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Article

A Comparison Study of Explicit and Implicit 3-D Transient Electromagnetic Forward Modeling Schemes on Multi-Resolution Grid

1
Department of Civil, Environmental and Natural Resources Engineering, Luleå University of Technology, 97187 Luleå, Sweden
2
Institute of Geophysics and Meteorology, University of Cologne, 50923 Cologne, Germany
3
College of Earth, Ocean and Atmospheric Sciences, Oregon State University, Corvallis, OR 97331, USA
*
Author to whom correspondence should be addressed.
Academic Editors: Lev V. Eppelbaum, Giuseppe Lacidogna, Rosa Di Maio, Jose M. Carcione and Jesus Martinez-Frias
Geosciences 2021, 11(6), 257; https://doi.org/10.3390/geosciences11060257
Received: 19 February 2021 / Revised: 23 April 2021 / Accepted: 8 June 2021 / Published: 15 June 2021
(This article belongs to the Special Issue 3D Modelling/Inversion for Mineral Exploration)
This study compares the efficiency of 3-D transient electromagnetic forward modeling schemes on the multi-resolution grid for various modeling scenarios. We developed time-domain finite-difference modeling based on the explicit scheme earlier. In this work, we additionally implement 3-D transient electromagnetic forward modeling using the backward Euler implicit scheme. The iterative solver is used for solving the system of equations and requires a proper initial guess that has significant effect on the convergence. The standard approach usually employs the solution of a previous time step as an initial guess, which might be too conservative. Instead, we test various initial guesses based on the linear extrapolation or linear combination of the solutions from several previous steps. We build up the implicit scheme forward modeling on the multi-resolution grid, which allows for the adjustment of the horizontal resolution with depth, hence improving the performance of the forward operator. Synthetic examples show the implicit scheme forward modeling using the linearly combined initial guess estimate on the multi-resolution grid additionally reduces the run time compared to the standard initial guess approach. The result of comparison between the implicit scheme developed here with the previously developed explicit scheme shows that the explicit scheme modeling is more efficient for more conductive background models often found in environmental studies. However, the implicit scheme modeling is more suitable for the simulation with highly resistive background models, usually occurring in mineral exploration scenarios. Thus, the inverse problem can be solved using more efficient forward solution depending on the modeling setup and background resistivity. View Full-Text
Keywords: transient electromagnetic method; 3-D forward modeling; explicit scheme; implicit scheme; initial guess; multi-resolution grid transient electromagnetic method; 3-D forward modeling; explicit scheme; implicit scheme; initial guess; multi-resolution grid
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MDPI and ACS Style

Gao, J.; Smirnov, M.; Smirnova, M.; Egbert, G. A Comparison Study of Explicit and Implicit 3-D Transient Electromagnetic Forward Modeling Schemes on Multi-Resolution Grid. Geosciences 2021, 11, 257. https://doi.org/10.3390/geosciences11060257

AMA Style

Gao J, Smirnov M, Smirnova M, Egbert G. A Comparison Study of Explicit and Implicit 3-D Transient Electromagnetic Forward Modeling Schemes on Multi-Resolution Grid. Geosciences. 2021; 11(6):257. https://doi.org/10.3390/geosciences11060257

Chicago/Turabian Style

Gao, Jingyu, Maxim Smirnov, Maria Smirnova, and Gary Egbert. 2021. "A Comparison Study of Explicit and Implicit 3-D Transient Electromagnetic Forward Modeling Schemes on Multi-Resolution Grid" Geosciences 11, no. 6: 257. https://doi.org/10.3390/geosciences11060257

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