2018年第3期524-535,共12页应用地球物理（英文版）

基　　金：supported by the Development of airborne gravity gradiometer(No.2017YFC0601601);open subject of Key Laboratory of Petroleum Resources Research,Institute of Geology and Geophysics,Chinese Academy of Sciences(No.KLOR2018-8)

摘　　要：This research proposes a novel three-dimensional gravity inversion based on sparse recovery in compress sensing. Zero norm is selected as the objective function, which is then iteratively solved by the approximate zero norm solution. The inversion approach mainly employs forward modeling; a depth weight function is introduced into the objective function of the zero norms. Sparse inversion results are obtained by the corresponding optimal mathematical method. To achieve the practical geophysical and geological significance of the results, penalty function is applied to constrain the density values. Results obtained by proposed provide clear boundary depth and density contrast distribution information. The method's accuracy, validity, and reliability are verified by comparing its results with those of synthetic models. To further explain its reliability, a practical gravity data is obtained for a region in Texas, USA is applied. Inversion results for this region are compared with those of previous studies, including a research of logging data in the same area. The depth of salt dome obtained by the inversion method is 4.2 km, which is in good agreement with the 4.4 km value from the logging data. From this, the practicality of the inversion method is also validated.重力反演是应用地球物理中一个经典的方法,可以获取地下空间的密度分布特征。本文研究了一种新的三维重力反演方法,以压缩感知中的稀疏恢复方法为基本原理。建立以零范数为约束的目标函数,采用近似零范数求解方法对目标函数进行迭代求解。以重力正演模型为基础进行反演方法研究,建立包含深度加权函数的零范数的目标函数,采用相应的最优化数学方法进行求解,得到稀疏的反演结果。同时,为了得到具有实际地质意义的反演结果,采用惩罚函数将反演密度值约束在具有实际地球物理和地质意义范围内。采用本文提出的反演方法得到的反演目标异常源具有较为清晰的边界、深度信息和剩余密度分布信息。本文利用理论模型实验来验证反演方法效果,并将得到的反演结果与设计的理论模型对比分析说明三维反演方法的有效性和可靠性。为了进一步说明本文采用的反演方法的可靠性,将其应用到美国德克萨斯州采集的实际重力数据反演,并将反演结果与前人研究结果和该地区的测井资料进行对比分析,盐丘的深度为4.2km与测井得到深度4.4km基本上是一致的,说明研究的反演方法具有实际应用价值。

关 键 词：THREE-DIMENSIONAL gravity inversion sparse recovery APPROXIMATE ZERO NORM iterative method density constraint PENALTY function 

分 类 号：O[理学]