Inversion of Audio Magnetotelluric Data Based on Residual Mixed Density Network With an Estimation of Posterior Distribution Probabilities

The inversion of audio magnetotelluric (AMT) data is affected by uncertainties stemming from various factors, including noise, initial model assumptions, and regularization parameters. Among the plethora of optimization algorithms available, Bayesian-based global search algorithms enable the determination of meaningful posterior probability distributions for inverted models, offering essential metrics for evaluating the reliability of inversion results. Nevertheless, conventional Bayesian inversion methods are impeded by intricate and time-consuming forward modeling processes. To mitigate this challenge, we propose an innovative one-dimensional AMT deep learning inversion technique based on a residual mixture density network (Res-MDN). We incorporate a new residual structure into the mixture density network(MDN), enabling it to output posterior probability distributions, thereby addressing the vanishing gradient problem and enhancing the reliability of the inversion process. In addition, to improve generalization, a comprehensive set of sample data was generated for network training, allowing it to accommodate a wider spectrum of geological conditions and data variations. Extensive testing using synthetic data was conducted to validate the efficiency, noise resistance, and generalization ability of the newly developed Res-MDN-based one-dimensional AMT inversion technique. The method’s effectiveness was further corroborated by its successful application to field data collected in the Da Qaidam region of Qinghai Province, China. Notably, during these experiments, the posterior probability distributions predicted by the trained Res-MDN were crucial in evaluating the uncertainty associated with the derived resistivity models.