• 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.25 no.1
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• pp.44-49
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• 2022

Closed-form expressions of vector gravity and gravity gradient tensor based on a line segment are derived. If a cylindrical object with axial symmetry is observed from a distance, it is possible to approximate it as a line segment; therefore, it is necessary to compute the gravity and the gravity gradient tensor due to a line source by using closed-form expressions. The gravitational potential for a line segment is defined as a one-dimensional integral, and this integral is differentiated with respect to the Cartesian coordinate system to derive the vector gravity. The expressions of the gravity gradient tensor are derived by differentiating the vector gravity once more in the same coordinate system.

• Geophysics and Geophysical Exploration
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• v.24 no.1
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• pp.1-5
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• 2021

The closed-form expressions of the vector gravity and gravity gradient tensor due to a circular disk are derived. The gravity potential due to a circular disk with a constant density is defined for a cylindrical system. Then, the vector gravity is derived by differentiating the gravity potential with respect to cylindrical coordinates. The radial component of the vector gravity in the cylindrical system is converted into horizontal gravity components in the Cartesian system. Finally, the gravity gradient tensor due to a circular disk is obtained by differentiating the vector gravity with respect to the Cartesian coordinates.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.33 no.12
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• pp.1427-1432
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• 2009

The pitch motion of a generic gravity gradient satellite is investigated in terms of chaos. The Melnikov method is used for detecting the onset of chaotic behavior of the pitch motion of a gravity gradient satellite. The Melnikov method determines the distance between stable and unstable manifolds of a perturbed system. When stable and unstable manifolds transverse on the Poincare section, the resulting motion can be chaotic. The Melnikov analysis indicates that the pitch dynamics of a generic gravity gradient satellite can be chaotic when the orbit eccentricity is small.

• 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.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.

• 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.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.

• Korean Journal of Fisheries and Aquatic Sciences
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• v.51 no.3
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• pp.332-337
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• 2018

The Pacific cod Gadus macrocepahlus, lays demersal eggs and the hatching larvae rise toward the surface layer of the ocean to feed. The change in the specific gravity of eggs and larvae was investigated to examine their vertical distribution and movement in the water column. The specific gravities of fertilized eggs and various size classes of larvae were measured using a density gradient apparatus. In total, the instantaneous specific gravity of 146 eggs and 225 larvae were measured. To prevent any disturbance in the gradient water column due to larval movement, 0.004% MS222 was used for anesthesia. Due to their high specific gravity, eggs spawned were deposited over the sea-bed of the spawning ground. The specific gravity of hatching larvae decreased abruptly. However, Pacific cod larvae still had a comparatively high specific gravity at hatching ($1.03655{\pm}0.00146g/cm3$, n=4, mean SL=3.62 mm) and their specific gravities tended to decrease as they grew. The specific gravity stabilized 6 days after hatching ($1.02590{\pm}0.00212g/cm3$, n=15, mean SL=4.67 mm) and the cod larvae were eventually able to float in the water column.

• Journal of Astronomy and Space Sciences
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• v.13 no.2
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• pp.67-81
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• 1996

The attitude dynamics of KITSAT-1 are modeled including the gravity gradient stabilization method. We define the operation scenario during the initial attitude stabilization period by means of a magnetorquering control algorithm. The required constraints for the gravity gradient boom deployment are also examined. Attitude dynamics model and control laws are verified by analyzing in-orbit attitude sensor telemetry data.