A new statistical gravimetric model is derived which applies to the spherical earth. The model characterizes the gravity disturbing potential by a superposition of white noise spherical shells at selected depths beneath the earth's surface. Asymptotic forms of the model are presented which are equivalent to previously developed models but are obtained in a manner which allows errors of the 'flat earth' approximation to be assessed. Detailed formulas are given for covariance functions involving the disturbing potential and its derivatives. Power spectra expressions are developed for the Legendre, Hankel and one-dimensional Fourier frequency domains. Numerical comparisons are made between the spherical earth and asymptotic forms of the model. A set of model parameters is obtained by fitting to worldwide gravity anomaly data and GEM 10B degree variances.