  Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC)
simulation are well suited to quantify parameter and model uncertainty of
nonlinear inverse problems. Yet, application of such methods to CPU-intensive
forward models can be a daunting task, particularly if the parameter space is
high dimensional. Here, we present a two-dimensional (2D) pixel-based MCMC
inversion of plane-wave electromagnetic (EM) data. Using synthetic data, we
investigate how model parameter uncertainty depends on model structure
constraints using different norms of the likelihood function and the model
constraints, and study the added benefits of joint inversion of EM and
electrical resistivity tomography (ERT) data. Our results demonstrate that
model structure constraints are a necessity to stabilize the MCMC inversion
results of a highly-discretized model. These constraints decrease model
parameter uncertainty and facilitate model interpretation. A drawback is that
these constraints may lead to posterior distributions that do not fully include
the true underlying model, because some of its features exhibit a low
sensitivity to the EM data, and hence are difficult to resolve. This problem
can be partly mitigated if the plane-wave EM data is augmented with ERT
observations. The hierarchical Bayesian inverse formulation introduced and used
herein is able to successfully recover the probabilistic properties of the
measurement data errors and a model regularization weight. Application of the
proposed inversion methodology to field data from an aquifer demonstrates that
the posterior mean model realization is very similar to that derived from a
deterministic inversion with similar model constraints.
