Inversion of Magnetotelluric Data using Bayesian Neural Networks

Abstract: Magnetotelluric (MT) inversion is a key technique in geophysics for imaging deep subsurface resistivity structures. However, the inherent ill-posedness and non-uniqueness of inverse problems make them challenging to solve. While supervised deep learning approaches have shown promise in this domain, their predictions are typically deterministic and fail to capture the associated uncertainty, an essential factor for decision-making. To address this limitation, we explore the application of Bayesian Neural Networks (BNNs) for MT inversion with uncertainty quantification. Specifically, we train a Bayesian Convolutional Neural Network (BCNN) on a synthetically generated MT dataset. The BCNN effectively recovers resistivity profiles from apparent resistivity data, with the predicted means closely matching the ground truth across both the training and test sets, while also providing uncertainty estimates quantified within 3 standard deviations from the mean. These results underscore the potential of BNNs to enhance deep learning-based geophysical inversion frameworks by incorporating principled uncertainty quantification.