A Reversible Deep Operator Network for Grid-Independent, Multi-Scale Magnetotelluric Inversion and Uncertainty Quantification
- We propose Reversible Deep Operator Network to solve magnetotelluric inversion from arbitrarily sparse observational data.
- RDON trained on a single spatial scale can zero-shot generalize to unseen scales with transfer learning correcting scale-induced biases.
- A Bootstrap Resampling scheme based on RDON enables efficient uncertainty quantification of solutions.
Magnetotellurics (MT) is a powerful geophysical tool that probes subsurface electrical structures by utilizing natural electromagnetic signals, yet traditional inversion methods often face challenges related to high computational costs, non-uniqueness, and a strong sensitivity to initial model assumptions. Recently, deep neural networks have shown great promise in MT inversion. However, current deep learning methods struggle with sparse and irregularly gridded data, requiring retraining for each new observation setup, thus limiting their applicability to real-world sparse and multi-scale data. To address this limitation, we proposes a novel deep learning framework, Reversible Deep Operator Network (RDON) for efficient inversion of arbitrarily sparse MT data. RDON leverages a RealNVP-based invertible neural network integrated into DeepONet architecture to establish a bijective mapping between subsurface resistivity and MT data, enabling grid-independent forward and inverse modeling within a single network. This architecture demonstrates the capability to flexibly handle arbitrarily sparse MT data without retraining, and exhibits robust generalization across unseen variations in station layout and frequency configurations. As to scaling generalization, we establish the Scaling Invariance Theorem for MT, which provides both theoretical grounding and rigorous quantification of cross-scale generalization errors. This enables the trained network to perform zero-shot generalization across survey scales and further reduces scaling-related errors through transfer learning with fine-tuning. Additionally, RDON incorporates a Bootstrap Resampling-based approach for uncertainty quantification, offering significant computational efficiency improvements over conventional methods. Applied to real-world data from the West Junggar region, RDON validates its reliability and practicality under complex geological conditions. This work presents a transformative approach for MT inversion, addressing long-standing challenges of observation sparsity, computational inefficiency, and uncertainty quantification.
- 🧠 Bijective Operator Learning: Reversible architecture enables dual-directional modeling
- 🌐 Grid-Independent inversion: Handles arbitrary station/frequency configurations
- 📐 Scale-Invariant Predictions: Theoretical guarantees for cross-scale generalization
- 📊 Efficient Uncertainty Quantification: Bootstrap resampling for solution confidence
- ⚡ Real data test: Real-time inversion capabilities