Rapid Bayesian Geophysical Inversion Using General Geophysical Neural Operator

Bayesian inversion provides a rigorous framework for uncertainty quantification in geophysics， but is often computationally prohibitive due to the reliance on Markov Chain Monte Carlo (MCMC) sampling, which requires massive numbers of forward simulations. While deep learning surrogate models offer acceleration, existing architectures (e.g., CNNs, FNO, DeepONet) often struggle with fixed discretization constraints and cannot flexibly handle the irregular observation coordinates typical in field surveys.

To address these challenges, we propose the General Geophysical Neural Operator (GGNO), a novel Transformer-based architecture designed for mesh-independent operator learning. This design fulfills three fundamental requirements for forward solvers in the context of practical inversion: (1) Discretization-invariant, allowing the processing of input models with different mesh resolutions; (2) Prediction-free, enabling direct solution querying at arbitrary spatio-temporal coordinates; and (3) Domain-independent, decoupling input and output discretizations. 

We validate GGNO on Magnetotelluric (MT) forward modeling, demonstrating exceptional generalization while achieving accuracy two orders of magnitude higher than traditional methods. By integrating GGNO into a Bayesian framework, we achieve highly efficient MCMC sampling, reducing the computational time from tens of days to a few minutes, which allows for a comprehensive exploration of the posterior distribution. Applied to field data, this approach successfully recovers complex subsurface resistivity structures with rigorous uncertainty bounds. These results highlight GGNO's potential to enable high-precision subsurface imaging and robust probabilistic interpretation for complex geophysical exploration.