Applying Maxwell's EM Equations in the Low-Frequency Limit to Earth Investigations



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Standard seismic-processing methods have been applied to numerical simulations for several variations of a standard 1D numerical ISEM model. These calculations were justified by the mathematical similarity between dynamical equations in elastodynamics and electromagnetics, and demonstrated that, in simple cases, numerical ISEM data, appropriately acquired, and processed seismic-style, can be interpreted for subsurface effective resistivity. Previous 1D results are extended in the first section of this dissertation to numerical simulations for a 2.5D numerical ISEM model. Common shot gathers, common offset gathers, CMP gathers, and a proposed Q-compensated “resistivity moveout” correction show promise as indicators of resistivity variations in the subsurface. Naturally, the mathematical similarity is limited by essential differences between the physical quantities described in elastodynamics (underlying seismology) and electromagnetics. I explore these limits by defining an analogy between elastodynamic displacement and electromagnetic electric vector potential. Finally, I present a novel analytical solution for the problem of radiation emanating from an arbitrarily-oriented dipole and scattering from an infinite cylinder in 3D space. I then use the solution to perform a numerical study of crosshole electromagnetic tunnel detection.



elastodynamics-electromagnetics analogy, seismic processing of electromagnetic data, scattering from infinite dielectric cylinder, crosshole electromagnetic tunnel detection


Portions of this document appear in: Neese, J. W., and L. Thomsen (2014), Seismic processing of numerical EM data, SEG Technical Program Expanded Abstracts, 33, 870-874; and in: Neese, J. W., and L. A. Thomsen (2015), Robustness of the EM-Radon Transform, 77th EAGE Conference Proceedings, 2015(1), 1-5; and in: Neese, John W., David R. Jackson, and Leon A. Thomsen. "Analogy Between Elastodynamic Displacement and Electromagnetic Vector Potentials." In 2019 URSI International Symposium on Electromagnetic Theory (EMTS), pp. 1-3. IEEE, 2019; and in: Neese, J. W., D. R. Jackson, Y. Zheng, and L. A. Thomsen (2018), TMz/TEz vector potentials due to an arbitrarily oriented dipole in 3-D space in the presence of an infinite dielectric cylinder, Radio Science, 53(4), 509-524; and in: Neese, J. W., D. R. Jackson, and Y. Zheng (2016), Electromagnetic tunnel detection using a magnetic dipole source in three-dimensional space, SEG Technical Program Expanded Abstracts, 35, 2464-2468; and in: Neese, J. W., D. R. Jackson, Y. Zheng, and L. A. Thomsen (in press 2021a), Numerical study of crosshole electromagnetic tunnel detection, Geophysics, 86(3), 1-14; and in: Neese, J. W., D. R. Jackson, Y. Zheng, and L. A. Thomsen. "Underground Tunnel Detection using EM Waves." In 2021 IEEE Texas Symposium on Wireless and Microwave Circuits and Systems (WMCS), pp. 1-5. IEEE, 2021.