Joint 3D Gravity and Magnetic Inversion via Latent Rectified-Flow Posterior Sampling

Joint gravity and magnetic inversion, which recovers 3D subsurface density and magnetic susceptibility from surface measurements, is among the cheapest and most widely used tools in mineral exploration, but it is severely non-unique: many subsurface models explain the same data. Classical inversions resolve this ambiguity with hand-crafted regularization, and learning-based inversions are trained on simplified synthetics. However, both return a single model. We instead sample from the posterior under a learned geological prior. We train a 3D variational autoencoder and a latent rectified-flow prior on paired density–susceptibility volumes from Noddyverse, a physics-based collection of one million 3D geological models, and condition the prior on both fields with flow-based posterior sampling at the full $2\times 200^3$ resolution. Evaluated against the 3D ground truth of held-out models from largely unseen geological histories, our method reduces susceptibility RMSE by 31–58% relative to twelve established inversions. The learned prior alone already outperforms hand-crafted regularization in susceptibility error. Our samples also counteract the shallow bias of classical inversion: on average, they place bodies within 100 m of their true depth, while the baselines place them 171–961 m too shallow.