空间—波数混合域二度体重力异常正演  

Forward modeling for 2D-body gravity anomaly in the space-wavenumber mixed domain

作　　者：戴世坤 王旭龙[1,2] 赵东东 刘志伟 张钱江[4] 孙金飞 DAI Shikun;WANG Xulong;ZHAO Dongdong;LIU Zhiwei;ZHANG Qianjiang;SUN Jinfei(Key Laboratory of Metallogenic Prediction of NJonfcrrous Metals and Geological Environment Monitoring,Ministry of Education,Changsha*Hu­nan 410083.China;School of Geosciences and Info-physics,Central South University,Changsha,Hunan 410083,China;Guangdong Electric Power Design Institute,China Energy Engineering Group CO.,Guangzhou,Guangdong 510663,China;College of Earth Sciences,Guilin University of Technology,Guilin,Guangxi 541004,China;No.1 Daqing Geophysical Exploration Company of BGP,CNPC,Daqing,Heilongjiang 163357,China)

机构地区：[1]有色金属成矿预测与地质环境监测教育部重点实验室,湖南长沙410083 [2]中南大学地球科学与信息物理学院,湖南长沙410083 [3]中国能源建设集团广东省电力设计研究院有限公司,广东广州510663 [4]桂林理工大学地球科学学院,广西桂林541004 [5]东方地球物理公司大庆物探一公司,黑龙江大庆163357

出　　处：《石油地球物理勘探》2019年第6期1383-1389,I0014,I0015,共9页Oil Geophysical Prospecting

基　　金：国家重大研发计划项目“可控源电磁法三维逆散射电阻率极化率精细反演成像方法研究与软件研发”(2018YFC0603602);国家自然科学基金项目“各向异性介质多次覆盖可控源电磁法三维高效数值模拟与反演成像及最佳观测系统研究”(41574127);中南大学研究生自主探索创新项目“重磁位场空间波数混合域二维正反演研究”(2018ZZTS710);广西自然科学基金项目“含激电效应的可控源电磁法正反演成像、最优化观测系统及应用研究”(2018GXSFAA050070);广西科技基地和人才专项“基于电磁场分量的RMT/CSRMT二维正反演算法及应用研究”(AD19110058)联合资助

摘　　要：针对任意密度分布的二度体重力异常的计算,提出了一种空间-波数混合域二度体重力异常正演方法。该方法将二度体引力位满足的偏微分方程通过一维傅里叶变换,转化为不同波数相互独立的常微分方程,并采用基于二次插值的一维有限单元法求解该常微分方程。该方法充分利用了傅里叶变换的高效性和垂向网格剖分的灵活性,实现了二度体重力异常的高效、高精度数值模拟。采用截面为矩形的常密度和变密度的二度体模型,对所提算法的计算精度和速度进行检验,结果表明,与传统的二度体正演方法相比,算法在保证计算精度的同时,提高了计算效率。An efficient and high-precision forward modeling of 2D-body gravity anomaly in a space-wavenumber mixed domain is proposed to calculate the gravity anomaly in the case of arbitrary density distribution.By performing 1D Fourier transform,2D partial differential equation governing gravity potential in the spatial domain is transformed into a group of independent 1D differential equations engaged with different wavenumbers.The method preserves the vertical direction in the spatial domain,thus shallow and deep meshes for modeling can be fine and coarse respectively.By this way,both the accuracy and the efficiency of calculation are taken into account.1D finite element method is used to solve the transformed differential equations with different wave numbers.Moreover,the efficiency of solving linear equations with a fixed bandwidth assembled by the finite element analysis is further improved by a chasing method.To test the proposed algorithm,a constant-density 2D model and a variable-density 2D model are designed.Numerical test results show that the proposed algorithm not only guarantees the calculation accuracy,but also improves the calculation efficiency compared with the conventional methods.

关 键 词：重力异常 空间-波数混合域 二度体 正演 

分 类 号：P631[天文地球—地质矿产勘探]