applied sciences Article  
Efficient Trans-Dimensional Bayesian Inversion of C-Response Data from Geomagnetic Observatory and Satellite Magnetic Data  
[PERSON] 1,2,3, [PERSON] 1,2,3, [PERSON] 1,2,3  
either from geomagnetic observatories or satellites and typically covering a period range from several hours to several hundred days, are sensitive to the conductivity structure of the Earth's mantle [9]. In practice, time-domain geomagnetic data are Fourier transformed to estimate geomagnetic responses, for instance, the commonly used C-responses [10]. Quantitative inversion in geomagnetic depth sounding (GDS) is routinely required to obtain the mantle conductivity from the response data [11]. Due to the non-uniqueness of inversion, the interpretation of the C-response data is commonly carried out based on gradient-based inversions, by subjectively enforcing a structure constraint (e.g., flattest structure) to yield a unique solution [12; 13; 14; 15; 16]. One obvious advantage of the over-parameterization method is that the best-fit solution can be obtained efficiently. However, the purpose of this approach is to achieve the optimal solution by incorporating regularization information based on gradient-based methods, and it cannot provide quantitative uncertainty estimation on the recovered model, indicating how well one specific structure of a model is constrained by the data. Due to the application of an artificial structure constraint, the recovered model typically manifests the important characteristics enforced artificially rather than from data itself. This complicates the interpretation process and reduces the credibility of the inference model [17; 18; 19; 20; 21]. Bayesian inversion produces models with parsimonious structure and quantitative uncertainty, determined from the actual data. Thus, it is constantly applied in geophysical data interpretation for subsurface structures [22; 23; 24; 25; 26]. It is attracting increasing attention in the interpretation of geomagnetic data from observatories and satellites [27; 28; 29; 30]. In their work, the model parameterization is assumed a priori and considered fixed during inversions. This conflicts with the fact that the prior knowledge of model parameterization is typically not available in most geophysical applications. In the most recent work [16], they developed a joint trans-D inversion based on an essentially single-chain sampling algorithm and physical parameter space for magnetotelluric data and local geomagnetic data from observatories. In their work, the model parameterization is treated as unknown and included in the inversion, determined by the actual data. The effect of unknown model parameterization is contained in the uncertainty estimation of the conductivity profile. To the best of our knowledge, trans-D Bayesian inversions for geomagnetic data both from observatories and satellites have not been reported in the literature. Trans-D Bayesian inversion based on a single-chain sampling algorithm can potentially be trapped in local high-probability regions separated by low-probability areas [20]. This can be addressed by the application of a parallel tempering scheme to sample the model space more completely [31; 32]. Another challenge is that if the parameters of a model are strongly correlated, the parameter perturbation can be inefficient. To minimize this effect, a parameter perturbation technique based on the unit-lag model covariance matrix can be applied [20; 33]. In this paper, an efficient trans-D Bayesian inversion [20; 33] is applied to invert both observatory and satellite geomagnetic data. In our algorithm, the parallel tempering scheme is utilized to guarantee a complete sampling over the model space for geomagnetic inversion. Parameter perturbation is carried out in the principal-component space, defined by the eigenvectors of the unit-lag model covariance. Two synthetic examples are designed to show the resolution of the model structure according to the data information.