Extended Applicability of the Spherical-Harmonic and Point-Mass Modeling of the Gravity Field,
NOVA UNIV OCEAN SCIENCE CENTER DANIA FL
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Recent research aimed at improving the knowledge of the earths gravity field and its fundamental surface, the geoid, has been based to a large extent on a short-arc mode of satellite altimetry. The global geoidal parameters have consisted of spherical harmonic potential coefficients, and the local parameters have consisted of point mass magnitudes. It is shown that an adjustment solely in terms of the point masses is not desirable due to the spherical approximation in the point-mass algorithm which would compromise the accuracy in the determination of the oceanic geoid, attainable with the SEASAT altimetry or with a similar high-precision observational system. A mathematical framework is provided in order to model observations such as the horizontal north and east and vertical gradients of gravity or gravity disturbance. This development is based on the tensor approach to theoretical geodesy and is mostly concerned with the second-order derivatives, along local Cartesian axes, of a general scalar function of position the derivatives are expressed in spheroidal and, for a variety of practical applications, in spherical coordinates. The scalar function of position is specialized to represent the total earths potential, the standard or normal potential and, especially, the disturbing potential.