지구물리와물리탐사 (Geophysics and Geophysical Exploration)

  • 제27권1호
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  • Pages.51-56
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  • 2024
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  • 1229-1064(pISSN)
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  • 2384-051X(eISSN)
한국지구물리·물리탐사학회 (Korean Society of Earth and Exploration Geophysicists)
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타원판에 의한 벡터 중력 및 중력 변화율 텐서 반응식

The Expressions of Vector Gravity and Gravity Gradient Tensor due to an Elliptical Disk

  • 임형래 (부산대학교 지구과학교육과, 부산대학교 미래지구환경연구소)
  • Hyoungrea Rim (Department of Earth Science Education, Pusan National University, Institute for Future Earth, Pusan National University)
  • 투고 : 2024.01.16
  • 심사 : 2024.02.23
  • 발행 : 2024.02.29
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초록

논문에서는 타원판의 벡터 중력과 중력 변화율 텐서 반응식을 유도하였다. 타원판의 벡터 중력은 이중 적분으로 표현한 타원판에 의한 중력 퍼텐셜을 각 축 방향으로 미분하여 유도한다. 이중 적분으로 정의된 타원판에 의한 벡터 중력은 복소 그린 정리를 이용하여 타원판 경계를 따라 폐곡선의 선적분으로 변형한다. 최종적으로 타원판 경계를 매개변수로 설정하여 1차원 수치적분을 통하여 타원판에 의한 벡터 중력을 유도한다. 타원판에 의한 중력 변화율 텐서의 xz, yz, zz성분은 타원판의 벡터 중력을 수직 방향으로 미분하여 구한다. xx, yy, xy성분은 이중 적분 형태의 벡터 중력의 수평 성분을 먼저 수평 방향으로 미분한 후 복소 그린 정리를 이용하여 유도한다.

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.

키워드

과제정보

이 논문은 2023년도 정부(교육부)의 재원으로 한국연구재단의 램프(LAMP) 사업 지원을 받아 수행된 연구임(No. RS-2023-00301938).

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