• 한국지구물리탐사학회:학술대회논문집
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• 2008.10a
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• pp.51-56
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• 2008

The waveform inversion for isotropic media has ever been studied since the 1980s, but there has been few studies for anisotropic media. We present a seismic waveform inversion algorithm for 2-D heterogeneous transversely isotropic structures. A cell-based finite difference algorithm for anisotropic media in time domain is adopted. The steepest descent during the non-linear iterative inversion approach is obtained by backpropagating residual errors using a reverse time migration technique. For scaling the gradient of a misfit function, we use the pseudo Hessian matrix which is assumed to neglect the zero-lag auto-correlation terms of impulse responses in the approximate Hessian matrix of the Gauss-Newton method. We demonstrate the use of these waveform inversion algorithm by applying them to a two layer model and the anisotropic Marmousi model data. With numerical examples, we show that it's difficult to converge to the true model when we assumed that anisotropic media are isotropic. Therefore, it is expected that our waveform inversion algorithm for anisotropic media is adequate to interpret real seismic exploration data.

• Journal of electromagnetic engineering and science
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• v.1 no.1
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• pp.1-10
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• 2001

• Proceedings of the Optical Society of Korea Conference
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• 1997.08a
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• pp.45-45
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• 1997

• Proceedings of the Korea Association of Crystal Growth Conference
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• 1998.06a
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• pp.23-26
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• 1998

The domain formation phenomena of {{{{ { LiLbO}_{ 3} }}}} crystals was investigated and the method for the periodic domain formation in {{{{ { LiLbO}_{ 3} }}}} single crystals during growth was proposed in this study. The strees-induced domain formation mechanism was proposed and explained. The strong piezoelectric effect of{{{{ { LiLbO}_{ 3} }}}} at elevated temperature would be the direct driving force for the inversion of the tensile component of the internal stresses can inverse the original direction of the spontaneous polarization.

• 한국지구물리탐사학회:학술대회논문집
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• 2010.10a
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• pp.87-91
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• 2010

• Journal of the Korean earth science society
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• v.37 no.5
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• pp.277-285
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• 2016

We introduce a depth scaling strategy to improve the accuracy of frequency-domain elastic full waveform inversion (FWI) using the new pseudo-Hessian matrix for seismic data without low-frequency components. The depth scaling strategy is based on the fact that the damping factor in the Levenberg-Marquardt method controls the energy concentration in the gradient. In other words, a large damping factor makes the Levenberg-Marquardt method similar to the steepest-descent method, by which shallow structures are mainly recovered. With a small damping factor, the Levenberg-Marquardt method becomes similar to the Gauss-Newton methods by which we can resolve deep structures as well as shallow structures. In our depth scaling strategy, a large damping factor is used in the early stage and then decreases automatically with the trend of error as the iteration goes on. With the depth scaling strategy, we can gradually move the parameter-searching region from shallow to deep parts. This flexible damping factor plays a role in retarding the model parameter update for shallow parts and mainly inverting deeper parts in the later stage of inversion. By doing so, we can improve deep parts in inversion results. The depth scaling strategy is applied to synthetic data without lowfrequency components for a modified version of the SEG/EAGE overthrust model. Numerical examples show that the flexible damping factor yields better results than the constant damping factor when reliable low-frequency components are missing.

• Geophysics and Geophysical Exploration
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• v.21 no.3
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• pp.139-149
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• 2018

The resistivity monitoring is a practical method to resolve changes in resistivity of underground structures over time. With the advance of sophisticated automatic data acquisition system and rapid data communication technology, resistivity monitoring has been widely applied to understand spatio-temporal changes of subsurface. In this study, a new 4D inversion algorithm is developed, which can effectively emphasize significant changes of underground resistivity with time. To overcome the overly smoothing problem in 4D inversion, the Lagrangian multipliers in the space-domain and time-domain are determined automatically so that the proportion of the model constraints to the misfit roughness remains constant throughout entire inversion process. Furthermore, a focusing model constraint is added to emphasize significant spatio-temporal changes. The performance of the developed algorithm is demonstrated by the numerical experiments using the synthetic data set for a time-lapse model.

• 한국지구물리탐사학회:학술대회논문집
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• 2007.06a
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• pp.167-172
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• 2007

The frequency-domain small-loop electromagnetic (EM) instruments are increasingly used for shallow environmental and geotechnical surveys because of their portability and speed. However, it is well known that the data quality is generally so poor that quantitative interpretation of the data is not justified in many cases. We present an inversion method that allows the correction for the calibration errors and also constructs multidimensional resistivity models. The key point in this method is that the data are collected at least at two different heights. The forward modeling used in the inversion is based on an efficient 3-D finite-difference method, and its solution was checked against 2-D finite-element solution. The synthetic and real data examples demonstrate that the joint inversion recovers reliable resistivity models from multi-frequency data severely contaminated by the calibration errors.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.16 no.2
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• pp.53-58
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• 2006

When external field was applied to congruent $LiNbO_3$, it was investgated for domain formation and expansion of $LiNbO_3$. The domain wall velocities of 0.5 mm thickness $LiNbO_3$ were 28.70, 16.02 and $5.75{\mu}m/sec$ under poling field of 23.5, 22.0 and 21.0 kV/mm, respectively. As $1 M{\Omega}$ resistor was used in domain inversion system, harmonic domain inversion was not achieved by rapid domain expansion. And 50% duty cycle periodically poled $LiNbO_3$ have been fabricated by charge control using $10 M{\Omega}$ resistor.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.1
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• pp.41-53
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• 2008

Polynomials are one of most important and widely used numerical tools in dealing with a smooth function on a bounded domain and trigonometric functions work for smooth periodic functions. However, they are not the best choice if a function has a bounded support in space and in frequency domain. The Prolate Spheroidal wave function (PSWF) of order zero has been known as a best candidate as a basis for band-limited functions. In this paper, we review some basic properties of PSWFs defined as eigenfunctions of bounded Fourier transformation. We also propose numerical inversion schemes based on PSWF and present some numerical examples to show their feasibilities as signal processing tools.