Sampling Functions for Geophysics

Details Sampling Functions for Geophysics Sampling Functions for Geophysics

Jul 1972

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1972saosr.344.....g&link_type=abstract

SAO Special Report #344 (1972)

Statistics

Applications

3

Scientific paper

A set of spherical sampling functions is defined such that they are related to spherical-harmonic functions in the same way that the sampling functions of information theory are related to sine and cosine functions. An orderly distribution of (N + 1)2 sampling points on a sphere is given, for which the (N + 1)2 spherical sampling functions span the same linear manifold as do the spherical-harmonic functions through degree N. In this case, the transformations between the spherical sampling functions and the spherical-harmonic functions are given by recurrence relations. The spherical sampling functions of two arguments are extended to three arguments and to nonspherical reference surfaces. Typical applications of this formalism to geophysical topics are sketched.

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