• 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.

• Progress in Medical Physics
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• v.19 no.4
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• pp.227-230
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• 2008

The purpose of this study was to design and construct an ultrasound phantom for volume calibration and evaluate the volume measurement accuracy of a 2 dimensional ultrasonic system. Ultrasound phantom was designed, constructed and tested. The phantom consisted of a background material and a target. The background was made by mixing agarose gel with water. A target, made with an elastic material, was filled with water to vary its volume and shape and inserted into background material. To evaluate accuracy of a 2 dimensional ultrasonic system (128XP, ACUSON), three different shapes of targets (a sphere, 2 ellipsoids and a triangular prism) were constructed. In case of ellipsoid shape, two targets, one with same size length and width (ellipsoid 1) and another with the length 2 times longer than width (ellipsoid 2) were examined. The target volumes of each shape were varied from 94cc to 450cc and measurement accuracy was examined. The volume difference between the real and measured target of the sphere shape ranged between 6.7 and 11%. For the ellipsoid targets, the differences ranged from 9.2 to 10.5% with ellipsoid 1 and 25.7% with ellipsoid 2. The volume difference of the triangular prism target ranged between 20.8 and 35%. An easy and simple method of constructing an ultrasound phantom was introduced and it was possible to check the volume measurement accuracy of an ultrasound system.