Efficient Trans-Dimensional Bayesian Inversion of C-Response Data from Geomagnetic Observatory and Satellite Magnetic Data

To investigate deep Earth information, researchers often utilize geomagnetic observatories and satellite data to obtain the conversion function of geomagnetic sounding, C-response data, and employ traditional inversion techniques to reconstruct subsurface structures. However, the traditional gradient-based inversion produces geophysical models with artificial structure constraint enforced subjectively to guarantee a unique solution. This method typically requires the model parameterization knowledge a priori (e.g., based on personal preference) without uncertainty estimation. In this paper, we apply an efficient trans-dimensional (trans-D) Bayesian algorithm to invert C-response data from observatory and satellite geomagnetic data for the electrical conductivity structure of the Earth’s mantle, with the model parameterization treated as unknown and determined by the data. In trans-D Bayesian inversion, the posterior probability density (PPD) represents a complete inversion solution, based on which useful inversion inferences about the model can be made with the requirement of high-dimensional integration of PPD. This is realized by an efficient reversible-jump Markov-chain Monte Carlo (rjMcMC) sampling algorithm based on the birth/death scheme. Within the trans-D Bayesian algorithm, the model parameter is perturbated in the principal-component parameter space to minimize the effect of inter-parameter correlations and improve the sampling efficiency. A parallel tempering scheme is applied to guarantee the complete sampling of the multiple model space. Firstly, the trans-D Bayesian inversion is applied to invert C-response data from two synthetic models to examine the resolution of the model structure constrained by the data. Then, C-response data from geomagnetic satellites and observatories are inverted to recover the global averaged mantle conductivity structure and the local mantle structure with quantitative uncertainty estimation, which is consistent with the data.