## 5 Conclusions  
We used the Kalman ensemble generator (KEG) as a framework for performing geophysical joint inversion. Joint inversion was performed for two synthetic data sets and one field data set, each consisting of direct current (DC) resistivity and frequency-domain electromagnetic (FDEM) data. When compared to the results of separate KEG inversion of VES and FDEM data, joint inversion resulted in better estimations with smaller uncertainty. Like most probabilistic inversions, the KEG is readily extendable into a joint inversion framework, without the need for specific input for weighing the influence of each considered data set. It should be noted though that the KEG is a much more efficient solver for the non-linear joint inversion than the commonly applied probabilistic methods, i.e., Markov chain Monte Carlo (MCMC) approaches. This efficiency is achieved by restricting all probability density function to Gaussianity. On the one hand, this means that the KEG only yields a Gaussian approximation to the posterior PDF. On the other hand, the KEG works without rejection sampling and a burn-in phase. Thus, each sample can be used for the direct characterization of the posterior. Additionally, the joint KEG inversion is fully parallelizable, especially concerning the most computationally expensive step, the computation of the forward problems for the two (or more) types of geophysical methods. Joint KEG inversion of DC resistivity and FDEM yielded two major benefits over separate KEG inversions, namely (1) a reduction of uncertainty in the joint posterior model and (2) a best fit model that is closer to the true subsurface parameter variation. This is illustrated by the reduction of the range of estimated model parameters using the joint framework. Additionally, in our study, the estimated joint parameter range is not a simple mean or average of the range estimated in the corresponding separate inversions. The joint inversion resolved distinct features that were not resolved by both separate inversion results providing that an ensemble size is used that is large enough to sufficiently  
Figure 7: Kalman ensemble generator (KEG) inversion results for the same synthetic true model using the same prior model for vertical electrical sounding (VES) data, frequency domain electromagnetic (FDEM) data, and joint inversion of VES and FDEM data. suppress spurious correlation. In the investigated synthetic example, a sample size of 10,000 was sufficient as adding more samples did not significantly improve the posterior estimates computed. The KEG application to the VES and FDEM field data set shows that the joint processing of both data sets is straightforward in a real world setting. Here, the only difference between synthetic and field data processing consists in the additional offset parameters added to the simulation of FDEM forward responses, mediating the often encountered severe systematic errors in FDEM field data. The joint KEG inversion resulted in an EC profile that was well in accordance with the soil profile derived by auger drilling. Additionally, like for the synthetic data case, but less pronounced, the posterior uncertainty derived from joint inversion is smaller than the uncertainty derived from separate inversions. Overall, the KEG is a functional tool for joint probabilistic inversion. In the future, the limitations of the method, in particular the Gaussian assumption and possibility of normal-score transform for non-Gaussian prior models should be further investigated. Due to the computational advantages of the KEG over MCMC methods, we believe that the KEG has great potential for inverse modelling of complex two- and three-dimensional subsurface structures. Moreover, the KEG might be used for modeling of highly-parametrized problems as for such the KEG might not only outperform MCMC methods but also most gradient-based inversion methods that rely on many calls of the forward model.