Abstract We propose a machine learning approach to geophysical inversion problems for the exploration of earth resources. Our approach is based on nonparametric Bayesian methods, specifically, Gaussian processes, and provides a full distribution over the predicted geophysical properties whilst enabling the incorporation of data from different modalities. We assess our method both qualitatively and quantitatively using a real dataset from South Australia containing gravity and drill-hole data and through simulated experiments involving gravity, drill-holes and magnetics, with the goal of characterizing rock densities. The significance of our probabilistic inversion extends to general exploration problems with potential to dramatically benefit the industry.