Three-dimensional magnetotelluric Bayesian inversion based on Stein variational gradient descent

To address the challenge of assessing the reliability of three-dimensional (3D) magnetotelluric (MT) inversion results, we have developed a variational inference (VI) inversion framework (VI-MT) based on the Stein Variational Gradient Descent (SVGD) method. Through parallel particle optimization, we efficiently approximate the model posterior distribution, overcoming the computational limitation of traditional Markov Chain Monte Carlo (MCMC) methods. Synthetic test shows the VI-MT inversion results align with deterministic solutions while better recovering resistivity amplitudes. In comparison, the VI-MT inversion can effectively identify large model uncertainties in the boundary region by the associated multimodal posterior characteristics. Furthermore, the VI-MT inversion is applied to the field MT data collected at the Weishan volcano in northeast China, with the posterior mean model consistent with the deterministic inversion model. Depth-dependent model uncertainties indicate strong data constraints in the upper crust. A clear low resistivity body of ~5 Ω·m with small uncertainties is imaged at depths of ~2-6 km beneath the volcanic crater, suggesting the existence of a shallow magma chamber. Our study shows that the VI-MT inversion based on the SVGD method can efficiently solve the 3D MT Bayesian inversion, providing reliable model uncertainties.