A deep reparameterized framework for three-dimensional magnetotelluric inversion with automatic-differentiation sensitivities

Three-dimensional (3D) magnetotelluric (MT) inversion is computationally demanding and strongly ill posed, and practical workflows often hinge on reliable gradient calculation and effective regularization. Here we present AD3DMT, a modular 3D MT inversion framework that combines implicit automatic differentiation (ADID) for sensitivity computation with deep reparameterization of the resistivity model. Gradients are obtained by differentiating through the Maxwell solver via implicit differentiation, enabling flexible construction of objective functions, regularization terms, and optimizers within a modern machine-learning environment. We validate the forward MT responses and sensitivities using a 1D three-layer benchmark and then evaluate the reparameterized inversion on a 3D two-block synthetic model. The deep reparameterization (DR) is implemented with a compact CNN and acts as an implicit structural prior that reduces tailing and suppresses artifacts, while moderate explicit damping further improves reconstruction quality. We also demonstrate a practical uncertainty proxy using Monte Carlo dropout with repeated stochastic forward passes. Finally, we apply the method to field MT data from the Weishan volcano in the Wudalianchi volcanic field in northeast China. The recovered model images a two-level conductive system, including a shallow conductor at ∼2–6 km depth and a deeper conductor near ∼12 km, and yields a conductivity pattern consistent with previous deterministic inversion while providing clearer structural continuity and fewer spurious small-scale features. These results suggest that combining AD-based gradient calculation with DR provides a promising framework for developing and testing new 3D MT inversion strategies.