Geophysics and Geophysical Exploration (지구물리와물리탐사)

Korean Society of Earth and Exploration Geophysicists (한국지구물리·물리탐사학회)
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Closed-form Expressions of the Vector Gravity and Gravity Gradient Tensor Due to a Circular Disk

원판형 이상체에 의한 벡터 중력 및 중력 변화율 텐서 반응식

  • Rim, Hyoungrea (Department of Earth Science Education, Pusan National University)
  • 임형래 (부산대학교 지구과학교육과)
  • Received : 2021.01.19
  • Accepted : 2021.02.15
  • Published : 2021.02.28
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Abstract

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.

이 논문에서는 축 방향 대칭성을 가지면서 두께를 무시할 수 있는 원판형 이상체 대한 벡터 중력과 중력 변화율 텐서 반응식을 유도하였다. 밀도가 일정한 원판형 이상체의 중력 포텐셜을 원통 좌표계를 이용하여 정의한 후, 미분을 통하여 벡터 중력의 r 성분과 z 성분을 유도하였다. 벡터 중력 r 성분을 직교 좌표계에서 2개의 수평 성분으로 분해하여 벡터 중력을 구한다. 원판형 이상체의 중력 변화율 텐서는 직교 좌표계로 표현된 벡터 중력을 각 성분 방향으로 미분하여 유도하였다.

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References

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