A statistical model of topographic heights and density contrasts within the earth is inferred from the empirical worldwide, free air gravity anomaly covariance function and the Bullen and Haddon earth model HB1. Models for relief and loading at the crust-mantle and mantle-core boundaries are also inferred. A worldwide Bouguer anomaly model is derived by suppressing terrain-related portions of the free air anomaly model. Self-consistent models are given for the cross-covariance functions between topography, free air gravity anomalies, Bouguer gravity anomalies, and density contrasts within the earth.