Abstract
The operator operations between the disturbing potential and the geoidal undulation, the gravity anomaly, the deflection of the vertical are defined based on the relations among the gravity potential, the normal gravity potential and the disturbing potential. With the sphere as the boundary surface, based on the solution of the external boundary value problem for the disturbing potential by the spherical harmonics in the physical geodesy, the general inverse Stokes’ formula, the general inverse Vening-Meinesz formula and the general Molodensky’s formula are derived from the operator operations defined. The general formulae can get rid of the restriction of the classical formulae only used on the geoid. If the boundary surface is defined as the geoid, the general formulas are degenerated into the classic ones.
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Cheng, L., Xu, H. General inverse of Stokes, Vening-Meinesz and Molodensky formulae. SCI CHINA SER D 49, 499–504 (2006). https://doi.org/10.1007/s11430-006-0499-x
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DOI: https://doi.org/10.1007/s11430-006-0499-x