万晓云. 引力场梯度张量的非奇异公式推导[J]. 武汉大学学报 ( 信息科学版), 2011, 36(12): 1486-1489.
引用本文: 万晓云. 引力场梯度张量的非奇异公式推导[J]. 武汉大学学报 ( 信息科学版), 2011, 36(12): 1486-1489.
WAN Xiaoyun. New Derivation of Nonsingular Expression for Gravitational Gradients Calculation[J]. Geomatics and Information Science of Wuhan University, 2011, 36(12): 1486-1489.
Citation: WAN Xiaoyun. New Derivation of Nonsingular Expression for Gravitational Gradients Calculation[J]. Geomatics and Information Science of Wuhan University, 2011, 36(12): 1486-1489.

引力场梯度张量的非奇异公式推导

New Derivation of Nonsingular Expression for Gravitational Gradients Calculation

  • 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。

     

    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.

     

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