Random orthogonal set functions and stochastic models for the gravity potential of the earth

The covariance function of the Newtonian potential of a random orthogonal set function on the unit sphere in three dimensions is derived, and it is shown that the coefficients to the series expansion of this are simply related to the moments of the covariance measure of the random set function. Furthermore, as an application, it is shown that available gravity data indicate a mass distribution inside the Earth which becomes more and more irregular as one approaches the centre of the Earth.