• 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.

• 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.

• 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.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.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.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.24 no.2
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• pp.183-191
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• 2006

The accuracy of the upward continuation is assessed through the gravity modeling using an ultra-high degree spherical harmonic expansion. The difficulties in the numerical calculation of Legendre function with ultra-high degree, underflow and/or overflow, is successfully resolved in 128 bit calculation scheme. Using the generated Legendre function, the gravity anomaly with spatial resolution of $1'{\times}1'$ on the geoid is calculated. The generated gravity anomaly is degraded and extracted with various noise levels and data intervals, then upward continuation is applied to each data sets. The comparison between the upward continued gravity disturbances and the directly calculated from the spherical harmonics showed that the accuracy on the direct method was significantly better than that of Poisson method. In addition, it is verified that the denser and less noised gravity data on the geoid generates better gravity disturbance vectors at an altitude. Especially, it is found that the gravity noise level less than 5mGal, and the data interval less than 2arcmin is necessary for next generation precision INS navigation which requires the accuracy of 5mGal or better at an altitude.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.6
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• pp.254-259
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• 2013

A newly developed fall recognition algorithm using gravity weighted 3-axis accelerometer data as the input of HMM (Hidden Markov Model) is introduced. Five types of fall feature parameters including the sum vector magnitude(SVM) and a newly-defined gravity-weighted sum vector magnitude(GSVM) are applied to a HMM to evaluate the accuracy of fall recognition. A GSVM parameter shows the best accuracy of falls which is 100% of sensitivity and 97.96% of specificity, and comparing with SVM, the results archive more improved recognition rate, 5.2% of sensitivity and 4.5% of specificity. GSVM shows higher recognition rate than SVM due to expressing falls characteristics well, whereas SVM expresses the only momentum.

• Journal of the Korean earth science society
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• v.38 no.4
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• pp.263-268
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• 2017

The determination algorithm of the location of a line source with strike and dip using the gravity gradient tensor on a single profile is proposed. We already proposed the determination of strike and dip in the previous paper and then, now we improved the algorithm to locate a line source after determining strike and dip. The strike and dip of the line source can be determined by rotating the gravity gradient tensor matrix as reducing 2 independent components. Using the ratio of remaining 2 components, the location can be determined by the least square manner of the pointing vectors on each observation point. A synthetic model is tested for proving the usefulness of the proposed algorithm.

• Geophysics and Geophysical Exploration
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• v.23 no.1
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• pp.50-54
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• 2020

Herein, the closed-form expressions of the magnetic field due to an axially symmetric body such as a right cylinder, are derived. The magnetic field due to a right cylinder is converted from the gravity gradient tensor using Poisson's relation; the magnetic field induced by a constant magnetization can be obtained from the gravity gradient tensor with a constant density. Because of the axial symmetry of the cylinder, the expressions of gravity gradient tensor are derived in cylindrical coordinate and then transformed into Cartesian coordinates for the three components of the magnetic field using an arbitrary magnetization direction.

• Proceedings of the Korea Contents Association Conference
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• 2004.11a
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• pp.197-202
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• 2004

도시의 변화탐지와 예측을 위한 기존의 중력모델은 주로 벡터기반 거리와 면적척도를 사용하였다. 위성영상이 폭넓게 활용되는 추세를 보이고 있는 최근에는 이 위성영상을 이용한 효과적인 래스터GIS기반 중력모델에 대한 연구가 필요하다. 본 연구는 래스터GIS기반 중력모델 방법을 제안하여 이를 전북 군산시 도시변화탐지에 적용하고 지표온도, 토지피복, 식생 변수를 검증하여 지표온도와 코지피복, 식생지수와의 +0.794의 강한 정의 상관관계를 검출함으로써 제안한 위성영상을 이용한 래스터GIS기반 중력모델이 육상 도시변화탐지 모니터링에 매우 효과적임을 입증할 수 있었다.