• Proceedings of the KSEEG Conference
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• 2000.04b
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• pp.194-196
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• 2000

• Geophysics and Geophysical Exploration
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• v.2 no.1
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• pp.43-53
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• 1999

Numerical modeling and inversion for electromagnetic exploration methods are essential to understand behaviour of electromagnetic fields in complex subsurface. In this study, a finite element method was adopted as a numerical scheme for the 2.5-dimensional forward problem. And a finite element equation considering linear conductivity variation was proposed, when 2.5-dimensional differential equation to couple eletric and magnetic field was implemented. Model parameters were investigated for near-field with large source effects and far-field with responses dominantly by homogeneous half-space. Numerical responses by this study were compared with analytic solutions in homogeneous half-space. Blocky inversion model was modified to be applied to the forward calculation in this study and it was also adopted in the inversion algorithm. Resolution for isolated bodies were investigated to confirm possibility and limitation of inversion for electromagnetic exploration data.

• Geophysics and Geophysical Exploration
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• v.10 no.4
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• pp.308-313
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• 2007

The small-loop electromagnetic technique has been used successfully for many geophysical qualitative investigations, particularly for shallow engineering and environmental surveys. Recently, various geophysical imaging methods based on numerical modeling and inversion have been tried in order to get more quantitative subsurface structure. However, conventional 2.5D small loop EM modeling takes a lot of time because responses should be calculated for several wave numbers and transformed into space domain. In this study, we developed a 2.5D HCP small loop EM modeling algorithm using extended Born approximation, which does not require transformation. Also, we checked its validity by comparison with other numerical results.

• Proceedings of the KSEEG Conference
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• 2001.04a
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• pp.53-55
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• 2001

• Geophysics and Geophysical Exploration
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• v.3 no.1
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• pp.13-18
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• 2000

We describe the concept of the singularity in the integral equation of electromagnetic (EM) modeling in comparison with that in the integral representation of electric fields in EM theory, which would clarify the singular integral problems of the Green's tensor. We have also derived and classified the singular integrals of the Green's tensors in 3-D, 2.5-D and 2-D as well as in the thin sheet integral equations of the EM scattering problem, which have the most important effect on the accuracy of the numerical solution of the problems.

• Geophysics and Geophysical Exploration
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• v.4 no.2
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• pp.25-33
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• 2001

Loop-loop electromagnetic (EM) survey in frequency domain has been carried out in order to provide basic solution to geotechnical applications. Source and receiver configuration may be horizontal co-planar (HCP) and/or vertical co-planar (VCP). Three quadrature components of mutual impedance ratio for each configuration are used to construct the subsurface image. For the purpose of obtaining the model response and validating the reasonable performance of the inversion, we obtained each responses of two-layered and three-layered earth models and two-dimensional (2-D) isolated anomalous body. The response of 2-D isolated anomalous body has been calculated using extended Born approximation for the solution of 2.5-D integral equation describing EM scattering problem. As a result of the least-squares inversion with variable Lagrangian multiplier, we could construct more resolvable image from HCP data than VCP data. Furthermore, joint inversion of HCP and VCP data made better stability and resolution of the inversion. Resistivity values, however, did not exactly match the true ones. Loop-loop EM field data was obtained with EM34-3XL system manufactured by Geonics Ltd. (Canada). Electrical resistivity survey was conducted on the same line for the comparison in advance. Since the constructed image from loop-loop EM data by 2-D inversion algorithm showed almost similar resistivity distribution to that from electrical resistivity one, we expect the developed 2.5-D loop-loop EM inversion program can be applied for the reconnaissance site survey.

• Geophysics and Geophysical Exploration
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• v.1 no.2
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• pp.127-135
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• 1998

The Born approximation is widely used for solving the complex scattering problems in electromagnetics. Approximating total internal electric field by the background field is reasonable for small material contrasts as long as scatterer is not too large and the frequency is not too high. However in many geophysical applications, moderate and high conductivity contrasts cause both real and imaginary part of internal electric field to differ greatly from background. In the extended Born approximation, which can improve the accuracy of Born approximation dramatically, the total electric field in the integral over the scattering volume is approximated by the background electric field projected to a depolarization tensor. The finite difference and elements methods are usually used in EM scattering problems with a 2D model and a 3D source, due to their capability for simulating complex subsurface conductivity distributions. The price paid for a 3D source is that many wavenumber domain solutions and their inverse Fourier transform must be computed. In these differential equation methods, all the area including homogeneous region should be discretized, which increases the number of nodes and matrix size. Therefore, the differential equation methods need a lot of computing time and large memory. In this study, EM modeling program for a 2D model and a 3D source is developed, which is based on the extended Born approximation. The solution is very fast and stable. Using the program, crosshole EM responses with a vertical magnetic dipole source are obtained and the results are compared with those of 3D integral equation solutions. The agreement between the integral equation solution and extended Born approximation is remarkable within the entire frequency range, but degrades with the increase of conductivity contrast between anomalous body and background medium. The extended Born approximation is accurate in the case conductivity contrast is lower than 1:10. Therefore, the location and conductivity of the anomalous body can be estimated effectively by the extended Born approximation although the quantitative estimate of conductivity is difficult for the case conductivity contrast is too high.

• Geophysics and Geophysical Exploration
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• v.11 no.1
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• pp.68-77
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• 2008

We have developed an inversion algorithm for loop-loop electromagnetic (EM) data, based on the localised non-linear or extended Born approximation to the solution of the 2.5D integral equation describing an EM scattering problem. Source and receiver configuration may be horizontal co-planar (HCP) or vertical co-planar (VCP). Both multi-frequency and multi-separation data can be incorporated. Our inversion code runs on a PC platform without heavy computational load. For the sake of stable and high-resolution performance of the inversion, we implemented an algorithm determining an optimum spatially varying Lagrangian multiplier as a function of sensitivity distribution, through parameter resolution matrix and Backus-Gilbert spread function analysis. Considering that the different source-receiver orientation characteristics cause inconsistent sensitivities to the resistivity structure in simultaneous inversion of HCP and VCP data, which affects the stability and resolution of the inversion result, we adapted a weighting scheme based on the variances of misfits between the measured and calculated datasets. The accuracy of the modelling code that we have developed has been proven over the frequency, conductivity, and geometric ranges typically used in a loop-loop EM system through comparison with 2.5D finite-element modelling results. We first applied the inversion to synthetic data, from a model with resistive as well as conductive inhomogeneities embedded in a homogeneous half-space, to validate its performance. Applying the inversion to field data and comparing the result with that of dc resistivity data, we conclude that the newly developed algorithm provides a reasonable image of the subsurface.

• Journal of Industrial Technology
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• v.18
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• pp.131-138
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• 1998

Numerical modeling for electromagnetic exploration methods are essential to understand behaviours of electromagnetic fields in complex subsurfaces. In this study, a finite element method was adopted as a numerical scheme for the 2.5-dimensional forward problem. And a finite element equation considering linear conductivity variation was proposed when 2.5-dimensional differential equation to couple eletric and magnetic field was implemented. Model parameters were investigated for near-field with large source effects and far-field with responses dominantly by homogeneous half-space. Numerical responses by this study were compared with analytic solutions in homogeneous half-space and compared with other three dimensional numerical results.

• Geophysics and Geophysical Exploration
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• v.5 no.2
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• pp.84-92
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• 2002

In this study, the new modeling scheme has been developed for recently designed and tested electromagnetic survey, which adapts horizontal magnetic dipole with $1\;kHz\~1\;MHz$ frequency range as a source. The 2.5-D secondary field formulation in wavenumber domain was constructed using finite element method and verified through comparing results with layered-earth solutions calculated by integral equations. 2-D conductive- and resistive-block models were constructed for calculating electric field, magnetic field and impedance - the ratio of electric and magnetic fields which are orthogonal each other. This study showed that electric field and impedance are superior in identifying 2-D isolated-body model to magnetic field. In particular, impedance gives more stable results than electric field with similar spatial resolving power, because electric field is divided by magnetic field in impedance. Thus the impedance analysis which uses electric and magnetic fields together would give better result in imaging the shallow anomalies than conventional EM method.