• Geophysics and Geophysical Exploration
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• v.25 no.4
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• pp.242-251
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• 2022

Automatic differentiation automatically calculates the derivatives of a function using the chain rule once the forward operation of a function is defined. Given the recent development of computing libraries that support automatic differentiation, many researchers have adopted automatic differentiation techniques to solve geophysical inverse problems. We analyzed the advantages, disadvantages, and performances of automatic differentiation techniques using the gradient calculations of seismic full waveform inversion objective functions. The gradients of objective functions can be expressed as multiplications of the derivatives of the model parameters, wavefields, and objective functions using the chain rule. Using numerical examples, we demonstrated the speed of analytic differentiation and the convenience of complex gradient calculations for automatic differentiation. We calculated derivatives of model parameters and objective functions using automatic differentiation and derivatives of wavefields using analytic differentiation.

• 한국지구물리탐사학회:학술대회논문집
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• 2003.11a
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• pp.459-463
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• 2003

Waveform inversion requires extracting a reliable low frequency content of seismic data for estimating of the low wave number velocity model. The low frequency content of the seismic data is usually discarded or neglected because of the band-limited response of the source and the receivers. In this study, however small the spectral of the low frequency seismic data is, we assume that it is possible to extract a reliable phase information of the low frequency from the seismic data and use it in waveform inversion. To this end, we exploit the frequency domain finite element modeling and source-receiver reciprocity to calculate the $Frech\`{e}t$ derivative of the phase of the seismic data with respect to the earth model parameter such as velocity, and then apply a damped least squares method to invert the phase of the seismic data. Through numerical example, we will attempt to demonstrate the feasibility of our method in estimating the correct velocity model for prestack depth migration.

• Proceedings of the KIEE Conference
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• 2015.07a
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• pp.772-773
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• 2015

This paper presents a dynamic model of 2-D magnetostriction in electrical steel sheet (ESS) under rotating flux magnetization conditions and its implementation in finite element method (FEM). For an arbitrary waveform of magnetic flux density (B), the corresponding magnetostriction waveform can be predicted by the model. In order to apply the model to FEM easily, the model is based on trilinear interpolation method. As an example, the model is applied to a three-phase transformer constructed by highly grain-oriented electrical steel sheets and the numerical results by the magnetostriction model are discussed.

• 한국정보디스플레이학회:학술대회논문집
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• 2002.08a
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• pp.423-426
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• 2002

New driving waveform which can be inferred by analyzing fundamental LC mechanism is suggested. The main idea of the new waveform is the stabilizing LC layer fast in the cell by controlling the middle director of LC layer. Consequently, we can get not only numerical reduction of optical response merely but also the change of dynamic transmittance from applied voltage exactly

• 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 the Korean Institute of Electrical and Electronic Material Engineers
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• v.24 no.10
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• pp.822-833
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• 2011

A Xe plasma flat lamp, which has been noticed as a new eco-friendly LCD (liquid crystal display) backlight, requires the improvement of the luminance and the luminous efficiency although it has several advantages. To improve the performance of a lamp, it is necessary to understand the effects of discharge variables on the luminous characteristics of the lamp. Since it is difficult to diagnose a lamp discharge experimentally, the numerical analysis can be used instead. In this study, the luminous characteristics of a planar type Xe plasma flat lamp were analyzed with the variation of an input voltage and a pulse frequency. The numerical analysis of a lamp discharge was then performed using a RCT (relaxation continuum) model and a LFA (local field approximation) model. The comparison with the experimental results showed that the RCT model is valid for the numerical analysis of the flat lamp. The numerical analysis also showed that the modifications of a high frequency component and a voltage falling rate in the input voltage waveform could improve the luminous characteristics of the lamp.

• Journal of Ocean Engineering and Technology
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• v.36 no.1
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• pp.11-20
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• 2022

Generally, tsunamis are generated by the rapid crustal movements of the ocean floor. Other factors of tsunami generation include landslides on coastal and ocean floor slopes, glacier collapses, and meteorite collisions. In this study, two numerical analyses were conducted to examine the formation, propagation, and deformation properties of landslide tsunamis. First, LS-DYNA was adopted to simulate the formation and propagation processes of tsunamis generated by dropping rigid bodies. The generated tsunamis had smaller wave heights and wider waveforms during their propagation, and their waveforms and flow velocities resembled those of theoretical solitary waves after a certain distance. Second, after the formation of the landslide tsunami, a tsunami based on the solitary wave approximation theory was generated in a numerical wave tank (NWT) with a computational domain that considered the stability/steady phase. The comparison of two numerical analysis results over a certain distance indicated that the waveform and flow velocity were approximately equal, and the maximum wave pressures acting on the upright wall also exhibited similar distributions. Therefore, an effective numerical model such as LS-DYNA was necessary to analyze the formation and initial deformations of the landslide tsunami, while an NWT with the wave generation method based on the solitary wave approximation theory was sufficient above a certain distance.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.28A no.1
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• pp.8-14
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• 1991

A new algorithm for calculation of overcurrent and overvoltage at load for parallel two-wire transmission line with nonlinear protection circuits induced by and external electromagnetic pulse is suggested. The rigorous solution is obtained for a particular type of the incident waveform and protection circuit. The validity of our algorithm is checked by comparing numerical results to the analytic solution in the particular case.

• Proceedings of the IEEK Conference
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• 2000.07b
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• pp.1096-1099
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• 2000

A method to analyze the high speed inter-connects that are composed of frequency dependent lossy distributed lines is presented. Network modeling of hybrid systems is implemented by using the modified nodal admittance matrix in the Laplace transformation domain. The network response is computed by different two methods. One method Is the asymptotic waveform evaluation (AWE) method and other is numerical Laplace inversion method. The merits and demerits of two methods are discussed by applying to several concrete illustrative networks.

• 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.