Three-Dimensional Finite-Volume Modelling And Truncated Newton Inversion For Frequency-Domain Land EM Methods

There are varieties of frequency-domain electromagnetics(FD EM)methods for ground exploration.Especially in the study of deep-earth structures,geothermal,mining,oil & gas exploration,environmental and engineering investigation,they played important roles.With the development of EM techniques and the demand for three-dimensional(3D)detailed exploration,the ground FDEM has become important and potential exploration method.Therefore,3D FDEM modeling and inversion becomes the key issue in detailed and quantitative interpretation of large-scale data.Due to the singularity of source,modeling speed and accuracy,3D inversion applicability and computing efficiency have limited their uses.This paper adopts finite-volume(FV)method to solve coupling equations in Lorenz gauge to realize the 3D FDEM modeling for arbitrary transmitting source;I propose a “global” optimization algorithm – truncated Newton method(TRN)and typical inversion methods to do 3D FDEM inversion and study its feasibility by inverting 3D magnetotelluric(MT)data,based on which I establish a platform for ground FDEM modeling and inversion to provide basis for the improvement of 3D interpretation of EM exploration.To solve problems with air-earth coupling,varieties of sources and different observed data in FDEM modeling,I first present a m agnetic vector and a sca lar potential with Lorenz gauge based on Maxwell equations,then I use the staggered grids and finite-volume method to discrete the potential equations.After that,I divide different sources into short wires and implement the quasi-minimum-residual(QMR)iterative solver with Jacobian to solve the large,linear,sparse,and symmetrical equations system.Finally,I accomplish frequency-domain EM modeling for different source types and application areas.Through analyses and comparison with 1D results,Idemonstrate the efficiency and accuracy of my algorithm.Based on this,I analyze the EM responses for different source types.To further speed up the 3D FDEM modeling,I present a novel algebraic multigrid—aggregation-based algebraic multigrid(AGMG).Based on the coarsening and nested iteration of AGMG method,I couple AGMG and conventional Krylov subspace algorithm(generalized minimum residual/GCR,flexible conjugate gradient method/FCG)and propose five different AGMG methods.Then,I perform 3D MT modeling for typical geo-electric models with different iterative methods and analyze the features of my AGMG techniques by comparing with Mod EM algorithm.After comparing my results for different grids and polarization modes with those of Quas-minimum residual(QMR)method,it is seen that K-AGMG-GCR improves the stability of AGMG and possesses quick convergence,high speed,and considerable efficiency.K-AGMG-GCR algorithm speeds up the modeling ten times more than the Mod EM algorithm,especially for large-scale 3D FDEM cases.This paper also presents a global optimization algorithm –TRN that is based on the combination of global trusted-domain algorithm and Newton method.Firstly,I establish 3D FDEM objective functional,covariance matrix of the model and the expression of data covariance according to the optimization and regularization theory.Then,I derivative the FDEM gradients for different data types,and the general expressions and calculation methods of Hessian and Jacobi matrix.The theory and key techniques(step-length searching,adaptive truncation error and annealing regularization factor)of TRN and the conventional optimization algorithms(steepest descent method/STD,non-linear conjugate gradient/NLCG,Gauss-Newton-conjugate gradient/GNCG and limited-memory BFGS)are also studied.Finally,based on the module concept and MPI parallel technique,I accomplish the 3D ground FDEM inversion with different methods.By taking MT inversion as an example,I design two models(combination of poor and good conductors and an arch bridge model)and compare the inversion results calculated with different inversion methods.The results show that we can obtain good results with all these inversion methods(TRN,STD,NLCG,L-BFGS,and GNCG)and they have a good consistency.Also,the results with TRN perform similar with those of Mod EM that is a widely-used in MT data processing.The proposed TRN that is a global optimization algorithm has quick convergence and few iterations.It inverts the data as well as the GNCG algorithm,better than gradient-based algorithm(STD,NLCG,L-BFGS and Mod EM)and It improves the efficiency and local optimization of GNCG.Then,I take for instance the underground conductive ore and discuss the influence of inversion parameters(regularization factors,initial truncation error,initial model and grids)and the observed data(noise level,data type,number of frequencies and survey stations)on algorithms.The results show that TRN has less dependence on t he initial model and has stronger anti-interference ability.Finally,this algorithm is used to process the MT survey data in Mongolia.By comparing the results with 2D inversion and the seismic profile,it is seen that the results with TRN inversion reveal the topographic basement well.It solves the problem that 2D inversion has distortion caused by 3D abnormal body,which further demonstrates the efficiency of TRN algorithm.