A comparison between Kalman ensemble generator and geostatistical frequency-domain electromagnetic inversion: the impacts on near-surface characterization

The spatial distribution of the physical properties of the first meters beneath the Earth’s surface is often complex due to its highly dynamic nature and small-scale heterogeneities resulting from both natural and anthropogenic processes. Therefore, obtaining numerical three-dimensional models that accurately describe the spatial distribution of these properties is often challenging, yet essential for different fields such as environmental assessment and remediation, geoarchaeological conservation, and precision agriculture. Frequency-domain electromagnetic (FDEM) induction methods have proven their potential to image these properties in high (spatial) detail as FDEM measurements are sensitive to two key soil properties: electrical conductivity; and magnetic susceptibility. Predicting subsurface properties from FDEM data requires solving an ill-posed and nonlinear inverse problem with multiple solutions. Recently, there has been a rapid growth of FDEM inversion methods, which may be broadly divided into probabilistic and deterministic methods. We compare two stochastic FDEM inversion approaches: the Kalman ensemble generator (KEG); and another one formulated as an iterative geostatistical FDEM inversion. Both methods are applied to a synthetic data set with spatially heterogeneous physical properties of interest, mimicking a real landfill mining site. The predicted models are compared to the reference models in terms of histogram and variogram models reproduction and in their ability to quantify spatial uncertainty. The results show the ability of both methods to predict the reference values. While the KEG is computationally efficient, it struggles to reproduce the extreme values. On the contrary, the geostatistical inversion approach ensures the reproduction of the imposed histograms and variogram models in the predicted models. As the prior information is included in both inversion methods in different ways, the pointwise variance models computed from all the posterior models has different information. The synthetic data set is available to the community so it can be used as benchmark for other FDEM inversion methods.