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Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC)simulation are well suited to quantify parameter and model uncertainty ofnonlinear inverse problems. Yet, application of such methods to CPU-intensiveforward models can be a daunting task, particularly if the parameter space ishigh dimensional. Here, we present a two-dimensional (2D) pixel-based MCMCinversion of plane-wave electromagnetic (EM) data. Using synthetic data, weinvestigate how model parameter uncertainty depends on model structureconstraints using different norms of the likelihood function and the modelconstraints, and study the added benefits of joint inversion of EM andelectrical resistivity tomography (ERT) data. Our results demonstrate thatmodel structure constraints are a necessity to stabilize the MCMC inversionresults of a highly-discretized model. These constraints decrease modelparameter uncertainty and facilitate model interpretation. A drawback is thatthese constraints may lead to posterior distributions that do not fully includethe true underlying model, because some of its features exhibit a lowsensitivity to the EM data, and hence are difficult to resolve. This problemcan be partly mitigated if the plane-wave EM data is augmented with ERTobservations. The hierarchical Bayesian inverse formulation introduced and usedherein is able to successfully recover the probabilistic properties of themeasurement data errors and a model regularization weight. Application of theproposed inversion methodology to field data from an aquifer demonstrates thatthe posterior mean model realization is very similar to that derived from adeterministic inversion with similar model constraints.

geophysical journal international

Two-dimensional probabilistic inversion of plane-wave electromagnetic  data: Methodology, model constraints and joint inversion with electrical  resistivity data