• Honam Mathematical Journal
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• v.36 no.4
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• pp.831-852
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• 2014

The obstacle shape reconstruction problem has been known to be difficult to solve since it is highly nonlinear and severely ill-posed. The use of local or locally supported basis functions for the problem has been addressed for many years. However, to the authors' knowledge, any research report on the proper usage of local or locally supported basis functions for the shape reconstruction has not been appeared in the literature due to many difficulties. The aim of this paper is to introduce the general concepts and methodologies for the proper choice and their implementation of locally supported basis functions through the two-dimensional Helmholtz equation. The implementations are based on the complex nonlinear parameter estimation (CNPE) formula and its robust algorithm developed recently by the authors. The basic concepts and ideas are simple. The derivation of the necessary properties needed for the shape reconstructions are elementary. However, the capturing abilities for the local geometry of the obstacle are superior to those by conventional methods, the trial and errors, due to the proper implementation and the CNPE algorithm. Several numerical experiments are performed to show the power of the proposed method. The fundamental ideas and methodologies described in this paper can be applied to many other shape reconstruction problems.

• Korean Journal of Remote Sensing
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• v.36 no.3
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• pp.461-474
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• 2020

Korea launched Geostationary Environmental Monitoring Satellite (GEMS), a UV/visible spectrometer that measure pollution gases on 18 February 2020. Because satellite retrieval is an ill-posed inverse solving process, the validation with ground-based measurements or other satellite measurements is essential to obtain reliable products. For this purpose, satellite-based OMI and OMPS total column ozone (TCO), and ground-based Pandora TCO in Busan and Seoul were selected for future GEMS validation. First of all, the goal of this study is to validate the ground ozone data using characteristics that satellite data provide coherent ozone measurements on a global basis, although satellite data have a larger error than the ground-based measurements. In the cross validation between Pandora and OMI TCO, we have found abnormal deviation in ozone time series from Pandora #29 observed in Seoul. This shows that it is possible to perform inverse validation of ground data using satellite data. Then OMPS TCO was compared with verified Pandora TCO. Both data shows a correlation coefficient of 0.97, an RMSE of less than 2 DU and the OMPS-Pandora relative mean difference of >4%. The result also shows the OMPS-Pandora relative mean difference with SZA, TCO, cross-track position and season have insignificant dependence on those variables.In addition, we showed that appropriate thresholds depending on the spatial resolution of each satellite sensor are required to eliminate the impact of the cloud on Pandora TCO.

• Journal of the Institute of Electronics and Information Engineers
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• v.53 no.4
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• pp.117-128
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• 2016

Installation of earth grounding system is essential to ensure personnel safety and correct operation of electrical equipment. Earth parameters, especially, soil resistivity has to be determined in designing an efficient earth grounding system. The most common applied technique to measure soil resistance is Wenner four-point method. Implementation of this method is expensive, time consuming and cumbersome as large set of measurements with variable electrode spacing are required to obtain a one dimensional resistivity plot. It is advantageous to have a method which is of low cost and provides fast measurements. In this perspective, electrical resistance tomography (ERT) is applied to estimate subsurface resistivity profile. Electrical resistance tomograms characterize the soil resistivity distribution based on the measurements from electrodes placed in the region of interest. The nonlinear ill-posed inverse problem is solved using iterated Gauss-Newton method with Tikhonov regularization. Through extensive numerical simulations, it is found that ERT offers promising performance in estimating the three-dimensional soil resistivity distribution.

• Geophysics and Geophysical Exploration
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• v.7 no.3
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• pp.207-212
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• 2004

This article reviews recent developments in three-dimensional (3-D) magntotelluric (MT) imaging. The inversion of MT data is fundamentally ill-posed, and therefore the resultant solution is non-unique. A regularizing scheme must be involved to reduce the non-uniqueness while retaining certain a priori information in the solution. The standard approach to nonlinear inversion in geophysis has been the Gauss-Newton method, which solves a sequence of linearized inverse problems. When running to convergence, the algorithm minimizes an objective function over the space of models and in the sense produces an optimal solution of the inverse problem. The general usefulness of iterative, linearized inversion algorithms, however is greatly limited in 3-D MT applications by the requirement of computing the Jacobian(partial derivative, sensitivity) matrix of the forward problem. The difficulty may be relaxed using conjugate gradients(CG) methods. A linear CG technique is used to solve each step of Gauss-Newton iterations incompletely, while the method of nonlinear CG is applied directly to the minimization of the objective function. These CG techniques replace computation of jacobian matrix and solution of a large linear system with computations equivalent to only three forward problems per inversion iteration. Consequently, the algorithms are efficient in computational speed and memory requirement, making 3-D inversion feasible.