A block iterative algorithm for 3-D electromagnetic modeling using integral equations with symmetrized substructures

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 291-295 ◽  
Author(s):  
Zonghou Xiong ◽  
Alan C. Tripp
Keyword(s):  
Integral Equation ◽  
Iterative Algorithm ◽  
Computation Time ◽  
Cost Effective ◽  
Integral Equation Method ◽  
Scattering Matrix ◽  
Electromagnetic Response ◽  
Electromagnetic Modeling ◽  
Large Structures ◽  
Computer Storage

The integral equation method is in many cases a cost effective way of modeling the electromagnetic response of 3-D conductivity structures. Yet the requirements on computer storage and on computation time in forming and inverting the scattering matrix limit its applications for large structures.

Symmetry properties of the scattering matrix in 3-D electromagnetic modeling using the integral equation method

Geophysics ◽  
1992 ◽  
Vol 57 (9) ◽  
pp. 1199-1202 ◽  
Author(s):  
Zonghou Xiong
Keyword(s):  
Integral Equation ◽  
Three Dimensional ◽  
Computation Time ◽  
Integral Equation Method ◽  
Scattering Matrix ◽  
Electromagnetic Modeling ◽  
Symmetry Properties ◽  
Computer Storage ◽  
Earth Conductivity ◽  
Number Of Cells

Modeling large three‐dimensional (3-D) earth conductivity structures continues to pose challenges. Although the theories of electromagnetic modeling are well understood, the basic computational problems are practical, involving the quadratically growing requirements on computer storage and cubically growing computation time with the number of cells required to discretize the modeling body.

Quasi‐analytical approximations and series in electromagnetic modeling

Geophysics ◽  
2000 ◽  
Vol 65 (6) ◽  
pp. 1746-1757 ◽  
Author(s):  
Michael S. Zhdanov ◽  
Vladimir I. Dmitriev ◽  
Sheng Fang ◽  
Gábor Hursán
Keyword(s):  
Integral Equation ◽  
Linear Approximation ◽  
Linear Equations ◽  
Integral Equation Method ◽  
Forward Modeling ◽  
Computational Effort ◽  
Correct Result ◽  
Electromagnetic Modeling ◽  
Analytical Approximations ◽  
Analytical Series

The quasi‐linear approximation for electromagnetic forward modeling is based on the assumption that the anomalous electrical field within an inhomogeneous domain is linearly proportional to the background (normal) field through an electrical reflectivity tensor λ⁁. In the original formulation of the quasi‐linear approximation, λ⁁ was determined by solving a minimization problem based on an integral equation for the scattering currents. This approach is much less time‐consuming than the full integral equation method; however, it still requires solution of the corresponding system of linear equations. In this paper, we present a new approach to the approximate solution of the integral equation using λ⁁ through construction of quasi‐analytical expressions for the anomalous electromagnetic field for 3-D and 2-D models. Quasi‐analytical solutions reduce dramatically the computational effort related to forward electromagnetic modeling of inhomogeneous geoelectrical structures. In the last sections of this paper, we extend the quasi‐analytical method using iterations and develop higher order approximations resulting in quasi‐analytical series which provide improved accuracy. Computation of these series is based on repetitive application of the given integral contraction operator, which insures rapid convergence to the correct result. Numerical studies demonstrate that quasi‐analytical series can be treated as a new powerful method of fast but rigorous forward modeling solution.

Induced‐polarization and electromagnetic modeling of a three‐dimensional body buried in a two‐layer anisotropic earth

Geophysics ◽  
1986 ◽  
Vol 51 (12) ◽  
pp. 2235-2246 ◽  
Author(s):  
Zonghou Xiong ◽  
Yanzhong Luo ◽  
Shoutan Wang ◽  
Guangyao Wu
Keyword(s):  
Integral Equation ◽  
Green’S Function ◽  
Green's Function ◽  
Lower Layer ◽  
Integral Equation Method ◽  
Induced Polarization ◽  
Equation Method ◽  
Frequency Effect ◽  
Electromagnetic Modeling ◽  
The Earth

The integral equation method is used for induced‐polarization (IP) and electromagnetic (EM) modeling of a finite inhomogeneity in a two‐layer anisotropic earth. An integral equation relates the exciting electric field and the scattering currents in the homogeneity through the electric tensor Green’s function deduced from the vector potentials in the lower layer of the earth. Digital linear filtering and three‐point parabolic Lagrangian interpolation with two variables speed up the numerical evaluation of the Hankel transforms in the tensor Green’s function. The results of this integral equation method for isotropic media are checked by direct comparisons with results by other workers. The results for anisotropic media are indirectly verified, mainly by checking the tensor Green’s function. The calculated results show that the effects of anisotropy on apparent resistivity and percent frequency effect are to reduce the size of the anomalies, shift the anomaly region downward toward the lower centers of the pseudosections, and enhance the effect of overburden; in other words, to shade the target from detection. This is due to the increase of currents flowing horizontally through the earth over the target. The effects of anisotropy on horizontal‐loop EM responses are to reduce the amplitude and lower the critical frequency of the maximum of the quadrature component.

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