Abstract
Isotropic reproducing kernels for a sphere or spherical shell are derived as weighted product sums o fL 2 orthonormal base functions. For the sphere these functions are products of the surface spherical harmonics and the Jacobi polynomials of degree (0, 2). Reproducing kernels for a sphere are consistent with the covariance function of the outer anomalous gravity potential of the Earth. These reproducing kernels may be used for gravity field modeling which include density (anomaly) data as observations or which aims at predicting such quantities using optimal estimation methods, that is for solving the inverse gravimetric problem.
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Tscherning, C.C. Isotropic reproducing kernels for the inner of a sphere or spherical shell and their use as density covariance functions. Math Geol 28, 161–168 (1996). https://doi.org/10.1007/BF02084211
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DOI: https://doi.org/10.1007/BF02084211