基于代数重构算法的重力梯度张量反演  

Density inversion of gravity gradient tensor based on ART

作　　者：李红蕾[1,2] 方剑[1] 王新胜 刘杰[1,2] 崔荣花[1,2] 陈铭[1,2] 

机构地区：[1]中国科学院测量与地球物理研究所大地测量与地球动力学国家重点实验室,武汉430077 [2]中国科学院大学,北京100049 [3]地壳运动监测工程研究中心,北京100036

出　　处：《地球物理学进展》2016年第1期54-60,共7页Progress in Geophysics

基　　金：国家重点基础研究发展计划(973计划)(2013CB733301);国家自然科学基金(41274025;41274085;41574073)联合资助

摘　　要：本文基于重力梯度张量密度反演基本理论,建立了模型约束正则化密度反演矩阵方程.分析了代数重构算法(ART)中迭代初始值、松弛因子和终止条件三个关键参数的影响;与最小二乘求逆法对应比较分析了算法的时间和精度.结果表明:在地震、地质等地球物理手段提供初值、边界等约束较多的情况下,ART可以克服方程的不适定进行直接求解,并且合理的松弛因子和终止条件可有效提高反演效率.当初始信息不足时,添加光滑假设、深度加权等模型约束,正则化方程可以提高反演结果的可靠性.ART的行迭代可有效避免观测误差的积累和矩阵求逆的计算,从而使计算精度和速度提高数倍.最后基于GOCE地球重力场模型所得重力梯度,以地震层析成像所得速度模型为约束,对华北克拉通密度结构进行了反演,并与该区已有密度研究结果进行了对比.结果表明:利用GOCE重力场系数计算重力梯度扰动,以速度模型为约束,基于代数重构算法进行重力梯度反演所得密度模型与重力-地震联合反演所得密度模型具有很好的对应性.ART算法为重力梯度张量反演中大规模复杂问题的快速计算提供了又一种有效手段.This paper starts from the forward formula of gravity gradient. Established a model constrains objective function based on Tikhonov regulation. In the thesis, three key parameters of algebraic reconstruction technique,namely the initial value,the relaxation factor and the terminating condition have been discussed.The result shows： if there are enough initial values and boundary constraints that provided by seismic, geological or such other geophysical means, ART can overcome ill-posed equations for solving directly. Reasonable relaxation factor and termination conditions can improve the efficiency of the inversion effectively. If such information is insufficient,the reliability of inversion results can be improved by adding smooth hypothesis and depth weighted constraints to the equation. The line iterative process of ART can avoid the accumulation of observation error and the calculation of matrix inversion,hence calculation accuracy improved by several times and it gives a significant speed advantage. Obtain the density structure of north China carton by inversion the gravity gradient derive from GOCE earth gravity field models based on ART and seismic tomography provide initial values for the inversion. The results compared with the existing research results. Results show that： The density structures derive from GOCE gravity gradient disturbance has a good correspondence with gravity- seismic joint inverse results.（ ART） provides a reliable and rapid method to the inversion of a large sparse matrix.

关 键 词：重力梯度张量 模型约束 代数重构算法(ART算法) 3D大规模密度反演 

分 类 号：P631[天文地球—地质矿产勘探]