球外部空间的Neumann逆问题及逆Stokes公式

基金项目: 国家自然科学基金资助项目(40274004)

详细信息

Inverse Neumann Problem and Inverse Stokes Formula on Exterior Sphere

School of Geodesy and Geomatics, Wuhan University, 129 Luoyu Road, Wuhan, China, 430079

摘要: 基于修改的Poisson积分,首先给出了球面扰动位向上延拓的积分表达式。在此基础上,由微分原理得出了球外部空间Neumann逆问题的解式,利用物理大地测量学的基本微分方程,导出了球外部空间的逆Stokes公式,并对这两类积分公式的核函数进行了讨论。
- Neumann逆问题 /
- 逆Stokes公式 /
- 向上解析延拓
Abstract: An integral for the upward continuation of the disturbing potential is presented based on modified Poisson's integral in which the zero and the first degrees of spherical harmonics are excluded.Differentiating the integral expression with respect to the geocentric distance of computing point,the solution in a closed integral form for the inverse Neumann's exterior problem is then obtained.The closed integral expression for upward continuation of the solutions for inverse Stokes formula is derived in terms of the fundamental differential equation in physical geodesy.
- inverse Neumann's problem /
- inverse Stokes formula /
- upward analytical continutation