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Finite-Difference–Integral Method for Computing Low-Frequency Electromagnetic Fields in a Nonhomogeneous Medium

  • I. NUMERICAL METHODS
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We derive integral relationships for electromagnetic fields, integral recalculation formulas for anomalous electric and magnetic fields, and integral boundary conditions. The efficiency of the finite-difference–integral method is checked by computing the apparent resistance curves for the graben model. Apparent resistance curves computed from finite-difference formulas and from formulas with integral smoothing are compared. Finite-difference graphs are polygonal curves that for small wavelengths lie below the smoothed curves, because the finite-difference computation of the derivative as if reduces the impact of the surface skin effect on the apparent resistance. As the wavelength increases, the surface skin effect diminishes and the finite-difference curves approach the integral curves.

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References

  1. V. I. Dmitriev and I. S. Barashkov, “Calculation of magnetic-polarization magnetotelluric field in a two-dimensional nonhomogeneous medium,” in: Numerical Methods in Geophysical Research [in Russian], Izd. MGU, Moscow (1979), pp. 38–46.

  2. I. S. Barashkov, “Calculation of electric-polarization magnetotelluric field in a two-dimensional nonhomogeneous medium,” in: Numerical Methods in Geophysical Research [in Russian], Izd. MGU, Moscow (1980), pp. 29–36.

  3. I. S. Barashkov and N. A. Mershchikova, “Comparative analysis of apparent resistance curves in a two-dimensional nonhomogeneous medium for E- and H-polarized field,” in: Numerical Methods in Geophysical Research [in Russian], Izd. MGU, Moscow (1980), pp. 16–28.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

    V. I. Dmitriev & I. S. Barashkov

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  1. V. I. Dmitriev
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  2. I. S. Barashkov
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Correspondence to V. I. Dmitriev.

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Translated from Prikladnaya Matematika i Informatika, No. 49, 2015, pp. 5–21.

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Dmitriev, V.I., Barashkov, I.S. Finite-Difference–Integral Method for Computing Low-Frequency Electromagnetic Fields in a Nonhomogeneous Medium. Comput Math Model 27, 145–161 (2016). https://doi.org/10.1007/s10598-016-9310-9

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  • DOI: https://doi.org/10.1007/s10598-016-9310-9

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