• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.17 no.2 s.105
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• pp.158-164
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• 2006

In this paper, we proposed a new algorithm of the inverse scattering for the reconstruction of unknown dielectric scatterers using the finite-difference time-domain method and the design sensitivity analysis. We introduced the design sensitivity analysis based on the gradient information for the fast convergence of the reconstruction. By introducing the adjoint variable method for the efficient calculation, we derived the adjoint variable equation. As an optimal algorithm, we used the steepest descent method and reconstructed the dielectric targets using the iterative estimation. To verify our algorithm, we will show the numerical examples for the two-dimensional $TM^2$ cases.

• 한국지구물리탐사학회:학술대회논문집
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• 2005.05a
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• pp.227-232
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• 2005

Least squares (${\ell}^2-norm$) solutions of seismic inversion tend to be very sensitive to data points with large errors. The ${\ell}^p-norm$ minimization for $1{\le}p<2$ gives more robust solutions, but usually with higher computational cost. Iteratively reweighted least squares (IRLS) gives efficient approximate solutions of these ${\ell}^p-norm$ problems. I propose a simple way to implement the IRLS method for a hybrid ${\ell}^1/{\ell}^2$ minimization problem that behaves as ${\ell}^2$ fit for small residual and ${\ell}^1$ fit for large residuals. Synthetic and a field-data examples demonstrates the improvement of the hybrid method over least squares when there are outliers in the data.

• 한국지구물리탐사학회:학술대회논문집
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• 2006.06a
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• pp.161-166
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• 2006

Vertical gravity gradient measurement offers greater structural resolution and detectability than gravity alone. Practical difficulties of field measurement of vertical gravity gradient have raised questions of its accuracy and utility. But, modern automated gravimeter of $1\;{\mu}Gal$ sensitivity makes it easier to measure vertical gradient with required accuracy. It is particularly effective to engineering and environmental problems which target shallow subsurface structure. This paper attempts to apply the vertical gravity gradient technique to high resolution density mapping. The method was generally reviewed and numerical inverse modeling was executed for comparing with conventional gravity. And actual vertical gravity gradient data surveyed overt karstic cavity area at Muan was analysed and interpreted.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.9
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• pp.156-163
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• 2013

In this paper, we propose an algorithm for estimating media characteristics of sea water and subbottom multi-layers. The proposed algorithm for estimating reflection coefficients, uses a transmitted signal and reflected signal obtained from multiple layers of various shape and structure, and the algorithm is called Schur algorithm. The algorithm is efficient in estimating the reflection coefficients since it finds solution by converting the given inverse scattering problem into matrix factorization. To verify the proposed algorithm, we generate a transmit signal and reflected signal obtained from lattice filter model for sea water and subbottom of multi-level non-homogeneous layers, and then find that the proposed algorithm can estimate reflection coefficients efficiently.

• Geophysics and Geophysical Exploration
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• v.20 no.4
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• pp.232-240
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• 2017

Normal moveout correction is one of the main procedures of seismic reflection data processing and a crucial pre-processing step for AVO analysis. Unfortunately, stretch phenomenon, which is the intrinsic problem of NMO correction, degrades the quality of stack section and reliability of AVO analysis. Although muting is applied to resolve this problem, it makes far-offset traces more useful to develop an advanced NMO correction technique without stretch. In this paper, easy and detailed explanations are provided on the definition and methodology of NMO correction, and then the cause of stretch is explained with its characteristics. A graphical explanation for NMO correction is given for the intuitive understanding of stretch phenomenon. Additionally, the theoretical formulation is derived to quantitatively understand the NMO correction. Through explaining the muting process to remove NMO stretch, the limitations of conventional methods are investigated and the need for a new resolution comes to discussion. We describe a stretch-free NMO correction based on inverse theory among many different stretch-free NMO corrections. Finally, the stretch-free NMO correction is verified through synthetic example and real data.

• Geophysics and Geophysical Exploration
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• v.14 no.1
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• pp.7-17
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• 2011

We have developed an inversion code for three-dimensional (3D) resistivity tomography including the anisotropy effect. The algorithm is based on the finite element approximations for the forward modelling and Active Constraint Balancing method is adopted to enhance the resolving power of the smoothness constraint least-squares inversion. Using numerical experiments, we have shown that anisotropic inversion is viable to get an accurate image of the subsurface when the subsurface shows strong electrical anisotropy. Moreover, anisotropy can be used as additional information in the interpretation of subsurface. This algorithm was also applied to the field dataset acquired in the abandoned old mine area, where a high-rise apartment block has been built up over a mining tunnel. The main purpose of the investigation was to evaluate the safety analysis of the building due to old mining activities. Strong electrical anisotropy has been observed and it was proven to be caused by geological setting of the site. To handle the anisotropy problem, field data were inverted by a 3D anisotropic tomography algorithm and we could obtain 3D subsurface images, which matches well with geology mapping observations. The inversion results have been used to provide the subsurface model for the safety analysis in rock engineering and we could assure the residents that the apartment has no problem in its safety after the completion of investigation works.

• Geophysics and Geophysical Exploration
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• v.19 no.3
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• pp.136-144
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• 2016

Since seismic inversion is based on the wave equation, it is important to calculate the solution of wave equation exactly. In particular, full waveform inversion would produce reliable results only when the forward modeling is accurately performed because it uses full waveform. When we use finite-difference or finite-element method to solve the wave equation, the convergence of numerical scheme should be guaranteed. Although the general proof of convergence is provided theoretically, the consistency and stability of numerical schemes should be verified for practical applications. The implementation of source function is the most crucial factor for the consistency of modeling schemes. While we have to use the sinc function normalized by grid spacing to correctly describe the Dirac delta function in the finite-difference method, we can simply use the value of basis function, regardless of grid spacing, to implement the Dirac delta function in the finite-element method. If we use frequency-domain wave equation, we need to use a conservative criterion to determine both sampling interval and maximum frequency for the source wavelet generation. In addition, the source wavelet should be attenuated before applying it for modeling in order to make it obey damped wave equation in case of using complex angular frequency. With these conditions satisfied, we can develop reliable inversion algorithms.

• Geophysics and Geophysical Exploration
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• v.10 no.4
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• pp.383-392
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• 2007

Karstic features and mining-related cavities not only lead to severe restrictions in land utilizations, but also constitute serious concern about geohazard and groundwater contamination. A microgravity survey was applied for detecting, mapping and monitoring karstic cavities in the test site at Muan prepared by KIGAM. The gravity data were collected using an AutoGrav CG-3 gravimeter at about 800 stations by 5 m interval along paddy paths. The density distribution beneath the profiles was drawn by two dimensional inversion based on the minimum support stabilizing functional, which generated better focused images of density discontinuities. We also imaged three dimensional density distribution by growing body inversion with solution from Euler deconvolution as a priori information. The density image showed that the cavities were dissolved, enlarged and connected into a cavity network system, which was supported by drill hole logs. A time-lapse microgravity was executed on the road in the test site for monitoring the change of the subsurface density distribution before and after grouting. The data were adjusted for reducing the effects due to the different condition of each survey, and inverted to density distributions. They show the change of density structure during the lapsed time, which implies the effects of grouting. This case history at the Muan test site showed that the microgravity with accuracy and precision of ${\mu}Gal$ is an effective and practical tool for detecting, mapping and monitoring the subsurface cavities.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.55 no.3
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• pp.142-148
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• 2006

The resonances that contain the information on the properties of the scattering target can be used for target reconstruction approaches. The inverse scattering theory for the resonances has been applied to the problems of the scattering for a spherical, cylindrical dielectric objects and dielectrically coated conductors, shown reasonable results. Though by using this method the thickness and the dielectric constants of the target can be obtained from a determination of the spacing and of the widths of the scattering resonances, the radius of the target should be given. In this paper, we suggest the improved inverse theory combined with the resonance scattering theory to obtain the radius in addition to the dielectric constant of the target. The applications of this method for scattering problems of electromagnetic waves from cylindrical targets were accomplished, and it shows its validity.

• Geophysics and Geophysical Exploration
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• v.12 no.4
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• pp.361-366
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• 2009

Layered-earth Green's functions in electormagnetic (EM) surveys play a key role in modeling the response of exploration targets. They are computed through the Hankel transforms of analytic kernels. Computational precision depends upon the choice of algebraically equivalent forms by which these kemels are expressed. Since three-dimensional (3D) modeling can require a huge number of Green's function evaluations, total computational time can be influenced by computational time for the Hankel transform evaluations. Linear digital filters have proven to be a fast and accurate method of computing these Hankel transforms. In EM modeling for 3D inversion, electric fields are generally evaluated by the secondary field formulation to avoid the singularity problem. In this study, three components of electric fields for five different sources on the surface of homogeneous half-space were derived as primary field solutions. Moreover, reflection coefficients in TE and TM modes were produced to calculate EM responses accurately for a two-layered model having a sea layer. Accurate primary fields should substantially improve accuracy and decrease computation times for Green's function-based problems like MT problems and marine EM surveys.