Rapid Bayesian imaging of large‐scale transient electromagnetic data using probabilistic neural networks

Transient electromagnetic (TEM) can conduct efficient large-scale geological surveys on the near-surface. Exploring fast and comprehensive interpretation strategies for electromagnetic data is crucial for geoscientists to make high-quality decisions on site. In this study, we proposed a probabilistic neural network (PNN) structure to estimate the posterior probability density function (PDF) of model parameters. The feature of this structure is that it uses noisy data and the data standard deviation information as inputs of the training data set, and the model parameters retrieved through deterministic inversion are used as labels. Such a structure enables the posterior PDF output by the PNN to take into account the uncertainty information of the input data itself, and allows us to add existing field data to the training data set to continuously enrich reasonable prior information. Additionally, we aim to extract useful information from the posterior PDF, including smooth models similar to those obtained through laterally or spatially constrained inversion, as well as the estimation of the depth of investigation of the imaging results. The PNN structure was verified using 200 km of waterborne TEM survey data. The results shows that the PNN network efficiently delineated the subsurface electrical property distribution of a large-scale lake water system, and the lake depth and depth-uncertainty extracted from the imaging results demonstrated good consistency with the sonar bathymetric data. Besides, the smooth model extracted from the resistivity posterior PDF estimated by PNN not only improves the smoothness of the model but also reduces the data misfit.