• 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.

• 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.

• Proceedings of the Acoustical Society of Korea Conference
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• 1984.12a
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• pp.52-56
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• 1984

파동 이론에 의한 수중에서의 저주파 음파전달은 음향학적 경계 조건에 의해 결정되는 Normal Mode로 특징지어 진다. Normal Mode는 수층(Water Layer)뿐만 아니라 수직적으로 층상 구조인 해저 퇴적층(Subatrate)의 음향 특성을 포함하여 결정되는 파동 방정식의 해로서 이에 의해 수층 및 해저 퇴적층에서의 음압 분포와 감쇠를 계산할 수 있다. 본 논문은 저주파 음파 전달에 관한 Normal Mode 이론에 의하여 음원의 주파수와 해저 퇴적층에서의 음속 분포등에 따른 각 Mode의 음압 분포, 감쇠등에 관한 음향학적 해석으로 원거리까지 진행하는 수중 음파의 해저 퇴적층 투과 심도를 추출하였다.

• 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 Korean Journal of Petroleum Geology
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• v.1 no.1 s.1
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• pp.47-52
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• 1993

A method and results of computations are presented for the 2-D seismic migration process in the frequency-wavenumber domain for the laterally and vertically inhomogeneous medium. In order to take the intrinsic attenuation effect into account in the migration process the complex-valued wave velocity is used in the wavefield extrapolation operator, improving the generalized frequency-wavenumber migration technique. The imaginary part of the complex-valued wave velocity includes the seismic quality factor Q value. In derivation of the solution of the wave equation for the medium of inhomogeneous wave velocity and anelasticity, the inhomogeneous medium is mathematically converted to an equivalent system which consists of a homogeneous medium of averaged slowness and an inhomogeneous distribution of hypothetical wave source. The strength of the hypothetical wave source depends on the deviation of squared slowness from the averaged value of the medium. Results of numerical computation using the technique show more distinct geologic images than those using the convensional generalized frequency-wavenumber migration. Especially, the obscured images due to the wave attenuation by anelasticity are restored to show sharp boundaries of structures. The method will be useful in the imaging of the reflection data obtained in the regions of possible petroleum or natural gas reservoir and of fractured zone.

• 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.

• Journal of the Korean Society of Propulsion Engineers
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• v.23 no.6
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• pp.1-10
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• 2019

The wave motion inside the nozzle is known as one of the major damping elements of the rocket's combustion instability by it's aeroacoustic effects that result from the flow passage through the nozzle throat. These effects can be quantitatively evaluated by the nozzle admittance. In this study, one-dimensional linearized Euler equation was adopted to calculate the nozzle admittance, and trend analysis was performed depending on the nozzle's main design variables. As a result, when nozzle converging part shortens, it is verified that the frequency dependency of the nozzle admittance is decreased due to the widened frequency range with lowered longitudinal nozzle admittance. Also, admittance estimation using the short nozzle theory is not appropriate when the first tangential mode of the pressure perturbation arises.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.5
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• pp.629-640
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• 2007

In this paper an analytical study is carried out to improve the capacity of absorbing boundary using dashpot, one of the most widely used absorbing boundaries in FEM. Using 2-D harmonic plane wave equation, absorbing boundary condition is modified to maximize its capacity according to the incident angle. Validity of the absorbing boundary conditions which is modified is investigated by adopting the solution of Miller and Pursey. The Miller and Pursey's problem is then numerically simulated using the finite element method. The absorption ratios are calculated by comparing the displacements at the absorbing boundary to those at the free field without the absorbing boundary. The numerical study is carried out through comparison of displacement at the interior region and the boundary of the numerical model.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.28 no.3B
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• pp.323-334
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• 2008

Present study examined the functionality of the solitary wave (tsunami) control of the two-rowed porous submerged breakwater by numerical experiments, using a numerical wave tank which is based on the Navier-Stokes equation to explain fluid fields and uses a Volume of Fluid (VOF) method to capture the free water surface. Solitary wave was generated by the internal wave source installed within the computational zone in the numerical wave tank and its wave transformations by structure were compared with those in the previous study. Comparisons with the precious numerical results showed a good agreement. Based on these results, several tow-dimensional numerical modeling investigations of the water fields, including wave transformations, reflection, transmission and energy flux, by the one- and two-rowed permeable submerged breakwater under solitary waves were performed. Even if, it is a research of the limited scope, in case of two-rowed permeable submerged breakwater with $h_0/h=0.925$ ($h_0$ is height of submerged breakwater and h is water depth), the wave height damping in range of $l/L_{eff}>0.4$($L_{eff}$ is effective distance of solitary wave) can reach nearly 60% of the incident wave height. In addition, it is found that reflection coefficient increases nearly 47% and transmission coefficient decreases nearly 18% than one-rowed one. The numerical results revealed that the tow-rowed submerged breakwater can control the incident solitary wave economically and more efficiently than the one-rowed one.

• Journal of the Society of Naval Architects of Korea
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• v.32 no.1
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• pp.42-57
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• 1995

An efficient and accurate scheme has been constructed by taking advantages of the hi-quadratic spline scheme and the higher-order boundary element method selectively depending on computation domains. Boundary surfaces are represented by 8-node boundary elements to describe curved surfaces of a ship and its neighboring free surface more accurately. The variation of the velocity potential complies with the characteristics of the 8-node element on the body surface. But on the free surface, it is assumed to follow that of the hi-quadratic spline scheme. By which, the free surface solution is free from numerical damping and has better numerical dispersion property. As numerical examples, steady and unsteady Neumann-Kelvin problems are considered. Numerical results for a submerged spheroid, Series 60($C_B=0.6$) and a modified support the proposed method. Finally, a new upstream radiation condition is derived using a wave equation operator in order to deal with problems for subcritical reduced frequency. The relevance of this operator has been confirmed in the case of unsteady Kelvin source potential.