Efficient Trans-dimensional Bayesian inversion of C-response data from geomagnetic observatory and satellite magnetic data

Abstract

The traditional gradient-based inversion produces geophysical models with artificial structure constraint enforced subjectively to guarantee a unique solution.This method typically needs the model parameterization knowledge a priori (e.g.,based on the 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 data itself. In trans-D Bayesian inversion, the posterior probability density (PPD) represents a complete inversion solution, based on which useful inversion inference 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 algorithmbased on 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 model structure constrained by the data. Then C-response data from geomagnetic satelliteand observatory are inverted to recover the global averaged mantle conductivity structure and the local mantle structure with quantitative uncertainty estimation,consistent with the data.