Summary Joint inversion of magnetotelluric (MT) and geomagnetic depth sounding (GDS) responses can constrain the crustal and mantle conductivity structures. Previous studies typically use either deterministic inversion algorithms that provide limited information on model uncertainties or using stochastic inversion algorithms with a predetermined number of layers that is generally not known a priori. Here, we present a new open-source Bayesian framework for the joint inversion of MT and GDS responses to probe one-dimensional (1D) layered Earth’s conductivity structures. Within this framework, model uncertainties can be accurately estimated by generating numerous models that fit the observed data. A trans-dimensional Markov chain Monte Carlo (MCMC) method is employed to self-parametrize the model parameters, where the number of layers is treated as an inversion parameter that is determined automatically by the data. This adaptability can overcome the under or over-parametrization problem and may be able to automatically detect the conductivity discontinuities in the Earth’s interior. To accelerate the computations, a large number of Markov chains with different initial states can be run simultaneously using the MPI parallel technique. Synthetic data sets are used to validate the feasibility of our method and illustrate how separate and joint inversions, as well as various priors affect the posterior model distributions. The trans-dimensional MCMC algorithm is then applied to jointly invert the MT and GDS responses estimated at the Tucson geomagnetic observatory, North America. Our results not only contain model uncertainty estimates but also indicate two distinct conductivity discontinuities at around 85 and 440 km, which are likely related to the lithosphere-asthenosphere boundary and the upper interface of the mantle transition zone, respectively.

We present a multi‐resolution finite‐element approach for three‐dimensional (3D) electromagnetic (EM) induction modeling in spherical Earth. First, the secondary electric field approach is employed so that both magnetospheric and ionospheric current sources are naturally considered. Second, the multi‐resolution tetrahedral grids are used to approximate the heterogeneous crust and mantle, so that the local ocean effects at coastal and island observatories can be accurately simulated. Furthermore, a parallel goal‐oriented hp‐adaptive finite‐element method with Nédélec vector elements is employed to guarantee the accuracy of solutions for arbitrary 3D conductivity distributions. Finally, two synthetic models are used to verify the accuracy and efficiency of our newly developed forward modeling solver. Results show that accurate solutions can be obtained for problems with several million to hundreds of millions of unknowns in a few minutes using 128 cores on a cluster. We apply this approach to correct the near‐surface ocean effects for several unused Chinese coastal observatories by performing multi‐resolution 3D modeling. The corrected data are inverted for the subsurface layered mantle conductivity structures. The conductivity model beneath southeast China is more resistive than that beneath northeast China by more than half an order of magnitude. By comparing the inverse models with the latest laboratory conductivity‐depth profiles, the estimated transition zone water content is less than 0.01 wt% beneath southeast China irrespective of which laboratory data is used. Considering the low‐velocity anomalies in this region, which suggest high‐temperature structures, less water is expected. We, therefore, infer that the mantle transition zone beneath southeast China is dry.

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