A set of N rectangular blocks of unit density form the basis of a linear vector space. This space will be a Hilbert space with reproducing kernel, when equipped with the L2 norm (and inner product). The kernel, K ( P , Q), will be the product sum of the (maximally N) orthonormalized base functions evaluated at two points P, Q, in space. Multiplied by an appropriate scaling constant, this function will be a covariance function for a random density (anomaly) function. Using covariance propagation, auto-and cross-covariance functions for and with quantities related to the (anomalous) gravity field created by the random density function may be computed.When blocks of varying volume are used, the density variance will vary within the structure described by the blocks. For disjoint blocks, the variance is inversely proportional to the volume. The use of overlapping blocks generally creates correlations between density values in different blocks, a possibility which does not exist when using disjoint blocks.Computational examples are presented which show that it is possible to create realistic covariance models for the gravity anomaly, and that the cross-correlation between surface gravity and surface density may obtain values in the interval from 0.4 to 0.7. These values are more realistic than values obtained in earlier studies using quasi-harmonic density models.