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Author Posting. © The Authors, 2019. This article is posted here by permission of The Royal Astronomical Society for personal use, not for redistribution. The definitive version was published in Geophysical Journal International 218(3), (2019): 1822-1837, doi: 10.1093/gji/ggz253., Joint inversion of multiple electromagnetic data sets, such as controlled source electromagnetic and magnetotelluric data, has the potential to significantly reduce uncertainty in the inverted electrical resistivity when the two data sets contain complementary information about the subsurface. However, evaluating quantitatively the model uncertainty reduction is made difficult by the fact that conventional inversion methods—using gradients and model regularization—typically produce just one model, with no associated estimate of model parameter uncertainty. Bayesian inverse methods can provide quantitative estimates of inverted model parameter uncertainty by generating an ensemble of models, sampled proportional to data fit. The resulting posterior distribution represents a combination of a priori assumptions about the model parameters and information contained in field data. Bayesian inversion is therefore able to quantify the impact of jointly inverting multiple data sets by using the statistical information contained in the posterior distribution. We illustrate, for synthetic data generated from a simple 1-D model, the shape of parameter space compatible with controlled source electromagnetic and magnetotelluric data, separately and jointly. We also demonstrate that when data sets contain complementary information about the model, the region of parameter space compatible with the joint data set is less than or equal to the intersection of the regions compatible with the individual data sets. We adapt a trans-dimensional Markov chain Monte Carlo algorithm for jointly inverting multiple electromagnetic data sets for 1-D earth models and apply it to surface-towed controlled source electromagnetic and magnetotelluric data collected offshore New Jersey, USA, to evaluate the extent of a low salinity aquifer within the continental shelf. Our inversion results identify a region of high resistivity of varying depth and thickness in the upper 500 m of the continental shelf, We gratefully acknowledge funding support from National Science Foundation grants 1458392 and 1459035. We thank the captain and crew of the R.V. Marcus G. Langseth for a successful cruise and the Marine EM Lab at Scripps Institution of Oceanography for providing the instrumentation. We also thank Chris Armerding, Marah Dahn, John Desanto, Jimmy Elsenbeck, Matt Folsom, Keiichi Ishizu, Jeff Pepin, Charlotte Wiman and Georgie Zelenak for participating in the cruise. We gratefully acknowledge Alberto Malinverno for the idea to use a Monte Carlo scheme to estimate the distribution of pore fluid salinity, and William Menke for many constructive conversations and suggestions.