引力场梯度张量的非奇异公式推导

基金项目: 国家自然科学基金资助项目(41074015);中国科学院资源环境科学与技术局专项资助项目(XMXX280730)

详细信息

New Derivation of Nonsingular Expression for Gravitational Gradients Calculation

¹ Key Laboratory of Computational Geodynamics,Chinese Academy of Sciences,A19 Yuquan Road,Beijing 100049,China;² Graduate University of Chinese Academy of Sciences,A19 Yuquan Road,Beijing 100049,China

Funds: 国家自然科学基金资助项目(41074015);中国科学院资源环境科学与技术局专项资助项目(XMXX280730)

摘要: 传统的引力场梯度计算公式在两极附近存在奇异性,需要换用其他的非奇异计算公式。从奇异性产生的原因入手,并结合勒让德函数的有关性质,推导了一组新的计算公式。实际计算验证了该公式的正确性和有效性。
- GOCE卫星 /
- 引力场梯度 /
- 非奇异 /
- 勒让德函数
Abstract: GOCE has released gravity gradients,but there aren't data in polar regions because the inclination of the orbit is about 96.7°.We need to simulate data with known gravity field model in this area,whereas many formulas to compute the gravity gradients are singular at poles,which can cause a lot of difficulties in gravity field recovery using GOCE data.In order to overcome the so-called singularities,we firstly analyze the singular term,then derives a new nonsingular expression for gravitational gradients calculation based on properties of Legendre function.At last we compare several different formulas through calculation.The proposed formulas is more accurate than conventional methods.
- GOCE satellite /
- gradient of the gravitational field /
- nonsingular /
- Legendre function