无网格方法及其在地球物理勘探中的应用与展望  

Study on meshfree methods in geophysics:application and progress

作　　者：黄尧 刘彦[1,2] 吕庆田 孟贵祥[1,2] 史大年[1,2] 刘双 严加永[1,2] HUANG Yao;LIU Yan;Lü QingTian;MENG GuiXiang;SHI DaNian;LIU Shuang;YAN JiaYong(Chinese Academy of Geological Sciences,Deep Earth Science and Exploration Technology Laboratory,Ministry of Natural Resources,Beijing 100037,China;SinoProbe Center,Chinese Academy of Geological Sciences and China Geological Survey,Beijing 100037,China;Institute of Geophysics and Geomatics,China University of Geoscience,Wuhan 430074,China)

机构地区：[1]中国地质科学院,自然资源部深地科学与探测技术实验室,北京100037 [2]中国地质调查局中国地质科学院,地球深部探测中心,北京100037 [3]中国地质大学,地球物理与空间信息学院,武汉430074

出　　处：《地球物理学进展》2022年第5期1946-1959,共14页Progress in Geophysics

基　　金：国家自然科学基金(42174169);中国地质调查项目(DD20190707,DD20190012);中央级公益性科研院所基本科研业务费(JKY202014)联合资助。

摘　　要：产生于20世纪70年代的无网格法是一类新兴的数值方法,现已被广泛运用于科学计算及工程问题并取得了显著成效.相较于有限元方法,无网格法具有网格依赖性弱、精度高、收敛速度快、方便构造高阶拟合函数等优点.经过几十年的发展,无网格法取得了长足的进步,诞生了多种方法.无网格方法之间的主要区别在于构造近似函数的不同和加权余量法的选择.本文概述了无网格法的发展历史和研究进展以及在地球物理学中的应用状况;详细阐述了多种无网格的近似方法,包括:移动最小二乘近似、径向基函数近似、核积分近似、再生核粒子近似等,以及常用的加权余量法—配点法、伽辽金法、局部伽辽金法.并对这些无网格方法的差异性作了系统对比分析,同时指出了在地球物理领域的适用范围.还例举了无网格法在地震勘探领域的波动方程、重磁勘探领域的位场延拓以及异常体正演的求解过程.最后讨论了无网格方法应用于地球物理勘探领域时存在的困难和挑战,并分析了未来无网格方法的应用前景和潜力方向.Meshfree method is a new class of numerical methods,which has been widely used in scientific calculation and engineering problems with considerable success.Compared with finite element method,meshfree method has the advantages of mesh-dependent weak,high precision,high convergence speed,convenient construction of high-order fitting function and so on.The main differences between meshfree methods are the different construction of approximate functions and the choice of weighted residuals.This study summarizes the progress of meshfree method and its application in geophysics.Several meshfree approximation methods(moving least square approximation,radial basis function approximation,kernel integral approximation,reproducing kernel particle approximation,etc.)and common weighted residual method(collocation method,Galerkin method,local Galerkin method,etc.)are described in detail.The differences of various meshfree methods are systematically analyzed and their application in geophysical field is also explained.We introduce the solution process of meshfree method in wave equation,potential field continuation and geological body forward modeling.Finally,the difficulties and challenges in the application of meshfree method to geophysical exploration are discussed,and the application prospect of meshfree method in the future are analyzed.

关 键 词：无网格法 近似函数 加权余量法 地球物理勘探 

分 类 号：P631[天文地球—地质矿产勘探]