In this work we discuss the triple correlation function on a sphere, having in view its application to the gravity field of the earth. This is done mainly in the short-wavelength limit, which requires a special mathematical technique, the ''high-frequency approximation.'' In order to test the significance of the triple correlation coefficients in any given earth model we define a random earth, in which the phases of the harmonic coefficients are random and, on the average, there is no triple correlation. The numerical value of a given coefficient can be then compared with its root mean square value; it will be larger (and hence significant) if the phases are correlated in triplets. A significant test of triple correlation in realtion, for example, to elongatsed structures in the crust must extend to values of l of order radius of the earth/crust thickness; we believe that the presently available earth models are not yet sufficiently reliable for this.