基于Lanczos-模型降阶算法的三维频率域可控源电磁快速正演  

Fast 3D forward modeling of frequency domain controlled-source electromagnetic method using Lanczos-model order reduction algorithm

作　　者：刘寄仁 汤井田[1,2,3,4] 任政勇 张继锋[5] LIU JiRen;TANG JingTian;REN ZhengYong;ZHANG JiFeng(School of Geosciences and Info-physics of Central South University,Changsha 410083,China;Key Laboratory of Metallogenic Prediction of Nonferrous Metals and Geological Environment Monitoring,Ministry of Education,Central South University,Changsha 410083,China;Hunan Key Laboratory of Nonferrous Resources and Geological Hazards Exploration,Changsha 410083,China;Technical Innovation Center of Coverage Area Deep Resources Exploration,Ministry of Natural Resources,Hefei 230001,China;School of Geology Engineering and Geomatics,Chang'an University,Xi'an 710061,China)

机构地区：[1]中南大学地球科学与信息物理学院,长沙410083 [2]中南大学有色金属成矿预测与地质环境监测教育部重点实验室,长沙410083 [3]有色资源与地质灾害探查湖南省重点实验室,长沙410083 [4]自然资源部覆盖区深部资源勘查工程技术创新中心,合肥230001 [5]长安大学地质工程与测绘学院,西安710061

出　　处：《地球物理学报》2022年第6期2326-2339,共14页Chinese Journal of Geophysics

基　　金：国家自然科学基金项目(41922027,41830107);陕西省自然科学基金(2021JM-159)资助。

摘　　要：快速的电磁法正演模拟是反演的核心要素之一.本文针对陆地可控源电磁(CSEM)问题,实现了三维多频的快速正演.首先基于电场的微分控制方程,利用非结构化网格和伽辽金方法建立关于电场矢量的有限元线性方程组.为快速求解大规模复系数有限元线性方程组,本文引入了基于有理Krylov子空间的单极点模型降阶算法.该方法只需求解实系数矩阵方程,然后使用Lanczos算法快速构建有理Krylov正交基子空间,达到系数矩阵维数降阶的目的,从而加快正演求解速度.层状模型和低阻块体模型的计算模拟表明:在精度满足条件的情况下,同常规有限元方法相比,加速比达到10~20多倍.对于百万未知数级、几十至上百个频率的三维可控源电磁正演问题,在个人PC机上只需几分钟便可快速求解.Fast electromagnetic forward modeling is one of the core elements of inversion.In order to solve the problem of land controlled-source electromagnetic(CSEM)modeling,we have realized the fast forward modeling of 3-D multi-frequency CSEM.Firstly,based on the differential governing equation of electric field,the expression of finite element linear equations about electric field vector is established by using unstructured grid and Galerkin method.In order to solve the large-scale complex linear equations quickly,we introduce a model order reduction algorithm based on rational Krylov subspace which only needs to select a single pole.This method only needs to solve the real coefficient matrix equations,and then uses the Lanczos algorithm to quickly construct the orthogonal basis of rational Krylov subspace,so as to reduce the dimension of the coefficient matrix and speed up the forward modeling.The modeling results of the layered model and block low resistivity body model show that the speedup ratio is more than 10~20 times compared with the conventional finite element method when the accuracy meets the requirements.For the three-dimensional controlled-source electromagnetic forward modeling problem with millions of unknowns and tens to hundreds of frequencies,it only takes a few minutes to solve it on a personal computer.

关 键 词：多频可控源电磁正演 非结构化网格 矢量有限元 模型降阶 LANCZOS算法 

分 类 号：P631[天文地球—地质矿产勘探]