• 한국지구물리탐사학회:학술대회논문집
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• 2006.06a
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• pp.161-166
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• 2006

Vertical gravity gradient measurement offers greater structural resolution and detectability than gravity alone. Practical difficulties of field measurement of vertical gravity gradient have raised questions of its accuracy and utility. But, modern automated gravimeter of $1\;{\mu}Gal$ sensitivity makes it easier to measure vertical gradient with required accuracy. It is particularly effective to engineering and environmental problems which target shallow subsurface structure. This paper attempts to apply the vertical gravity gradient technique to high resolution density mapping. The method was generally reviewed and numerical inverse modeling was executed for comparing with conventional gravity. And actual vertical gravity gradient data surveyed overt karstic cavity area at Muan was analysed and interpreted.

• Geophysics and Geophysical Exploration
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• v.23 no.1
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• pp.55-60
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• 2020

The closed-form expressions of gravity, magnetic, gravity gradient tensor, and magnetic gradient tensor due to a rectangular prism are derived. The vertical gravity is derived via triple integration of a rectangular prism in Cartesian coordinates, and the two horizontal components of vector gravity are then derived via cycle permutation of the axis variables of vertical gravity through the axial symmetry of the rectangular prism. The gravity gradient tensor is obtained by differentiating the vector gravity with respect to each coordinate. Using Poisson's relation, a vector magnetic field with constant magnetic direction can be obtained from the gravity gradient tensor. Finally, the magnetic gradient tensor is derived by differentiating the vector magnetic with respect to appropriate coordinates.

• Geophysics and Geophysical Exploration
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• v.26 no.1
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• pp.1-7
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• 2023

This study derives the expressions of vector gravity and gravity gradient tensor due to an elliptical cylinder. The vector gravity for an arbitrary three-dimensional (3D) body is obtained by differentiating the gravitational potential, including the triple integral, according to the shape of the body in each axis direction. The vector gravity of the 3D body with axial symmetry is integrated along the axial direction and reduced to a double integral. The complex Green's theorem using complex conjugates subsequently converts the double integral into a one-dimensional (1D) closed-line integral. Finally, the vector gravity due to the elliptical cylinder is derived using 1D numerical integration by parameterizing a boundary of the elliptical cross-section as a closed line. Similarly, the gravity gradient tensor due to the elliptical cylinder is second-order differentiated from the gravitational potential, including the triple integral, and integrated along the vertical axis direction reducing it to a double integral. Consequently, all the components of the gravity gradient tensor due to an elliptical cylinder are derived using complex Green's theorem as used in the case of vector gravity.

• Geophysics and Geophysical Exploration
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• v.27 no.1
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• pp.51-56
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• 2024

In this paper, the vector gravity and gravity gradient tensor of an elliptical disk are derived. The vector gravity of an elliptical disk is defined by differentiating the gravitational potential due to the elliptical disk expressed by a double integral with respect to each axial direction. The vector gravity defined by the double integral is then transformed into a line integral of a closed curve along the elliptical disk boundary using the complex Green's theorem. Finally, vector gravity due to the elliptical disk is derived by 1D parametric numerical integration along the elliptical disk boundary. The xz, yz, zz components of the gravity gradient tensor due to the elliptical disk are obtained by differentiating the vector gravity with respect to vertical direction. The xx, yy, xy components are derived by differentiating the horizontal components of the vector gravity in the form of a double integral with respect to horizontal directions and then using the complex Green's theorem.

• Journal of the Korean earth science society
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• v.35 no.7
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• pp.529-536
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• 2014

In this paper, the automatic determination algorithm of strike and dip of a line source using gravity gradient on a single profile is proposed. In general, the gravity gradient tensor due to a line source has only two independent components because of its 2-Dimensional (2-D) characteristics. However, if the line source has the strike and dip regarding the observation profile, it comes to have five independent components. The proposed algorithm of the determination both strike and dip is based on the rotational transform that converts full gravity gradient tensor to reduced 2-D gravity gradient tensor. The least-square method is applied in order to find optimum rotational angles that make one of the row components minimalized simultaneously. The two synthetic cases of a line source are represented; one has strike only and the other has both strike and dip. This study finds that the automatic determination method using gravity gradient tensor can find directions of a line source in each case.

• Geophysics and Geophysical Exploration
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• v.25 no.1
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• pp.38-43
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• 2022

In case axial symmetrical bodies with varying cross sections such as volcanic conduits and unexploded ordnance (UXO), it is efficient to approximate them by adding the response of thin disks perpendicular to the axis of symmetry. To compute the vector magnetic and magnetic gradient tensor respones by such bodies, it is necessary to derive an analytical expression of the circular disk. Therefore, in this study, we drive closed-form expressions of the vector magnetic and magnetic gradient tensor due to a circular disk. First, the vector magnetic field is obtained from the existing gravity gradient tensor using Poisson's relation where the gravity gradient tensor due to the same disk with a constant density can be transformed into a magnetic field. Then, the magnetic gradient tensor is derived by differentiating the vector magnetic field with respect to the cylindrical coordinates converted from the Cartesian coordinate system. Finally, both the vector magnetic and magnetic gradient tensors are derived using Lipschitz-Hankel type integrals based on the axial symmetry of the circular disk.

• Journal of the Earthquake Engineering Society of Korea
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• v.5 no.1
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• pp.63-72
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• 2001

상부 벽체와 하부 골조로 구성되는 주상복합건물은 전이층에서 수직적인 강성과 강도의 불연속성을 갖는다. 이러한 복합구조는 전이층에서 춤이 큰 보에 의하여 하중이 전달되면 설계시 매우 중요하게 고려하여야 하는 사항이다. 그러나 이에 대한 연구가 충분히 이루어져 있지 않으며 실제 전이보의 설계시 춤을 매우 크게 하여 요구되는 강도보다 큰 안전율이 고려되고 있다. 본 연구에서는 전이층의 단순화모델을 이용하여 보의 높이 및 지지면의 길이에 따른 아치거동의 변화를 조사하였다. 유한요소법을 이용하여 구조물을 분석하고 두 변수를 포함하는 헌치부재를 이용하여 그 효과를 기존 시스템과 비교하였다. 중요 변수와 헌치의 기울기는 1:1의 비율에서 사장 효율이 좋은 것으로 나타났으며, 이러한 결과를 전이보를 대신하여 사용한 결과 중력방향의 상부 아치거동에 대하여 효과적으로 작용하는 것으로 나타났다. 또한 응력 집중부위에서의 응력 감소와 깊이 전이보의 높이감소에 효과적으로 작용하는 것으로 나타났다.

• Geophysics and Geophysical Exploration
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• v.26 no.2
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• pp.77-83
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• 2023

In this study, the expressions of magnetic vector and magnetic gradient tensor due to an elliptical cylinder were derived. Igneous intrusions and kimberlite structures are often shaped like elliptical cylinders with axial symmetry and different radii in the strike and perpendicular directions. The expressions of magnetic fields due to this elliptical cylinder were derived from the Poisson relation, which includes the direction of magnetization in the gravity gradient tensor. The magnetic gradient tensor due to an elliptical cylinder is derived by differentiating the magnetic fields. This method involves obtaining a total of 10 triple derivative functions acquired by differentiating the gravitational potential of the elliptical cylinder three times in each axis direction. As the order of differentiation and integration can be exchanged, the magnetic gradient tensor was derived by differentiating the gravitational potential of the elliptical cylinder three times in each direction, followed by integration in the depth direction. The remaining double integration was converted to a complex line integral along the closed boundary curve of the elliptical cylinder in the complex plane. The expressions of the magnetic field and magnetic gradient tensor derived from the complex line integral in the complex plane were shown to be perfectly consistent with those of the circular cylinder derived by the Lipschitz-Hankel integral.

• Journal of KSNVE
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• v.6 no.1
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• pp.107-114
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• 1996

The damping characteristics of a cylindrical structure containing oil and bearing balls is investigated for external bending forces. The experimental data obtained through the use of bearing balls with viscous oil in a column is given and analyzed. The viscous action of the oil and inertia effects of the balls on the inside of column create a drag force. The drag force dampens the vibration of the column. This study aims to search for an optimum combination of oil and balls which would produce maximum damping. Machining oils of various viscosities along with ball bearings of various sizes place inside cantilevered aluminium tubes of various diameters to create a rig on which the damping properties of the oil and balls can be studied. The contileved tubes are studied in both horizontal and vertical positions in order to gauge the effect of gravity on the system. The actions of the ball in the column and damping characteristics are investigated according to the dimensionless terms. The Buckingham theorem is used to reduce the variables and to predict the damping of an oil ball column. Though the damping ratio remains fairly constant in the horizontal position of column, the damping ratio begins to increase as the ratio of the number of balls and column length rise above 0.28 in the vertical position of oil ball column. The ratio of the ball diameter to column diameter influences the damping ratio with an optimum diameter ratio. Slenderness ratio and gravity effects on the damping ratio ane investigated.

• Journal of the Korean Society for Marine Environment & Energy
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• v.11 no.2
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• pp.92-97
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• 2008

Salt wedge into the river from the sea or fresh water flume (fresh wedge) in the ocean from the sea has density current characteristics. However, when temperature and salinity simultaneously determine the density of wedges, one of salinity and temperature can distributed in the reversed profiles against gravity, even though the density profile is stable. In this case, the double diffusive process is critical in determining mixing rate. The present work studies relative contribution of shear driven mechanical mixing component and double diffusive layering process, when warm salty denser water is introduced into the cold fresh lighter water column. Laboratory experiment releases warm salty denser water into cold fresh lighter water controlling discharge amount to achieve the steady state of density current. When longitudinal density rate becomes 15, the released amount ratio of salt and heat changes sharply and in the releasing point, vigorous mixing occurs with increase of discharged amount due to double diffusion. Double diffusion distabilizes gravitational stability and enhances the mixing rate up to $6{\times}10$ times at the lower density ratio comparing to the higher density ratio.