Detailed Spherical-Harmonic Representation of the Earth's Gravity Field and Tidal Effects from Altimetric Adjustments.
Final rept. 1 Jan 82-31 Dec 84,
NOVA UNIV OCEANOGRAPHIC CENTER DANIA FL
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Two second-phase techniques have been developed based on the results of the global spherical-harmonic treatment of altimetric data. One of these techniques has been documented as the point-mass adjustment, and the other has been described under the name of modified collocation with noise. The term modified does not concern the philosophy of the least-squares collocation with noise, but, rather, its specific application aimed at describing a smoothed-out gravity field, in which the part of the signal beyond the desired smoothing level is pushed into the realm of noise. The primary task consists in representing collocation results in terms of the spherical-harmonic expansion of the geopotential. In particular, an equilateral grid of geoid undulations referring to a higher order surface than an ellipsoid predicted through the modified collocation with noise at the smoothing level n,n can be utilized in a numerical integration algorithm, eventually producing an n, n set of spherical-harmonic coefficients consistent with the collocation results. The conditions under which the consistency requirement is satisfied are analyzed in computer simulations. As the most important outcome of these simulations, the familiar rule of thumb is singled out as an accurate and clearcut indicator of the highest degree and order spherical-harmonic model N, N which can still faithfully represent the gravity field as described by a discrete set of data -- here an equilateral grid of geoid undulations. This rule stipulates that N180 180 degtheta deg., where theta deg. symbolizes the grid interval in angular measure.