Efficient 2D MT Forward Modeling and Trans-Dimensional Bayesian Inversion with Physics-Informed Neural Operator Networks

Magnetotelluric (MT) sounding is a vital geophysical exploration method, renowned for its ability to investigate deep geological structures, detect low-resistivity anomalies, and support diverse applications. It is widely used in mineral and geothermal resource exploration, hydrogeological surveys, and deep structural studies, effectively delineating subsurface structures from hundreds of meters to hundreds of kilometers. However, MT inversion, essential for quantitatively analyzing subsurface electrical structures, faces challenges due to the inherent non-uniqueness of MT methods and noise in field data. Traditional deterministic inversion methods, which rely on gradient-based optimization, typically produce a single model or a set of models fitting the data but fail to quantify uncertainties, complicating interpretation and reducing reliability.

To address these challenges, this study adopts a Bayesian inference framework for MT inversion. Unlike deterministic methods, Bayesian inversion treats model parameters as random variables and iteratively updates their prior distributions using observational data, ultimately obtaining posterior probability distributions. This approach enables a quantitative assessment of inversion uncertainties. However, the computational demands of Bayesian inversion, particularly for 2D and 3D MT problems, pose significant challenges, with forward modeling efficiency being a critical bottleneck.

To overcome this, we propose an efficient MT forward modeling method based on the Extended Fourier Deep Operator Network (EFDO), a physics-informed neural operator network. EFDO leverages the principles of Fourier transforms and deep neural operator networks to learn the functional mapping between model conductivity inputs and MT forward responses. By embedding physical laws into the network, EFDO ensures accurate predictions while significantly improving computational efficiency. Once trained, EFDO predicts forward responses in milliseconds, achieving a speedup of 300 times compared to traditional Finite Volume Methods (FVM) while maintaining high accuracy. A multi-GPU distributed parallel training strategy further accelerates EFDO training, drastically reducing preparation time.

Additionally, we integrate Voronoi and Delaunay parameterization techniques with the reversible-jump Markov Chain Monte Carlo (rjMCMC) method to enhance model sampling efficiency. This establishes a robust 2D MT trans-dimensional Bayesian inversion framework. Numerical experiments and tests on the Coprod2 dataset demonstrate the method’s computational efficiency and reliability.

In summary, this study introduces a novel approach combining the physics-informed EFDO network and advanced parameterization techniques to improve efficiency and uncertainty quantification in MT Bayesian inversion, paving the way for rapid, high-dimensional geophysical exploration.