• 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.2
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• pp.85-92
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• 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.

• 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.

• Geophysics and Geophysical Exploration
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• v.23 no.2
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• pp.67-71
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• 2020

In this study, we derive closed-form expressions of magnetic gradient tensor due to a circular cylinder. Because the expression for magnetic field has been derived in a previously conducted study, expressions are developed for the magnetic gradient tensor based on the derivatives of the expressions of magnetic field with respect to the variables of the Cartesian coordinates. Furthermore, expressions are derived for the magnetic gradient tensor based on the relations between the Cartesian and cylindrical coordinates in the derivative because the expression for magnetic field contains variables of cylindrical coordinates owing to its axial symmetry.

• 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.

• Geophysics and Geophysical Exploration
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• v.6 no.1
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• pp.23-27
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• 2003

A magnetic survey on the lake war carried out to explore the possible UXO (unexploded ordnance) under the water. A magnetic gradiometer with 2 magnetometer sensors was used, which measures total magnetic intensity. For the positioning of the measurement points on the water, RTK (real time kinematic) survey system was used. The theoretical responses were calculated assumming the dimension and the material of the UXO so that the detectability could be investigated. Since the areal size of the survey vessel was rather small, the influence from the magnetic material of the vessel and the other equipments such as a laptop computer was not negligible, and the influence did not remain constant during the survey due to the change of survey direction. These effects were reduced remarkably using moving average technique. The result reveals the lineament of a pipe line laid on the bottom of the lake, which can be regarded as an indirect proof of detectability of the method.

• 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.

• Geophysics and Geophysical Exploration
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• v.27 no.2
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• pp.108-118
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• 2024

In this study, expressions for the magnetic field and magnetic gradient tensor due to an elliptical disk were derived. Igneous intrusions and kimberlite structures often have elliptical cylinders with axial symmetry and elliptical cross sections. An elliptical cylinder with varying cross-sectional areas was approximated using stacks of elliptical disks. The magnetic fields of elliptical disks were derived using the Poisson relation, which includes the direction of magnetization in the gravity gradient tensor, as described in a previous study (Rim, 2024). The magnetic gradient tensor due to an elliptical disk is derived by differentiating the magnetic fields, which is equivalent to obtaining ten triple-derivative functions acquired by differentiating the gravitational potential of the elliptical disk three times in each axis direction. Because it is possible to exchange the order of differentiation, the magnetic gradient tensor is derived by differentiating the gravitational potential of the elliptical disk three times, which is then converted into a complex line integral along the closed boundary curve of the elliptical disk in the complex plane. The expressions for the magnetic field and magnetic gradient tensor derived from a complex line integral in complex plane are perfectly consistent with those of the circular disk derived from the Lipschitz-Hankel integral.

• Journal of the Korean earth science society
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• v.38 no.4
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• pp.251-262
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• 2017

The system of magnetic exploration with a drone flight was constructed and applied to the iron mine site. The magnetic probe system installed on the drone used a sensor as Bartington's fluxgate type magnetometer, Mag639 and the A/D converter to collect magnetic intensity values on the tablet PC. The drone flight control module is a highly expandable Pixhawk with allowing 15 minutes of flight by loading 3kg. Experiments on the magnetic field interference range were performed to remove the erroneous effect from the drone with applying RTK GPS to obtain the magnetic intensity value at the accurate position. The accurate location information enabled to obtain the gradient measurement of magnetic field by measuring twice at different altitudes. Also, by using the terrain information, we could eliminate the terrain effect by setting the flight path to fly along the terrain. These results are in line with the field experiments using the nuclear proton magnetometer G-858 of Geometrics Co., Ltd, which adds to the reliability of the drone based aeromagnetic survey system we constructed.

• The Journal of the Korea Contents Association
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• v.12 no.8
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• pp.380-387
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• 2012

A complex seismic survey, which is nondestructive inspection, is used often recently in estimating the location of reclaimed cultural assets. Such a method is the best way to estimate the location of cultural assets most effectively in a short time at a construction site. This study estimated the reclamation location of a cultural asset by using magnetic gradient survey, earth resistivity survey, and ground penetrating radar survey (GPR) in order to figure out the distribution territory in the area with possibility of creation of reclaimed cultural assets in the past. As a result, it was located at +15m on the X axis and +90m on the Y axis on the floor plane coordinate of the study target area. It was shown that the major axis is about 20m long in the north-northeast direction and the width is about 5m. The depth of development distribution of anomaly zone was estimated as about 1.5~3.0m. Geophysical survey is expected to be used as a efficient and accurate way to excavate the reclaimed cultural assets in future.