Abstract
The Bessel functions can be represented as a limit of spherical harmonics. This fact serves as a basis for the transition from the covariance function of the gravity field on the sphere to the covariance function in the plane. It is proved that for the limit R→∞ the variance of the empirical covariance function becomes zero so that the famous nonergodicity proof of Lauritzen holds for the sphere but not for the plane.
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Wei, M. On the ergodicity of the covariance function in the case of a plane. Bull. Geodesique 59, 332–341 (1985). https://doi.org/10.1007/BF02521067
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DOI: https://doi.org/10.1007/BF02521067