• The Journal of the Acoustical Society of Korea
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• v.39 no.1
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• pp.1-7
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• 2020

The acoustic parabolic equation method in the ocean is an efficient technique to calculate the acoustic field in the range-dependent environment, emanating from a point source. However, we often need to use the directional source with a main beam in the practical problem. In this paper, we present two methods to implement the directional source in the acoustic parabolic equation code easily. One is simply to filter the Delta function idealized as an omni-directional point source. Another method is based on the rational filtering of the self-starter solution. It has a limitation not to separate the up-going and the down-going wave for the depth, but would be useful in implementing the mode propagation. Numerical examples for validation are given in the Pekeris environment and the deep sea environment.

• The Journal of the Acoustical Society of Korea
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• v.15 no.2
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• pp.72-78
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• 1996

This thesis deals with a method to solve a two-and-one-half-dimensional ($2\frac12$ D) problem, which means that the ocean environment is two-dimensional whereas the source is fully three-dimensionally propagating, including three-dimensional refraction phenomena and three-dimensional back-scattering, using two-dimensional two-way parabolic equation method combined with Fourier synthesis. Two dimensional two-way parabolic equation method uses Galerkin's method for depth and Crank-Nicolson method and alternating direction for range and provides a solution available to range-dependent problem with wave-field back-scattered from discontinuous interface. Since wavenumber, k, is the function of depth and vertical or horizontal range, we can reduce a dimension of three-dimensional Helmholtz equation by Fourier transforming in the range direction. Thus transformed two-dimensional Helmholtz equation is solved through two-way parabolic equation method. Finally, we can have the $2\frac12$ D solution by inverse Fourier transformation of the spectral solution gained from in the last step. Numerical simulation has been carried out for a canonical ocean environment with stair-step bottom in order to test its accuracy using the present analysis. With this spectral parabolic equation method, we have examined three-dimensional acoustic propagation properties in a specified site in the Korean Straits.

• The Journal of the Acoustical Society of Korea
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• v.36 no.1
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• pp.1-11
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• 2017

In this study, novel approximate form of the square-root operator of three dimensional acoustic Parabolic Equation (3D PE) is proposed using a rational approximant for two variables. This form has two advantages in comparison with existing approximation studies of the square-root operator. One is the wide-angle capability. The proposed form has wider angle accuracy to the inclination angle of ${\pm}62^{\circ}$ from the range axis of 3D PE at the bearing angle of $45^{\circ}$, which is approximately three times the angle limit of the existing 3D PE algorithm. Another is that the denominator of our approximate form can be expressed into the product of one-dimensional operators for depth and cross-range. Such a splitting form is very preferable in the numerical analysis in that the 3D PE can be easily transformed into the tridiagonal matrix equation. To confirm the capability of the proposed approximate form, comparative study of other approximation methods is conducted based on the phase error analysis, and the proposed method shows best performance.

• Journal of KSNVE
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• v.7 no.2
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• pp.215-222
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• 1997

The flow and acoustic fields due to a vortex ring interaction with a rigid sphere are simulated numerically. The flow field is regarded as three-dimensional inviscid and incompressible. The vorticity is assumed to be concentrated inside the finite core of vortex filament. The vortex filament curve, described by parabolic blending curve function, is used to effectively solve the modified Biot-Savart equation. The interaction between a vortex ring and a rigid sphere using the parabolic blending curve is calculated. The trajectory of the vortex ring is obtained with several different initial positions between the ring and the sphere. The force variations acting on the sphere are calculated by using the boundary integral method. Finally, we can also obtain the acoustic signals at the far field observation positions from the force variations acting on the rigid surface. We can find that the dipole axis of the directivity patterns are rotated during the interacting phenomena.

• The Journal of the Acoustical Society of Korea
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• v.19 no.5
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• pp.46-52
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• 2000

Internal waves existing in the stratified ocean significantly affect acoustic propagation. In order to understand the effects of internal waves on acoustic propagation, the sound speed fluctuations due to internal waves are generated based on the Garrett-Munk spectrum which is derived from measured data in the East Sea. The acoustic propagation, where internal waves are present, is simulated numerically using a Galerkin higher order parabolic equation method(SNUPE). These results show favorable comparison to in-situ acoustic propagation data from the East Sea. To investigate the effects of acoustic propagation in random media, scintillation index is adopted and comparison between the measured and numerically simulated data is made.

• The Journal of the Acoustical Society of Korea
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• v.18 no.4
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• pp.71-77
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• 1999

Exact forward modeling of acoustic propagation is crucial in MFP such as inverse problems and various other acoustic applications. As acoustic propagation in shallow water environments become important, range dependent modeling has to be considered of which PE method is considered as one of the most accurate and relatively fast. In this paper higher order numerical rode employing the PE method is developed. To approximate the depth directional operator, Galerkin's method is used with partial collocation to lessen necessary calculations. Linearization of tile depth directional operator is achieved via expansion into a multiplication form of (equation omitted) approximation. To approximate the range directional equation, Crank-Nicolson's method is used. Final1y, numerical self stater is employed. Numerical tests are performed for various occan environment scenarios. The results of these tests are compared to exact solutions, OASES and RAM results.

• The Journal of the Acoustical Society of Korea
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• v.41 no.2
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• pp.131-142
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• 2022

In order to examine the possibility of horizontal simulations of acoustic waves on the environments of big water depth variations, this study introduces a 3-dimensional model based on the pababolic equation. The model gives approximated solutions by separating the cross- and non cross-terms in the equation. Assuming artificial bathymetry (25 km × 4 km) with a source frequency 75 Hz, the simulations give clear horizontal refractions on the transmission loss distributions. The degree of refractions shows non-linear increase along the propagating range and proportional increase with water depth along the cross range. Another simulations with the real bathymetry (25 km × 8 km) also give clear horizontal refractions. The horizontal distributions present little difference with the depth resolution variations of the same data source because the model gives interpolations over the depth data before simulations. Meanwhile, the horizontal distributions show big difference with those of different data sources.

• Journal of the Korea Institute of Military Science and Technology
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• v.18 no.5
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• pp.538-547
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• 2015

The goal of this study is to develop an algorithm to propose optimal deployment of detection sensor nodes in the target area, based on a performance surface, which represents detection performance of active and passive acoustic sonar systems. The performance surface of the active detection system is calculated from the azimuthal average of maximum detection ranges, which is estimated with a transmission loss and a reverberation level predicted using ray-based theories. The performance surface of the passive system is calculated using the transmission loss model based on a parabolic equation. The optimization of deployment configurations is then performed by a hybrid method of a virtual force algorithm and a particle swarm optimization. Finally, the effectiveness of deployment configurations is analyzed and discussed with the simulation results obtained using the algorithm proposed in this paper.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.19 no.5
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• pp.1259-1268
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• 2015

The sonic layer depth (SLD) variability is important for understanding the acoustic properties of the upper ocean that influence acoustic communications, acoustic tomography, and naval operations related to searching and detecting marine underwater vessels. Generally, the SLD is the acoustical equivalent of the mixed layer depth (MLD), although they are defined differently. In this study the SLD was compared with the MLD over the annual cycle in the East Sea using an available set of temperature-salinity observation profiles. For the comparison, various definitions and methods of the MLD had applied. As a result, the SLD in the East Sea is slight similar to the curvature method applied MLD, but the other MLD have severe differences with the SLD. Futhermore, a parabolic equation transmission model is used to evaluate the cutoff frequency trapped in surface duct. It follow that there is an optimum frequency for propagation at which the loss of sound is minimum.

• The Journal of the Acoustical Society of Korea
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• v.37 no.1
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• pp.1-11
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• 2018

Sound propagation in shallow water changes from spherical spreading to cylindrical spreading, depending on boundary conditions, and this point is defined as a transition point of the sound propagation condition. Theoretically, the transition point can be estimated using the transmission loss as a function of source-receiver range. In this paper, the transmission loss curve in a Pekeris waveguide is predicted using a parabolic-equation based acoustic propagation model and using this transmission loss curve, the range from the source of the transition point is estimated, which is compared to the critical distance calculated using the sound speed ratio of water to sediment. In addition, the effects of the sound speed profile and source depth change on the transition point are investigated. Finally, the transition point is estimated using the transmission loss data measured during the period of the SAVEX15 (Shallow Water Acoustic Variability EXperiment 2015) conducted 65 km southwest of Jeju Island in May 2015, and it is compared to the ocean environmental parameters to understand the properties of sound propagation in the experimental area.