## 4 Field Data Case  
In order to demonstrate the joint KEG inversion for geophysical field data, we apply it to a FDEM and a VES data set acquired for estimating a vertical soil EC profile for a forest soil in Gontrode, \begin{table}
\begin{tabular}{c c} \hline \hline
**SS** & **RMS** \\ \hline
100 & 0.201 \\
1000 & 0.086 \\
2500 & 0.081 \\
10,000 & 0.069 \\
100,000 & 0.067 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Root mean square (RMS) values for the best fit functions (corrected for synthetic true) computed for different sample size (SS) in the joint inversion. Figure 4: Best fit functions of joint Kalman ensemble generator (KEG) inversion results of FDEM and DC resistivity data for the same synthetic true model using the different sample sizes (SS) for ensemble creation, EC-axis in logarithmic scale. Belgium. The exact measurement location was selected for its horizontal stratigraphy of different soil layers conformed to the one-dimensional (1D) assumption. The VES and FDEM data sets were recorded at the same day to minimize the possible effects of varying conditions in soil water saturation. In particular, the VES data set was collected by the commercial resistivity meter four-point light 10 W (LGM Lippmann, Schaufling, Germany) while using electrode spacings of one meter, with a total profile length of 14 m. FDEM data were collected in the center of the VES profile, with a setup of six receiver coils. This FDEM setup is similar to the one that is shown in Figure 1b, with an additional set of HCP and PRP coils at 4 and 4.1 m, respectively, a DUALEM-421S (Dualem Inc., Milton, ON, Canada). For calibration purposes [20], the FDEM data were collected with the same instrument at two heights: ground level and 0.6 m above ground (see Figure 5). For the validation of the EC profile, a vertical hole was drilled using an Edelmann auger. Figure 6 shows the drilling output. From the drilling output, multiple soil layers were visually distinguished. For the top 0.15 m, we found an organic rich forest material (plants and other organic material), including several air-filled voids. Below 0.15 m down to approximately 0.8 m, a clay-rich sand was found. Below 0.8 m, the clay content decreased with increasing depth, which resulted in a relatively higher sand content. Around 1.5 m, the groundwater table was reached. To link a possible inversion result to the above soil profile description, we explain some general relations of the present subsurface material and its influence on the bulk EC [29]. First, air is known as an insulator, thus, significant shares of air-filled voids will result in a relatively low bulk EC value. High clay content is known to result in relatively high conductivities as compared to the average soil due to surface charges on the mineral surface. In contrast, sand is known for its relatively low EC values, therefore, an increase in sand content is expected to lower the bulk EC of the soil. The presence of groundwater usually coincides with an increase in EC, due to the presence of free electrical charge carriers. For inverse modeling, we used an approach similar to the one described for the synthetic multi-layer inversion. First, a prior model was defined for discrete horizontal model layers of 8.5 cm thickness. The prior model mean was chosen to cover a large EC range expected from auger drilling. In particular, the prior model mean is 0.02 S/m with one STD ranging to an upper limit of 0.04 S/m and a lower limit of 0.01 S/m. Twelve offset parameters were added to the prior model for the calibration of the FDEM data: two offsets for each IP and QP signal of each receiver coil [20]. The prior offsets  
Figure 5: Multi-receiver FDEM measurement using a multi-receiver instrument at 0.6 m height; transmitter and receiver coils are arranged as sketched in Figure 1 with an additional HCP/PRP coil pair at 4 m/4.1 m, respectively.