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Integral formulas for computing the disturbing potential, gravity anomaly and the deflection of the vertical from the second-order radial gradient of the disturbing potential
Authors:J Li
Institution:(1) The Key Laboratory of Geospace Environment and Geodesy, Ministry of Education, School of Geodesy and Geomatics, Wuhan University Wuhan, 129 Luoyu Road, Wuhan, 430079, P.R. China
Abstract:Integral formulas are derived which can be used to convert the second-order radial gradient of the disturbing potential, as boundary values, into the disturbing potential, gravity anomaly and the deflection of the vertical. The derivations are based on the fundamental differential equation as the boundary condition in Stokes’s boundary-value problem and the modified Poisson integral formula in which the zero and first-degree spherical harmonics are excluded. The rigorous kernel functions, corresponding to the integral operators, are developed by the methods of integration.
Keywords:Disturbing potential  Second radial gradient of disturbing potential  Integral kernel  Gravity anomaly  Deflection of the vertical
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