On relation between information of data and determinacy of solution in inversion processes from geomagnetic field data with ABIC

When we solve ancient geomagnetic field models from paleomagnetic datasets using stochastic inversion (or Bayesian modeling), we have two major factors controlling the solution, determination of the hyperparameter and the type of the smoothing constraint on the model. To investigate contributions of the factors, we calculated some patterns of inversions from synthetic datasets from ideal and real site distributions. The ABIC (Akaike Bayesian Information Criteria) minimization method is a powerful tool to determine the hyperparameter and used here. The relationship between the hyperparameter and the ABIC index was demonstrated. Using results of an inversion of synthetic datasets with errors, the most suitable hyperparameters were found for each site distribution, and the good and stable solutions were obtained. However, when number of the sites is few or coverage of the site distribution is not uniform, it is found that the solution is not clearly determined. Moreover, it seems that the solution does not significantly depend on the type of the model constraint.