Frequency-domain electromagnetic (FDEM) data of the subsurface are determined by electrical conductivity and magnetic susceptibility. We apply a Kalman ensemble generator (KEG) to 1-D probabilistic multilayer inversion of the FDEM data to simultaneously derive conductivity and susceptibility. The KEG provides an efficient alternative to an exhaustive Bayesian framework for FDEM inversion, including a measure for the uncertainty of the inversion result. In addition, the method provides a measure for the depth below which the measurement is insensitive to the parameters of the subsurface. This so-called depth of investigation is derived from ensemble covariances. Synthetic and field data examples reveal how the KEG approach can be applied to FDEM data and how FDEM calibration data and prior beliefs can be combined in the inversion procedure. For the field data set, many inversions for 1-D subsurface models are performed at neighboring measurement locations. Assuming identical prior models for these inversions, we save computational time by reusing the initial KEG ensemble across all measurement locations.

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 natural and anthropogenic processes. Therefore, obtaining numerical 3D 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 because 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 with the reference models in terms of histogram and variogram models reproduction and in their ability to quantify spatial uncertainty. The results indicate the ability of both methods to predict the reference values. Although the KEG is computationally efficient, it struggles to reproduce the extreme values. In contrast, 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 of the posterior models have different information. The synthetic data set is available to the community, so it can be used as a benchmark for other FDEM inversion methods.

Often, multiple geophysical measurements are sensitive to the same subsurface parameters. In this case, joint inversions are mostly preferred over two (or more) separate inversions of the geophysical data sets due to the expected reduction of the non-uniqueness in the joint inverse solution. This reduction can be quantified using Bayesian inversions. However, standard Markov chain Monte Carlo (MCMC) approaches are computationally expensive for most geophysical inverse problems. We present the Kalman ensemble generator (KEG) method as an efficient alternative to the standard MCMC inversion approaches. As proof of concept, we provide two synthetic studies of joint inversion of frequency domain electromagnetic (FDEM) and direct current (DC) resistivity data for a parameter model with vertical variation in electrical conductivity. For both studies, joint results show a considerable improvement for the joint framework over the separate inversions. This improvement consists of (1) an uncertainty reduction in the posterior probability density function and (2) an ensemble mean that is closer to the synthetic true electrical conductivities. Finally, we apply the KEG joint inversion to FDEM and DC resistivity field data. Joint field data inversions improve in the same way seen for the synthetic studies.

Ferrous metals are a main recyclable waste fraction in Enhanced Landfill Mining (ELFM) projects. However, prior to mining, the metal content of municipal solid waste (MSW) landfills is unknown. We investigate if the metal content of MSW landfills can be estimated by inverse modeling of geophysical measurements as the magnetic properties of the subsurface are particularly sensitive to ferromagnetic metal enrichments. We conducted magnetic total-field measurements on a MSW landfill in Austria and estimated the bulk magnetic susceptibility (MS) of the subsurface by inverse modelling. For validation of the subsurface MS values, 32 drill-core samples from multiple locations and depths within the landfill were obtained and manually sorted into 12 waste fractions including ferrous metals (2.3 ± 1.4 wt.%, 1σ). To investigate if bulk MS could be accurately predicted from inverse modeling when the exact composition of the waste is known, the MS of iron and other expected waste fractions were investigated in laboratory analysis using reference samples from waste treatment plants and another ELFM project. Laboratory analyses partly yielded significantly larger MS values for waste materials than those given for virgin materials in literature. The bulk MS for each sample from the ELFM project was computed using a weighted mean with respect to the waste composition derived from manual sorting. The bulk MS derived from inverse modelling of the field data (0.06 to 0.11 SI) exceeded the bulk MS derived from the material composition of waste samples and the MS values of reference samples (0.01 to 0.05 SI).