• Geophysics and Geophysical Exploration
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• v.11 no.4
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• pp.318-325
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• 2008

Assigning an exact boundary condition is of great importance in three-dimensional (3D) magnetotelluric (MT) modeling, in which no source is considered in a computing domain. This paper presents a 3D MT modeling algorithm utilizing a Dirichlet condition for a 2D host. To compute boundary values for a model with a 2D host, we need to conduct additional 2D MT modeling. The 2D modeling consists of transverse magnetic and electric modes, which are determined from the relationship between the polarization of plane wave and the strike direction of the 2D structure. Since the 3D MT modeling algorithm solves Maxwell's equations for electric fields using the finite difference method with a staggered grid that defines electric fields along cell edges, electric fields are calculated at the same place in the 2D modeling. The algorithm developed in this study can produce reliable MT responses for a 3D model with a 2D host.

• Geophysics and Geophysical Exploration
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• v.10 no.2
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• pp.154-160
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• 2007

This paper compares the characteristics of three different algorithms for three-dimensional (3D) magnetotelluric (MT) modeling. These methods are developed by Mackie et al. (1994), Sasaki (1999) and Nam et al. (2007). The first and second methods are based on the finite difference method (FDM), while the last one the finite-element method (FEM). MT responses, apparent resistivities and phases, for a COMMEMI 3D-2 model show a good agreement with integral equation solutions and only minor discrepancies are found over the anomalous bodies in the 3D model. The computation time of the two methods based on FDM is short and the static divergence correction contributes to speed up. The FEM modeling scheme is accurate but slow.

• Geophysics and Geophysical Exploration
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• v.7 no.2
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• pp.148-154
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• 2004

This article reviews the development of three-dimensional (3-D) magnetotelluric (MT) modeling. The 3-D modeling of electromagnetic fields is essential in understanding the physics of MT soundings, and in implementing an inversion method to reconstruct a 3-D resistivity image. Although various numerical schemes have been developed over the last two decades, practical methods have been quite limited. However, the recent rapid improvement in computer speed and memory, as well as the advance in iterative solution algorithms for a large system of equations, makes it possible to model the MT responses of complex 3-D structures, which have been very difficult to simulate before. The use of staggered grids in finite difference method has become popular, conserving a magnetic flux and an electric current and allowing for realistic discontinuous fields. The convergence of numerical solutions has been greatly accelerated by adopting Krylov subspace methods, proper preconditioning techniques, and static divergence corrections. The vector finite-element method using edge elements is also free from the discontinuity problem, and seems a natural choice for modeling complex structures including irregular topography because its flexibility allows one to capture full geometric complexity.

• Geophysics and Geophysical Exploration
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• v.18 no.4
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• pp.232-240
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• 2015

Magnetotelluric (MT) survey investigates electrical structure of subsurface by measuring natural electromagnetic fields on the earth surface. For the accurate interpretation of MT data, the precise three-dimensional (3-D) modeling algorithm is prerequisite. Since MT responses are affected by electrical anisotropy of medium, the modeling algorithm has to incorporate the electrical anisotropy especially when analyzing time-lapse MT data sets, for monitoring engineered geothermal system (EGS) reservoir, because changes in different-vintage MT-data sets are small. This study developed a MT modeling algorithm for the simulation MT responses in the presence of electrical anisotropy by improving a pre-existing staggered-grid finite-difference MT modeling algorithm. After verifying the developed algorithm, we analyzed the effect of vertical transversely isotropic (VTI) anisotropy on MT responses. In addition, we are planning to extend the applicability of the developed algorithm which can simulate not only the horizontal transversely isotropic (HTI) anisotropy, but also the tiled transversely isotropic (TTI) anisotropy.

• Geophysics and Geophysical Exploration
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• v.10 no.4
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• pp.275-284
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• 2007

For precise interpretation of magnetotelluric (MT) data distorted by irregular surface terrain, topography effects are investigated by computing apparent resistivities, phases, tippers and induction vectors for a three-dimensional (3D) hill-and-valley model. To compute MT responses for the 3D surface topography model, we use a 3D MT modeling algorithm based on an edge finite-element method which is free from vector parasites. Distortions on the apparent resistivity and phase are mainly caused by distorted currents that flow along surface topography. The distribution of tipper amplitudes over both hill and valley are the same, while the tipper points toward the center of hill and the base of the valley. The real part of induction vector also points in the same direction as that of tipper, while the imaginary part in the opposite direction.

• Geophysics and Geophysical Exploration
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• v.11 no.4
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• pp.286-301
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• 2008

When magnetotelluric (MT) data are obtained in vicinity of the coast, the sea can distort observed MT responses, especially those of deep part of subsurface. We introduce an iterative method to correct the sea effect, based on the previous topographic correction method which removes the distortions due to topographic changes in seafloor MT data. The method first corrects the sea effect in observed MT impedance, and then inverts corrected responses in a model space without the sea. Due to mutual coupling between sea and subsurface structure, the correction and inversion steps are iterated until changes in each result become negligible. The method is validated for 1-D and 2-D structure using synthetic MT data produced by 3-D forward modeling including surrounding seas. In all cases, the method closely recovers the given structure after a few iterations. To test the applicability of the proposed method to field data, we generate synthetic MT data for the Jeju Island whose 1-D conductivity structure is well known, using 3-D forward modeling. The distortions due to the surrounding sea start to appear below the frequency about 1 Hz, and are relatively severe in the electrical field perpendicular to the coastline because of the location of the observation sites. The proposed method successfully eliminates the sea effect after three iterations, and both 1-D and 2-D inversion of corrected responses closely recover the given subsurface structure of the Jeju Island model.

• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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• pp.267-272
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• 2007

Uiseong subbasin belonging to Kyungsang basin resulted from volcanic activity in the late Cretaceous. In this study, we carry out MT and gravity survey at the Hwasan caldera, which was formed of volcanic and abyssal rocks complex, then analyze and identify geological substructure. Potential survey such as gravity and magnetic survey has been mainly carried out in former studies, so depth information for understanding substructure was not enough. To complement a potential survey, we use MT method, which has high vertical resolution. Moreover we make a simple 2D model comparing with former study. The result of MT and gravity 2D modeling shows that this area is roughly composed of 3 layers; The bottom layer is a basement. In the second layer, intrusive rocks having high resistivity is placed along the ring faults and the sedimentary layer of low resistivity is inside caldera. The highest layer is alluvium. To comprehend the 3D structure of the Hwasan caldera, we perform 3D gravity inversion, and construct the 3D model from the result of 3D gravity inversion. MT responses are calculated by using the constructed 3D model and the 3D model of the Hwasan caldera's structure is suggested after comparing the calculated values with the observed values at MT line.

• Geophysics and Geophysical Exploration
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• v.14 no.2
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• pp.164-175
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• 2011

Using natural electromagnetic (EM) fields at low frequencies, magnetotelluric (MT) surveys can investigate conductivity structures of the deep subsurface and thus are used to explore geothermal energy resources and investigate proper sites for not only geological $CO_2$ sequestration but also enhanced geothermal system (EGS). Moreover, marine MT data can be used for better interpretation of marine controlled-source EM data. In the interpretation of MT data, MT modeling schemes are important. This study improves a three dimensional (3D) MT modeling algorithm which uses edge finite elements. The algorithm computes magnetic fields by solving an integral form of Faraday's law of induction based on a finite difference (FD) strategy. However, the FD strategy limits the algorithm in computing vertical magnetic fields for a topographic model. The improved algorithm solves the differential form of Faraday's law of induction by making derivatives of electric fields, which are represented as a sum of basis functions multiplied by corresponding weightings. In numerical tests, vertical magnetic fields for topographic models using the improved algorithm overcome the limitation of the old algorithm. This study recomputes induction vectors and tippers for a 3D hill and valley model which were used for computation of the responses using the old algorithm.

• Economic and Environmental Geology
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• v.27 no.2
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• pp.191-199
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• 1994

We have developed an algorithm based on the method of integral equations to simulate the magnetotelluric (MT) responses of three-dimensional (3-D) bodies in a layered half-space. The inhomogeneities are divided into a number of cells and are replaced by an equivalent current distribution which is approximated by pulse basis functions. A matrix equation is constructed using the electric Green's tensor function appropriate to a layered earth, and is solved for the vector current in each cell. Subsequently, scattered fields are found by integrating electric and magnetic Green's tensor functions over the scattering current About a 3-D conductive body near the earth's surface, interpretation using 2-D transverse electric modeling schemes can imply highly erratic low resistivities at depth. This is why these routines do not account for the effect of boundary charges. However, centrally located profiles across elongate 3-D prisms may be modeled accurately with a 2-D transverse magnetic algorithm, which implicitly includes boundary charges in its formulation. Multifrequency calculations show that apparent resistivity and impedance phase are really two complementary parameters. Hence, they should be treated simultaneously in broadband MT interpretation.

• Journal of the Korean earth science society
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• v.30 no.5
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• pp.550-564
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• 2009

When magnetotelluric (MT) data are obtained in the vicinity of the coast, the surrounding seas make it difficult to interpret subsurface structure, especially the deep part of the subsurface. We introduce an iterative method to correct the sea effect, based on the previous topographic correction method that removes the distortion due to topographic changes in seafloor MT data. The method first corrects the sea effect in observed MT impedance, and then inverts corrected response in a model space without the sea. Due to mutual coupling between the sea and the subsurface structure, the correction and inversion steps are iterated until the changes in each result become negligible. The method is tested for 1- and 2-D structures using synthetic MT data produced by 3-D forward modeling including surrounding seas. In all cases, the method closely recovers the true structure assumed to generate synthetic responses after a few iterations.