Implicit neural representation for Magnetotelluric inversion

Magnetotelluric (MT) data inversion aims to recover subsurface resistivity model by minimizing an objective function, typically comprising a data misfit term and a regularization term (e.g., Tikhonov-style regularization). While gradients-based optimization is widely used, it is prone to local minima and highly sensitive to the initial model. In contrast, nonlinear stochastic algorithms explore a broader solution space but are computationally prohibitive for large-scale MT problems.

Deep learning (DL) has emerged as a powerful alternative. Unlike purely data-driven methods, physics-driven DL frameworks embed physical laws, such as wave propagation equation and Maxwell’s equation, as constraints, enhancing interpretability and reducing the need for massive datasets. Implicit neural representation (INR) is a novel physics-driven technique that represents physical properties as continuous functions of spatial coordinates. A key advantage of INR is its inherent ‘frequency principle’ (or spectral bias), where the network learns large-scale (low-frequency) structures before fine-tunning high-resolution (high-frequency) details. In MT inversion, this bias acts as an implicit regularization, improving stability without requiring manually tuned penalty terms.

In this paper, we propose an INR-based 2D MT inversion algorithm. Synthetic tests on block and layered models demonstrate that the proposed method recovers anomalous boundaries with higher resolution than traditional Occam-based inversions. Finally, application to the COPROD2 field dataset confirms the practical robustness of the approach and its potential for extension to three-dimensional, mesh-free inversions.