• Geophysics and Geophysical Exploration
• /
• v.24 no.1
• /
• pp.1-5
• /
• 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
• /
• v.27 no.1
• /
• pp.51-56
• /
• 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
• /
• v.26 no.1
• /
• pp.1-7
• /
• 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
• /
• v.23 no.1
• /
• pp.55-60
• /
• 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
• /
• v.25 no.1
• /
• pp.44-49
• /
• 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.

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

• 제어로봇시스템학회:학술대회논문집
• /
• 2001.10a
• /
• pp.64.1-64
• /
• 2001

Errors in inertial navigation system(INS) can be divided into two major groups which are system related errors and modeling errors due to approximation and linearization. Measurement noise, calibration, and alignment errors make up the first group, whereas the uncertainties in the gravity vector fall in the second category and are important error source for high quality INS, especially during high altitude and and/or long time missions, when the gravity errors tent to build up. The quality of a medium to high accuracy INS depends on the knowledge of the local gravity field. In this paper, the feasibility of improving airborns INS by use of more accurate gravity model is studied. To make consistent comparisons, WGS-84 parameters are used and ...

• Journal of the Korea Society of Computer and Information
• /
• v.19 no.5
• /
• pp.43-52
• /
• 2014

In this paper, we propose Gravity Removal and Vector Rotation algorithm for counting steps of wearable device, and we evaluated the proposed GRVR algorithm with Micro-Electro-Mechanical (MEMS) 3-axis accelerometer equipped in low-power wearable device while the device is mounted on various positions of a walking or running person. By applying low-pass filter, the gravity elements are canceled from acceleration on each axis of yaw, pitch and roll. In addition to DC-bias removal and the low-pass filtering, the proposed GRVR calculates acceleration only on the yaw-axis while a person is walking or running thus we count the step even if the wearable device's axis are rotated during walking or running. The experimental result shows 99.4% accuracies for the cases where the wearable device is mounted in the middle and on the right of the belt, and 91.1% accuracy which is more accurate than 83% of commercial 3-axis pedometer when worn on wrist for the case of axis-rotation.

• Geophysics and Geophysical Exploration
• /
• v.25 no.2
• /
• pp.85-92
• /
• 2022

An elongated object in one direction can be approximated as a line segment. Here, the closed-form expressions of a line segment's vector magnetic and magnetic gradient tensor are required to interpret responses by a line segment. Therefore, the analytical expressions of the vector magnetic and magnetic gradient tensor are derived. The vector magnetic is converted from the existing gravity gradient tensor using Poisson's relation where the gravity gradient tensor caused by a line segment can be transformed into a vector magnetic. Then, the magnetic gradient tensor is derived by differentiating the vector magnetic with respect to each axis in the Cartesian coordinate system. The synthetic total magnetic data simulated by an iron pile on boreholes are inverted by a nonlinear inversion process so that the physical parameters of the iron pile, including the beginning point, the length, orientation, and magnetization vector are successfully estimated.

• Journal of the Korean Crystal Growth and Crystal Technology
• /
• v.27 no.2
• /
• pp.80-88
• /
• 2017

In this research a time dependent thermal and solutal convection was computationally investigated for the physical vapor transport of the mixture of $Hg_2Cl_2-I_2$ system with for the convective regime from thermal Rayleigh number of $2.16{\times}10^6$ up to $1.7{\times}10^7$ with marching time to a steady state problem. With time marching, the convective cells are decreased for the thermal Rayleigh number of $2.16{\times}10^6$, and increased for the thermal Rayleigh number of $1.7{\times}10^7$. The convective flow structures are found to be essentially time independent on the horizontal orientation of the enclosure with respect to the gravity vector, and on the other hand, time dependent on the vertical orientation of the enclosure with respect to the gravity vector.