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 afull 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.