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

Abstract

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.

Design, Development and Application of a Modular Electromagnetic Induction (EMI) Sensor for Near-Surface Geophysical Surveys

“…Increasing the number of measurements per point allows to reduce the uncertainties during the inversion of conductivity models [43,44]. Moreover, the availability of the raw data before transformation to 𝜎𝜎 𝑎𝑎 using the LIN approach could be further exploited to improve the quantification of electrical conductivity as well as the magnetic susceptibility using, for instance, stochastic approaches [45,46]); thus, permitting an improved subsurface investigation.…”

Comparison of Electromagnetic Induction and Electrical Resistivity Tomography in Assessing Soil Salinity: Insights from Four Plots with Distinct Soil Salinity Levels

“…Both EMI and ERT techniques involve the mathematical inversion of the apparent data [25] to obtain models of the spatial distribution of the soil electrical conductivity (σ, mS m −1 ), and of the soil electrical resistivity (ρ, ohm m), respectively. Different inversion methods (e.g., [26][27][28]) and software (e.g., [29,30]) have been developed to estimate the distribution of σ based on measured EC a data. Similarly, various inversion codes are available to estimate the distribution of ρ based on measured ER a data (e.g., [31][32][33]).…”

Bayesian Inversion of Frequency-Domain Airborne EM Data With Spatial Correlation Prior Information

“…Both 1D layered model and 2D Voronoi unit can be regarded as the performance of strong spatial correlation. In order to avoid the difficulties of the trans-dimensional MCMC algorithm when it is extended to 3D Voronoi model, the spatial correlation of the model parameters can be explicitly added as prior information [40][41][42].…”

“…There are many forms of spatial correlation prior information, and a large class of methods that describe the spatial correlation of model parameters and the characteristics of more realistic geological structures are called geostatistical methods [44]. Bayesian inversion based on spatial correlation prior information has been applied in geophysics [4,14,[40][41][42]. In particular, sequential Gibbs sampling [43] and the extended Metropolis algorithm [45] construct an inversion method that can use arbitrarily complex prior information [46][47].…”

“…Spatial correlation prior information affects the inversion results [48], so how to give prior information is important. Spatially correlated prior information generally requires deriving the statistical properties from borehole data or prior geological information about the study area [40][41][42]. In practice, this previous drilling or geological information may be lacking.…”