## 1 Introduction
Bayesian inference is one way to quantify the non-uniqueness or uncertainty of an inverse problem. Moreover, Bayesian inversion approaches are readily available to be used as a joint inversion framework and they do not require weighing the different data types. Additionally, errors other than noise can be included in the processing, for example, using hierarchical or empirical Bayesian approaches [10]. However, we do not consider hierarchical or empirical Bayesian frameworks for the work presented in this manuscript, as we expect a relatively small influence of additional errors. For typical geophysical problems, i.e., non-linear and large dimensional problems, no analytical solution for [PERSON] theorem can be given, which makes the numerical sampling of probability density functions (PDFs) necessary. The standard approach in geophysics is the Markov chain Monte Carlo (MCMC) method applying Metropolis- or Gibbs-sampling [1]. This approach is well-known to converge to the exact posterior PDF for a infinite runtime of the algorithm approaching infinity. Highly-parametrized models result in computationally expensive forward model runs that limit the applicability of MCMC methods [11]. Only recently, efficient approximations of the posterior distribution have been proposed for geophysical problems, while using innovative methods, such as the Kalman ensemble generator (KEG, [12]) or Bayesian Evidential Learning [13]. Those techniques rely on a smaller number of forward model runs and are, thus, less expensive. Unfortunately, highly-parametrized models are often indispensable in order to model complex geological structures beyond horizontal stratigraphy. Ultimately, a convergence of the chain computations of MCMC might not be achievable within the number of affordable forward model runs, which is why MCMC approaches are rarely seen in geophysical literature on fully non-linear joint inversion. In this work, we apply the Kalman ensemble generator (KEG, [14]) as an efficient alternative to a MCMC inversion framework to solve the joint inverse problem. The KEG is a stationary implementation of the ensemble Kalman filter [15] and, thus, a Monte Carlo implementation of a probabilistic least-squares formulation [1]. If the Gaussian assumption is applicable to all parameters, it was shown that the ensemble Kalman filter can be applied to non-linear forward models. In contrast to MCMC approaches, we do not need the chain approach and conduct independent random sampling instead. Therefore, there is no burn-in phase and no rejection of proposed samples. Thus, in the KEG framework, all Monte Carlo samples can directly be used to characterize a Gaussian approximation to the posterior PDF. The objective of this paper is to apply the KEG for joint probabilistic inversion of DC resistivity and small-loop EM data. previously applied to the inversion of EM [12], yet, to the best of our knowledge, this is the first time that (1) the method is used for geophysical joint inversion and (2) that these types of data are jointly inverted in a probabilistic way. We present two examples of simulated geophysical measurements for synthetic one-dimensional subsurface models and one field data example showing vertical contrasts in electrical conductivity. This way, we investigate whether the expected uncertainty reduction of the inverse image using two types of data simultaneously can be assessed and resolved by the approximate Gaussian solution to the Bayesian update problem. For this purpose, we will compare KEG posterior PDFs of the separate inversions of DC resistivity data and of EM data with the joint KEG inversion result. Additionally, we investigate whether the posterior ensemble mean gives an improved image for the subsurface, i.e., if it is shifted closer to the true synthetic model of subsurface electrical conductivity. For one synthetic example, we investigate the influence of sample size on the posterior estimates. The remainder of this manuscript is structured as follows.