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Effects of the site distribution and the prior information on the inverted geomagnetic field model: a case study applying the ABIC method to the synthetic datasets

机译：站点分布和先验信息对反地磁场模型的影响：将ABIC方法应用于合成数据集的案例研究

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摘要

When we use stochastic inversion and Bayesian modelling in order to obtain geomagnetic field models from paleomagnetic data, there are 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's Bayesian Information Criteria) minimization method was used to determine the hyperparameter, and then 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.
机译：当我们使用随机反演和贝叶斯模型从古地磁数据中获取地磁场模型时，有两个主要因素控制着解决方案：超参数的确定和模型上平滑约束的类型。为了调查这些因素的贡献，我们从理想和实际站点分布的综合数据集中计算了一些反演模式。利用ABIC（赤池贝叶斯信息准则）最小化方法确定超参数，然后证明了超参数与ABIC索引之间的关系。使用带有错误的合成数据集的反演结果，找到每个站点分布的最合适的超参数，并获得了良好且稳定的解决方案。然而，当站点数量很少或站点分布的覆盖范围不均匀时，发现解决方案不确定。此外，似乎解决方案并不很大程度上取决于模型约束的类型。

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