A study of the convergence of spherical harmonic expansions of gravity using distributed point-mass Earth models
Abstract
A new Earth model consisting of flattened concentric ellipsoidal layers overlaid by a distribution of point masses is developed and used to study convergence of spherical harmonic expansions of gravity in the vicinity of the smallest sphere bounding all the mass. The ellipsoidal layers are formed by "flattening" the spherical layers from Dziewonski and Anderson's Preliminary Reference Earth Model (PREM). Cases are examined in which the point masses are distributed uniformly and randomly, with the majority of the masses placed within 5 km of the surface. The masses of the point sources are determined by a least-squares fit of the new model to NASA's experimentally derived GEM-T1 gravity model. Closed form expressions for gravity external to the model and for the expansion coefficients are derived, allowing convergence analysis to arbitrary accuracy to be performed. Results indicate that while spherical harmonic expansions of gravity do converge exterior to the bounding sphere, as theory indicates, when very close to the bounding sphere they may do so only after an initial period of divergence which can continue for several hundred or more terms and during which significant measurable errors can occur.
Degree
Ph.D.
Advisors
Kim, Purdue University.
Subject Area
Physics
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