• Geophysics and Geophysical Exploration
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• v.3 no.2
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• pp.70-75
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• 2000

In the seismic migration, Kirchhoff and reverse time migration are used in general. In the reverse time migration using wave equation, two-way and one-way wave equation are applied. The approach of one-way wave equation uses approximately computed downward continuation extrapolator, it need tess amounts of calculations and core memory in compared to that of two-way wave equation. In this paper, we applied one-way wave equation to pre-stack reverse time migration. In the frequency-space domain, forward propagation of source wavefield and back propagration of measured wavefield were executed by using monochromatic one-way wave equation, and zero-lag cross correlation of two wavefield resulted in the image of subsurface. We had implemented prestack migration on a massively parallel processors (MPP) CRAYT3E, and knew the algorithm studied here is efficiently applied to the prestck migration due to its suitability for parallelization.

• Geophysics and Geophysical Exploration
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• v.26 no.3
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• pp.114-125
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• 2023

The physics-informed neural network (PINN) has been proposed to overcome the limitations of various numerical methods used to solve partial differential equations (PDEs) and the drawbacks of purely data-driven machine learning. The PINN directly applies PDEs to the construction of the loss function, introducing physical constraints to machine learning training. This technique can also be applied to wave equation modeling. However, to solve the wave equation using the PINN, second-order differentiations with respect to input data must be performed during neural network training, and the resulting wavefields contain complex dynamical phenomena, requiring careful strategies. This tutorial elucidates the fundamental concepts of the PINN and discusses considerations for wave equation modeling using the PINN approach. These considerations include spatial coordinate normalization, the selection of activation functions, and strategies for incorporating physics loss. Our experimental results demonstrated that normalizing the spatial coordinates of the training data leads to a more accurate reflection of initial conditions in neural network training for wave equation modeling. Furthermore, the characteristics of various functions were compared to select an appropriate activation function for wavefield prediction using neural networks. These comparisons focused on their differentiation with respect to input data and their convergence properties. Finally, the results of two scenarios for incorporating physics loss into the loss function during neural network training were compared. Through numerical experiments, a curriculum-based learning strategy, applying physics loss after the initial training steps, was more effective than utilizing physics loss from the early training steps. In addition, the effectiveness of the PINN technique was confirmed by comparing these results with those of training without any use of physics loss.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.13 no.2
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• pp.149-157
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• 2001

From the weakly nonlinear mild-slope wave equations introduced by Nadaoka et al.(1994, 1997), a set of weakly nonlinear wave equations for rapidly varying topography are derived by including the bottom curvature and slope-squared tenns ignored in the original equations ofNadaoka et al. To solve the linear version of extended wave equations derived in this study one-dimensional finite difference numerical model is con¬structed. The perfonnance of the model is tested for the case of wave reflection from a plane slope with various inclination. The numerical results are compared with the results calculated using other numerical models reported earlier. The comparison shows that the accuracy of the numerical model is improved significantly in comparison with that of the original equations ofNadaoka et al. by including a complete set of bottom curva1w'e and slope¬squared terms for a rapidly varying topography.

• 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.14 no.3
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• pp.191-202
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• 2011

Reserve-time migration (RTM) using a two-way wave equation is one of the most accurate migration techniques. RTM has been conducted by assuming that subsurface media are isotropic. However, anisotropic media are commonly encountered in reality. Conventional isotropic RTM may yield inaccurate results for anisotropic media. In this paper, we develop RTM algorithms for vertical transversely isotropic media (VTI) and tilted transversely isotropic media (TTI). For this, the pseudo-acoustic wave equations are used. The modeling algorithms are based on the high-order finite-difference method (FDM). The RTM algorithms are composed using the cross-correlation imaging condition or the imaging condition using virtual sources. By applying the developed RTM algorithms to the Hess VTI and BP TTI models, we could obtain better images than those obtained by the conventional isotropic RTM.

• Journal of the Korean Geotechnical Society
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• v.19 no.4
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• pp.145-153
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• 2003

The resonant column testing determines the shear modulus and material damping factor dependent on the shear strain magnitude, based on the wave-propagation theory. The determination of the dynamic soil properties requires the theoretical formulation of the dynamic behavior of the resonant column testing system. One of the theoretical formulations is the use of the wave equation for the soil specimen in the resonant column testing device. Wood, Richart and Hall derived the wave equation by assuming the linear elastic soil, and didn't take the material damping into consideration. Hardin incorporated the viscoelastic damping of soil in the wave equation, but he had to assume the material damping factor for the determination of the shear modulus. For the better theoretical formulation of the resonant column testing, this study derived a new wave equation to include the viscosity of soil, and proposed an approach for the solution. Also, in this study, the equation of motion for the testing system, which is another approach of the theoretical formulation of the resonant column testing, was also derived. The equation of motion leads to the better understanding of the resonant column testing, which includes the dynamic magnification factor and the phase angle of the response. For the verification of the proposed equation of motion for the resonant column testing, the finite element analysis was performed for the resonant column testing. The comparison of the dynamic magnification factors and the phase angles far the system response were performed.

• Proceedings of the Korea Water Resources Association Conference
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• 2019.05a
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• pp.88-88
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• 2019

컴퓨터 성능향상과 수치해석기법의 발달로 인해 Navier-Stokes 방정식에 기초한 수치모델을 활용한 3차원 유동/파동장 해석이 증가하고 있는 추세이다. 그러나 아직까지 Navier-Stokes 방정식 모델의 계산부하를 PC에서 소화하기에는 무리가 따른다. 게다가 실험실 스케일을 벗어나, 실제 현장을 계산영역으로 설정할 경우에는 계산량이 엄청나게 증가하게 된다. 이것을 극복하기 위해서는 반듯이 병렬계산을 수행하여야 한다. 본 연구에서는 계산부하가 큰 Navier-Stokes 방정식 기반의 3차원 수치모델 LES-WASS-3D를 활용한 대용량 병렬계산체계를 구축한다. 나아가 3차원 정밀 또는 광역의 유동/파동장 해석에 있어서 병렬계산체계의 성능과 적용성을 검토한다. 현재 보급되고 있는 PC들은 모두 멀티프로세서가 장착됨으로 손쉽게 병렬계산을 수행할 수 있다. 그러나 정밀 또는 광역해석을 위해서는 대용량 병렬계산 컴퓨터가 요구된다. 따라서 본 연구에서는 보조프로세서를 장착한 공유메모리 환경의 고성능 병렬계산체계를 구축한다. 나아가 포트란 기반의 순차코드로 구축된 기존 3차원 Navier-Stokes 방정식 모델 LES-WASS- 3D를 병렬코드로 변환한다. 병렬계산 성능 및 적용성을 검토하기 위한 수치해석을 수행한다. 이상의 과정을 통해 본 연구에서 구축한 병렬계산체계의 성능 및 적용성을 확인할 수 있었다. 그리고 3차원 유동/파동장 해석에 있어서 정확도 향상뿐 아니라, 계산영역을 확장할 수 있는 계기가 마련되었다. 또한 유동/파동 해석보다 많은 계산시간이 필요한 지형변동 해석에도 충분히 적용될 수 있다고 판단된다.

• Proceedings of the Korea Water Resources Association Conference
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• 2005.05b
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• pp.527-531
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• 2005

지진해일파는 풍파에 비해 파장이 매우 길어 장파로 간주되지만 조석에 비하면 파장이 짧아 상대적으로 분산성이 강하므로, 먼거리를 전파하는 경우에는 분산성을 고려하여 해석하여야 한다. 특히 동해에서 발생하는 지진해일의 경우 파원이 작고 수심이 깊어 단주기파 성분이 강하므로 그 물리적인 분산효과가 매우 중요하다. 이에 본 연구에서는 지진해일 수치모의시 임의로 구성된 유한요소망과 양해법을 사용하면서도 복잡한 Boussinesq 방정식 대신 간단한 Boussinesq-type의 파동방정식을 사용하면서도 물리적 분산효과를 정도 높게 고려할 수 있는 능동적인 분산보정기법을 이용한 2차원 유한요소모형을 개발하여 가상진원에 의해 발생된 2차원 지진해일 전파에 대하여 수치모의한 결과, 요소크기와 시간간격이 고정되었음에도 불구하고 다양한 수심에 대해 선형 Boussinesq 방정식의 해석해와 매우 잘 일치하는 좋은 결과를 보였다.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2003.07a
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• pp.316-318
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• 2003

양자우물 구조를 사용한 HEMT(High Electron Mobility Transistor)는 고속 스위칭 소자와 초고주파 통신용 소자 및 센서에에 우수한 동작특성을 갖고 있다. 본 논문에서는 AlInAs/InP HEMT의 heterostructure를 파동방정식과 Poisson 방정식을 self-consistent 한 방법으로 해석하였다. 파동방정식으로 junction의 전자농도를 계산하고, Poisson 방정식을 해석하여 potential profile에 의한 전자 농도가 heterostructure에서 self-consistent가 되도록 연산하였다. 끝으로 AlInAs/InP 구조에서 positively ionized donor, valance band에서의 hole, conduction band의 free electron과 구조내의 2DEG를 AlGaAs/GaAs 및 AlGaAs/InGaAs/GaAs와 비교하였다.

• Korean Journal of Optics and Photonics
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• v.14 no.4
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• pp.429-433
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• 2003

We try to analyse the localization phenomenon of a lightwave in random media by means of considering the solution of the propagation equation on a transmission line in which the propagation constants are randomly distributed. Lightwave localization is generated at the turning point where the solution is changed suddenly from an increase to a decrease. First, in order to investigate the changing process of the solution, we have derived the approximated one-dimensional Schrodinger equation from the two-dimensional wave equation by using the Brags condition. Considering the many types of solutions of the wave equation, we have investigated the conditions that allow the solutions to exist. Also, we have investigated the relationships between the localization of the solution and the variation of the propagation constant. In case of the exponential solution, we know that the permittivity $\varepsilon$=(0,0$\varepsilon$$_{0}$) is a very important parameter to influence the phase of the lightwave and to generate the localization.