Trans-Scale Magnetotelluric Inversion via Deep Learning Guided by the Principle of Physical Similarity and Application

Deep learning methods are currently being effectively used by several geophysicists to achieve direct data-to-model mapping in magnetotelluric (MT) inversion. This method enables extremely quick inversion speeds in addition to removing the need on initial models. However, the MT method covers a broad frequency band range, and conventional deep learning inversion requires training separate networks for different frequency bands, leading to inefficiency. Here, we present a trans-scale MT inversion framework guided by the principle of physical similarity, which enables a network trained on a single frequency band to be applied across the entire MT spectrum. We first construct practical 2D smooth geoelectric models as network outputs. Using forward modeling, the apparent resistivities for the TE and TM polarization modes are calculated and used as network inputs. In order to improve network robustness, training samples also take data loss scenarios into account and incorporate random noise. A U-Net architecture based on PyTorch is developed to perform high-precision nonlinear mapping from MT data to resistivity models. Crucially, the principle of physical similarity is then applied to extend the trained network to other frequencies without retraining. Furthermore, using the network's predictions as the initial model for deterministic inversion effectively reduces the reliance on initial model selection, decreases the number of iterations, and enhances the final inversion resolution. Ultimately, by means of numerical model tests and the inversion of MT data from the Tamusu region in Inner Mongolia, we verify the efficacy of this inversion technique, offering useful perspectives and pointers for the implementation of intelligent MT inversion.This work was funded by the National Natural Science Foundation of China (42130811, 42374097 and 42304090), Autonomous deployment project of National Key Laboratory of Uranium Resources Exploration-Mining and Nuclear Remote Sensing (2025QZ-YZZ-03 and 2024QZ-TD-15) of East China University of Technology, and by the Science and Technology Project of Jiangxi Province (DHSQT42023001, 20242BAB20143 and 20204BCJL23058).