A quasi‐analytical boundary condition for three‐dimensional finite difference electromagnetic modeling

Abstract

[1] Numerical modeling of the quasi-static electromagnetic (EM) field in the frequency domain in a three-dimensional (3-D) inhomogeneous medium is a very challenging problem in computational physics. We present a new approach to the finite difference (FD) solution of this problem. The FD discretization of the EM field equation is based on the balance method. To compute the boundary values of the anomalous electric field we solve for, we suggest using the fast and accurate quasi-analytical (QA) approximation, which is a special form of the extended Born approximation. We call this new condition a quasi-analytical boundary condition (QA BC). This approach helps to reduce the size of the modeling domain without losing the accuracy of calculation. As a result, a larger number of grid cells can be used to describe the anomalous conductivity distribution within the modeling domain. The developed numerical technique allows application of a very fine discretization to the area with anomalous conductivity only because there is no need to move the boundaries too far from the inhomogeneous region, as required by the traditional Dirichlet or Neumann conditions for anomalous field with boundary values equal to zero. Therefore this approach increases the efficiency of FD modeling of the EM field in a medium with complex structure. We apply the QA BC and the traditional FD (with large grid and zero BC) methods to complicated models with high resistivity contrast. The numerical modeling demonstrates that the QA BC results in 5 times matrix size reduction and 2-3 times decrease in computational time.INDEX TERMS: 0644 Electromagnetics: Numerical methods; 0639 Electromagnetics: Nonlinear electromagnetics; 0925 Exploration Geophysics: Magnetic and electrical methods; KEYWORDS: finite difference, electromagnetic modeling, boundary conditions Citation: Mehanee, S., and M. Zhdanov (2004), A quasi-analytical boundary condition for three-dimensional finite difference electromagnetic modeling, Radio Sci., 39, RS6014,

An approximate hybrid method for modeling of electromagnetic scattering from an underground target

“…Mehanee and Zhdanov [79] used the fast QA approximation [133] (see subsection 5.3.2 for description of QA) to compute the boundary values of the anomalous electric field. These precomputed values are then used as boundary conditions for the FD modeling based on the balance method.…”

“…However, in the case of the quasi-static EM field, which is the subject of our research, it is difficult to use the model of EM waves and their reflection from the boundaries because the field propagates according to the diffusion law. That is why the original PML ABC, developed for the FD time domain EM field, has found little application in modeling the quasi-static EM field used in geophysical applications [79].…”

“…Solutions and Approaches in the Frequency Domain solve the corresponding equations separately for the electric or magnetic fields (see, e.g., [85,86,79,91,83,1]). Another approach to the formulation of EM boundary-value problem is to use the EM potentials.…”

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“…Potential field techniques have various successful applications in exploration geophysics [1][2][3][4][5][6][7][8][9][10]. One of the most essential applications of the magnetic dataset is to define the location and depth of magnetic bodies.…”