Fast forward modeling of gravity anomalies for two-dimensional bodies of arbitrary shape and density distribution  

任意截面形状和密度分布的二度体重力异常正演快速算法

作　　者：Chen Xin Chen Long-Wei Luo Tian-Ya Xiong Bin 陈欣;陈龙伟;罗天涯;熊彬(广西隐伏矿床勘查重点实验室,桂林理工大学地球科学学院,广西桂林541006;湖北省地球内部多尺度成像重点实验室,中国地质大学(武汉)地球物理与空间信息学院,湖北武汉430074)

机构地区：[1]Guangxi Key Laboratory of Exploration for Hidden Metallic Ore Deposits,College of Earth Sciences,Guilin University of Technology,Guilin 541006,China [2]Hubei Subsurface Multi-scale Imaging Key Laboratory,Institute of Geophysics and Geomatics,China University of Geosciences,Wuhan 430074,China

出　　处：《Applied Geophysics》2020年第5期776-783,902,903,共10页应用地球物理（英文版）

基　　金：This work is jointly sponsored by the National Natural Science Foundation of China(No.41404106);the Scientific Research Startup Fund for Doctoral Program of Guilin University of Technology,Guangxi Natural Science Foundation Program(No.2018GXNSFBA138049);Guangxi Natural Science Foundation Program for Innovation Research Team(No.2016GXNSFGA380004).

摘　　要：A fast and high precision spatial domain algorithm is presented for forward modeling of two-dimensional(2D)body gravity anomalies of arbitrary shape and density distribution.The new algorithm takes advantage of the convolution properties of the expression for 2D gravity anomalies,uses a rectangular cell as a grid subdivision unit,and then 2D bodies with irregular cross-sections are approximated by a combination of 2D bodies with a rectangular cross section.The closed-form expression is used to calculate the gravitational anomalies of the combination of 2D bodies with a rectangular cross section.To improve computing effi ciency,the new algorithm uses a fast algorithm for the implementation of the Toeplitz matrix and vector multiplication.The synthetic 2D models with rectangular and circular cross-sections and constant and variable densities are designed to evaluate the computational accuracy and speed of the new algorithm.The experiment results show that the computation costs less than 6 s for a grid subdivision with 10000×10000 elements.Compared to the traditional forward modeling methods,the proposed method significantly improved computational effi ciency while guaranteeing computational accuracy.针对任意截面形状和密度分布的二度体重力异常计算问题,本文提出一种空间域高精度、快速算法。新的算法利用了二度体重力异常积分表达式的卷积特性,采用矩形网格剖分策略,利用截面为矩形的二度体来逼近不规则二度体,并利用解析公式计算截面为矩形的二度体重力异常;引入Toeplitz矩阵与向量相乘的快速算法来实现组合矩形二度体重力异常的计算,保证算法的计算效率。分别利用截面为矩形、圆形,常密度和变密度的二度体模型,对本文算法的计算精度和计算速度进行了检验,数值实验结果表明,对于10000×10000的网格剖分,计算时间不超过6秒。比照现有二度体正演方法,本文给出的方法在保证正演精度的同时,极大提高了正演计算速度。

关 键 词：two-dimensional bodies gravity anomalies forward modeling Toeplitz matrix 

分 类 号：P631.1[天文地球—地质矿产勘探]