Stochastic inversion of transient electromagnetic data to derive aquifer geometry and associated uncertainties

SUMMARY Understanding processes in the Critical Zone requires reliable information about the vadose-zone aquifer, its geometry, and spatial variability. Commonly, such information is obtained from boreholes, yet large areas might render their application prohibitively expensive. Additionally, limited geological a-priori information might bias the interpretation due to lateral geological changes smaller than the borehole sampling scale. The transient electromagnetic method (TEM) has emerged in the last decades as a well-suited method to efficiently investigate the subsurface, as required for many hydrogeological applications. The interpretation of TEM measurements relies mainly on deterministic inversions, offering only a limited insight on the uncertainty of the subsurface model. Uncertainty quantification, however, is essential for integrating TEM results into hydrogeological models. Hence, we propose a combined approach using both deterministic and stochastic inversion of TEM soundings to investigate the uncertainty of shallow ($<$ $40 \,\mathrm{m}$) aquifers. Current stochastic approaches for TEM data rely on Markov chain Monte Carlo algorithms, which have to be run from scratch for each individual sounding. Alternatively, machine learning approaches, such as Bayesian Evidential Learning (BEL), can be much faster because they do not require retraining for every new data set. Hence, we investigate, in particular, the application of a single, common prior model space instead of multiple, individual prior model spaces to directly estimate the uncertainty of multiple TEM soundings. To this end, we combine forward modelling routines with the stochastic inversion approach BEL1D and assess our approach using both field data and numerical experiments.