Joint 3D Gravity and Magnetic Inversion via Rectified Flow and Ginzburg-Landau Guidance
This work provides a novel probabilistic inversion method for geophysicists, enabling uncertainty quantification in ore detection, though it is domain-specific and incremental in methodology.
The paper tackles the ill-posed problem of joint 3D gravity and magnetic inversion for subsurface ore detection. They introduce a rectified flow framework with Ginzburg-Landau guidance, achieving improved reconstruction quality over deterministic methods on the Noddyverse dataset.
Subsurface ore detection is of paramount importance given the rising depletion of shallow mineral resources in recent years. It is crucial to explore approaches that go beyond the limitations of traditional geological exploration methods. Due to readily available surface readings, joint magnetic and gravitational inversion is a promising new method - given magnetic and gravitational data on a surface, jointly reconstructing the underlying densities that generate them. However, this is ill-posed and has non-unique solutions. Deterministic methods often require handcrafted priors and converge to a single solution and do not capture the distribution, which is often of interest. We introduce a novel framework that reframes 3D gravity and magnetic joint inversion as a rectified flow on the Noddyverse dataset, the largest physics-based dataset for inversion. We introduce a Ginzburg-Landau (GL) regularizer, a generalized version of the Ising model that aids in ore identification, enabling physics-aware training. We also propose a guidance methodology based on GL theory that can be used as a plug-and-play module with existing unconditional denoisers. Lastly, we also train and release a VAE for the 3D densities, which facilitates downstream work in the field.