• 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.

• 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.

• The Journal of the Acoustical Society of Korea
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• v.20 no.4
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• pp.54-61
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• 2001

Magnetostrictive materials have nonlinear elasto-magnetic properties. However the constitutive equations to describe the nonlinear properties are not available, yet. In this study we develope the equation in magnetostrictive materials by use of piezomagnetic constitutive equation which is quasi-linearized. With the wave equation, we determine the propagation velocity inside the magnetostrictive materials when a plane wave propagates along a given magnetic field. Validity of the calculated velocity is verified through comparison with experimental velocity measurement results for the most representative magnetostrictive materials. Terfenol-D.

• Geophysics and Geophysical Exploration
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• v.15 no.2
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• pp.57-65
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• 2012

Various numerical methods in simulation of seismic wave propagation have been developed. Recently an innovative numerical method called as the Spectral Element Method (SEM) has been developed and used in wave propagation in 3-D elastic media. The SEM that easily implements the free surface of topography combines the flexibility of a finite element method with the accuracy of a spectral method. It is generally used a weak formulation of the equation of motion which are solved on a mesh of hexahedral elements based on the Gauss-Lobatto-Legendre integration rule. Variational formulations of velocity-stress motion are newly modified in order to implement ADE-PML (Auxiliary Differential Equation of Perfectly Matched Layer) in wave propagation in 3-D elastic media, because a general weak formulation has a difficulty in adapting CFS (Complex Frequency Shifted) PML (Perfectly Matched Layer). SEM of Velocity-Stress motion having ADE-PML that is very efficient in absorbing waves reflected from finite boundary is verified with simulation of 1-D and 3-D wave propagation.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.26 no.4
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• pp.223-231
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• 2013

This paper presents a time-domain Gauss-Newton full-waveform inversion method for the material profile reconstruction in heterogeneous semi-infinite solid media. To implement the inverse problem in a finite computational domain, perfectly-matchedlayers( PMLs) are introduced as wave-absorbing boundaries within which the domain's wave velocity profile is to be reconstructed. The inverse problem is formulated in a partial-differential-equations(PDE)-constrained optimization framework, where a least-squares misfit between measured and calculated surface responses is minimized under the constraint of PML-endowed wave equations. A Gauss-Newton-Krylov optimization algorithm is utilized to iteratively update the unknown wave velocity profile with the aid of a specialized regularization scheme. Through a series of one-dimensional examples, the solution of the Gauss-Newton inversion was close enough to the target profile, and showed superior convergence behavior with reduced wall-clock time of implementation compared to a conventional inversion using Fletcher-Reeves optimization algorithm.

• Journal of the KSME
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• v.34 no.7
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• pp.510-516
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• 1994

탄성파의 속도는 파동 전파 매질의 밀도와 탄선계수에 달려 있으므로, 박막이 입혀진 기판에서 전파하는 표면파에 대해서 기판과 박막의 밀도와 탄성계수 및 박막의 두께 등을 알면 전파 속 도를 계산할 수 있다. 박막의 탄성계수를 모르는 경우에는 표면파 속도를 측정하여 역으로 탄 성계수를 산출할 수 있다. 이러한 역산과정에는 일반적인 비선형 방정식의 curve-fitting에 이용될 수 있는 simplex법이 효율적으로 활용된다. 이 글에서는 표면파 속도를 측정하고 그 데이터로 부터 역산하여 박막의 탄성계수를 구하는 원리와 과정을 설명한다.

• Proceedings of the Acoustical Society of Korea Conference
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• autumn
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• pp.311-314
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• 2000

자왜 재료는 자계 포화 이하에서 비선형 특성을 갖는다고 알려져 있다. 그러나 지금까지 비선형 특성을 표현하는 자왜 재료의 구조 방정식을 유도한 사례는 전무한 실정이다. 본 연구에서는 자계 포화 이하에서 비선형 특성을 갖는 자왜 재료의 비선형 구조 방정식을 4차 텐서를 이용하여 유도하였다. 나아가 유도된 구조방정식을 이용하여 자왜 재료 내의 파동 방정식을 정식화하였다. 그리고 비선형 특성을 갖는 자왜 재료에서 평면파가 자계 방향을 따라 전파될 때 등방성 자왜 재료의 탄성파 속도를 구하였다. 이상의 결과를 검증하기 위해서 자왜 재료 중에서 가장 널리 사용되고 있는 Terfenol-D의 탄성파 속도를 측정하여 본 연구에서 유도한 자왜 재료 비선형 구조 방정식의 타당성을 일부 검증하였다. 향후에 자왜 재료의 정확한 특성을 측정하여 본 연구 결과와 비교함으로써 본 연구에서 유도한 비선형 구조 방정식의 타당성을 검증하고자 한다.

• 한국지구물리탐사학회:학술대회논문집
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• 2006.06a
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• pp.131-135
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• 2006

A seismic waveform inversion for prestack seismic data based on the Gauss-Newton method is presented. The Gauss-Newton method for seismic waveform inversion was proposed in the 80s but has rarely been studied. Extensive computational and memory requirements have been principal difficulties. To overcome this, we used different sizes of grids in the inversion stage from those of grids in the wave propagation simulation, temporal windowing of the simulation and approximation of virtual sources for calculating partial derivatives, and implemented this algorithm on parallel supercomputers. We show that the Gauss-Newton method has high resolving power and convergence rate, and demonstrate potential applications to real seismic data.

• 한국지구물리탐사학회:학술대회논문집
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• 2006.06a
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• pp.181-186
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• 2006

An imaging method of seismic sources using time-reversal wave propagation is presented. The method is based on the time-reversal invariance and the spatial reciprocity of the wave equation. Time-reversal wave propagation has been used to image anomalous features of a midium in medical imaging, non destructive testing and waveform tomography. Seismogram is the record whose energy is propagated from the seismic source. If time-reversed seismogram propagates back into the medium, seismic energy is concentrated at the origin time of the event and at the source location. In this work, a staggered-grid finite-difference method of the elastic wave equation is parallelized for 3-D wave propagation simulation. With numerical experiments, we show that the time-reversal imaging will enable us to explore the spatio-temporal history of complex earthquake.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.31 no.2
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• pp.87-95
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• 2018

This paper introduces a new explicit spectral element method for the simulation of SH-waves in semi-infinite domains. To simulate the wave motion in unbounded domains, it is necessary to reduce the infinite extent to a finite computational domain of interest. To prevent the wave reflection from the trunctated boundaries, perfectly matched layer(PML) wave-absorbing boundary is introduced. The forward problem for simulating SH-waves in PML-truncated domains can be formulated as second-order PDEs. The second-order semi-discrete form of the governing PDEs is constructed by using a mixed spectral elements with Legendre-gauss-Lobatto quadrature method, which results in a diagonalized mass matrix. Then the second-order semi-discrete form is transformed to a first-order, whose solutions are calculated by the fourth-order Runge-Kutta method. Numerical examples showed that solutions of SH-wave in the two-dimensional analysis domain resulted in stable and accurate, and reflections from truncated boundaries could be reduced by using PML boundaries. Elastic wave propagation analysis using explicit time integration method may be apt for solving larger domain problems such as three-dimensional elastic wave problem more efficiently.