3-D Magnetotelluric Deep Learning Inversion Guided by Pseudo-Physical Information

TL;DR

3-D MT inversion is computationally intensive and DL approaches often underutilize forward-model physics. The paper presents P-PhysInv, a pseudo-physical information-guided DL inversion that uses pretrained forward-modeling sub-networks as fixed operators and optimizes a combined loss $L_{obt} = \\alpha L_{inv} + \\beta \\sum L_{fm}$, along with a data-masking/noise augmentation mode to emulate field conditions. Results show that P-PhysInv improves inversion accuracy and mitigates overfitting compared with DirectInv, even when forward-model simulations carry errors, while enabling rapid inference (~0.016s per model). Field-data tests in Xinjiang indicate consistency with ModEM at the global resistivity level and enhanced layer delineation when end-to-end results seed deterministic inversion, highlighting practical potential for field deployment. Overall, the framework offers a scalable, physics-informed DL approach for large-scale 3-D MT problems and serves as a viable alternative or complement to traditional inversion workflows.

Abstract

Magnetotelluric deep learning (DL) inversion methods based on joint data-driven and physics-driven have become a hot topic in recent years. When mapping observation data (or forward modeling data) to the resistivity model using neural networks (NNs), incorporating the error (loss) term of the inversion resistivity's forward modeling response--which introduces physical information about electromagnetic field propagation--can significantly enhance the inversion accuracy. To efficiently achieve data-physical dual-driven MT deep learning inversion for large-scale 3-D MT data, we propose using DL forward modeling networks to compute this portion of the loss. This approach introduces pseudo-physical information through the forward modeling of NN simulation, further guiding the inversion network fitting. Specifically, we first pre-train the forward modeling networks as fixed forward modeling operators, then transfer and integrate them into the inversion network training, and finally optimize the inversion network by minimizing the multinomial loss. Theoretical experimental results indicate that despite some simulation errors in DL forward modeling, the introduced pseudo-physical information still enhances inversion accuracy and significantly mitigates the overfitting problem during training. Additionally, we propose a new input mode that involves masking and adding noise to the data, simulating the field data environment of 3-D MT inversion, thereby making the method more flexible and effective for practical applications.

Figures (12)

• Figure 1: Network Training Process for P-PhysInv
• Figure 2: Network Architecture Diagram. $C$ denotes the number of channels of the feature map during network encoding and decoding, $n$ denotes the number of channels of the input data, and $m$ denotes the number of channels of the output data, depending on the forward modeling and inversion tasks.
• Figure 3: Schematic diagram of dataset production. (a) - (f) shows the generation process of the geoelectric model, and (g) - (l) shows part of the geoelectric model in the training set.
• Figure 4: Variation curves of each metric in the training and validation sets of forward modeling sub-networks. (a) and (b) represent the SSIM and RMSE of the apparent resistivity, respectively; (c) and (d) represent the SSIM and RMSE of the phase, respectively.
• Figure 5: Input Data Mode. (a) Full data input mode, (b) Random mask & noise-added input mode, (c) Regular mask & noise-added input mode.