• Journal of the Korean Institute of Telematics and Electronics
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• v.26 no.9
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• pp.1317-1321
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• 1989

The nonuniqueness of solutions to inverse scattering problems for the reconstruction of cross sectional permitivity distributions on dielectric cylinder is illustrated in view of numerical analysis based on the spectral inverse scattering scheme with the moment-method procedures. It is also shown that some additional treatmenents such as multiple measurements, various incidences, etc. are not effective to assure the uniqueness.

• Journal of electromagnetic engineering and science
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• v.3 no.2
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• pp.133-139
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• 2003

The nonuniqueness of a mathematically rigorous solution to 2-dimensional inverse scattering problems is explained in a limiting view of the numerical calculations based on the spectral-domain moment method. It is illustrated that its theoretical uniqueness cannot be assured even by performing additional measurements of the scattered fields not only along multiple lines but also with angular/frequency-diversities. In a real situation, however, computational error and measurement noise are inevitable. Those limitations render it meaningless to controvert the existence of a theoretically rigorous solution. Hence the most practical issue is how to remedy the instability of its practically approximate solution.

• Geophysics and Geophysical Exploration
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• v.16 no.3
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• pp.131-138
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• 2013

We developed a method for inverting magnetic data to image 2D susceptibility models. The major difficulty in the inversion of the potential data is the nonuniqueness. Furthermore, generally the number of inversion blocks are greater than the number of the magnetic data available, and thus the magnetic inversion leads to under-determined problem, which aggravates the nonuniqueness. When the magnetic data were inverted by the general least-squares method, the anomalous susceptibility would be concentrated near the surface in the inverted section. To overcome this nonuniqueness problem, we propose a new resolution model constraint that is calculated from the parameter resolution. The model constraint imposes large penalty on the model parameter with good resolution, on the other hand small penalty on the model parameter with poor resolution. Thus, the deep-seated model parameter, generally having poor resolution, can be effectively resolved. The developed inversion algorithm is applied to the inversion of the synthetic data for typical models of magnetic anomalies and is tested on real airborne data obtained at the Okcheon belt of Korea.

• Journal of applied mathematics & informatics
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• v.3 no.2
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• pp.117-128
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• 1996

Complementation theory in krein spaces can be extended for any self-adjoint transformation. There is a close relation between Julia operators and linear systems. The theory of Julia operators can be used to construct distinct Krein spaces which are the state spaces of extended canonical linear systems with given transfer function.

• Geophysics and Geophysical Exploration
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• v.10 no.1
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• pp.44-49
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• 2007

It is difficult to obtain high-resolution images by 3D gravity inversion, because the problem is extremely underdetermined - there are too many model parameters. In order to reduce the number of model parameters we propose a 3D gravity inversion scheme utilising Euler deconvolution as a priori information. The essential point of this scheme is the reduction of the nonuniqueness of solutions by restricting the inversion space with the help of Euler deconvolution. We carry out a systematic exploration of the growing body process, but only in the restricted space within a certain radius of the Euler solutions. We have tested our method with synthetic gravity data, and also applied it to a real dataset, to delineate underground cavities in a limestone area. We found that we obtained a more reasonable subsurface density image by means of this combination between the Euler solution and the inversion process.

• Structural Engineering and Mechanics
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• v.11 no.3
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• pp.237-258
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• 2001

Structural identification via modal analysis in structural mechanics is gaining popularity in recent years, despite conceptual difficulties connected with its use. This paper is devoted to illustrate both the capabilities and the indeterminacy characterizing structural identification problems even in quite simple instances, as well as the cautions that should be accordingly adopted. In particular, we discuss an application of an identification technique of variational type, based on the measurement of eigenfrequencies and mode shapes, to a steel frame with friction joints under various assembling conditions. Experience has suggested, so as to restrict the indeterminacy frequently affecting identification issues, having resort to all the a priori acknowledged information on the system, to the symmetry and presence of structural elements with equal stiffness, to mention one example, and mindfully selecting the parameters to be identified. In addition, considering that the identification techniques have a local character and correspond to the updating of a preliminary model of the structure, it is important that the analytical model on the first attempt should be adequately accurate. Secondly, it has proved determinant to cross the results of the dynamic identification with tests of other typology, for instance, static tests, so as to fully understand the structural behavior and avoid the indeterminacy due to the nonuniqueness of the inverse problem.

• Proceedings of the KSME Conference
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• 2000.04a
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• pp.714-719
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• 2000

In this paper, an application program is made to simulate the behavior of a ship block under various crane works and to generate data of lu9 reactions and wire tensions. The program is based on a CAD program, Pro/ENGINEER. A ship is composed of more than 100 ship blocks. In order to lift, move, turn, or put a ship block at a convenient location fur assembling, workers in a shipyard use cranes, wires, and lugs temporarily attached to the block. In the procedure of lifting and turning a ship block with a crane, it is important to find suitable lug points and wires to do the handling efficiently and prevent accidents. Evaluation of forces in lugs and wires is necessary, but the problem is rather complex due to nonlinearity and nonuniqueness. In the present development, the nonlinear system of equations for quasi-static equilibriums is derived and a Newton type solution method is adopted to solve the system. The importance of initial estimates to the solution is illustrated and two approaches are utilized and compared. With the program developed, users can assign lug points on the CAD model by mouse and choose various linking devices at each crane point. Users can try to simulate the motion for any prescribed conditions, compare the motion of the block and the reactions and choose appropriate lug points and the type of wires and lugs.

• Journal of the Korean Geophysical Society
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• v.4 no.1
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• pp.35-46
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• 2001

한반도 중부에 위치한 대전 지진관측소(TJN) 하부의 세부 지각구조를 밝혀내기 위하여 수신함수를 이용한 선형화된 역산(linearized inversion) 방법을 적용하였다. 본 방법의 비단일해(nonuniqueness)와 초기 모델 의존성의 문제를 해결하기 위해 근사 초기 속도 모델로부터 72개의 서로 다른 초기 모델을 구하여 역산을 수행한 후 결과모델들의 평균 속도 모델을 제시하는 방법을 사용하였다. 역산 결과 총 72개의 모델 중 뚜렷한 지각-맨틀 경계를 보이는 43개의 모델만이 조건에 만족하는 결과를 나타내었다. 모든 모델에서 속도 구조는 전체적으로 깊이에 따라 속도의 불연속면이나 급격한 증가없이 연속적인 변화를 하며, 모호면의 깊이는 30～32.5 km의 범위로 나타났다. 평균적인 하부 지각의 속도는 6.5 km/s, 상부 맨틀의 속도는 7.8 km/s로 뚜렷한 속도 변화를 보였다. 결과 모델 군은 중부지각(mid-crust)에서의 속도를 기준으로 약한 저속도층을 나타내는 군과 상대적으로 일정한 속도를 가지는 군으로 구분되었다. 단지 지진파형의 비교만으로 두 모델군 중 합당한 모델군의 선택은 불가능하였다. 따라서 수신 함수를 이용하여 연구 지역의 신뢰할 만한 지각 구조를 구하기 위해서는 그 지역에 대한 지질학적, 지구물리학적 추가정보와의 동반 해석이 요구된다.

• Geophysics and Geophysical Exploration
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• v.1 no.1
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• pp.31-42
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• 1998

Recently crosshole seismic tomography has come to be widely used especially for the civil engineering, because it can provide more detail information than any other surface method, although the resolution of tomogram will be inevitably deteriorated to some extent due to the limited wavefield aperture on the nonuniqueness of traveltime inversion. In addition, our field sites often consist of a high-velocity bed rock overlain by low-velocity rock, sometimes with a contrast of more than 45 percent, and furthermore the bed rock is folded. The first arriving waves can be then the refracted ones that travel along the bed rock surface for some source/receiver distances. Thus, the desirable first arrivals can be easily misread that cause severe distortion of the resulting tomogram, if it is concerned with (straight ray) traveltime inversion procedure. In this case, comparision with synthetic data (forward modeling) is a valuable tool in the interpretation process. Besides, abundant information is contained in the crosshole data. For instance, examination of tube waves can be devoted to detecting discontinuities within the borehole such as breakouts, faults, fractures or shear zones as well as the end of the borehole. Specific frequency characteristics of marine silty mud will help discriminate from other soft rocks. The aim of this paper is to present several strategies to analyze and interpret the crosshole data in order to improve the ability at first to determine the spatial dimensions of interwell anomalies and furthermore to understand the underground structures. To this end, our field data are demonstrated. Possibility of misreading the first arrivals was illustrated. Tube waves were investigated in conjunction with the televiewer images. Use of shot- and receiver gathers was examined to benefit the detectabilities of discontinuities within the borehole.