In a previous study, a new snapshot modeling concept for the archeomagnetic field was introduced (Mauerberger et al., 2020, https://doi.org/10.1093/gji/ggaa336). By assuming a Gaussian process for the geomagnetic potential, a correlation-based algorithm was presented, which incorporates a closed-form spatial correlation function. This work extends the suggested modeling strategy to the temporal domain. A space-time correlation kernel is constructed from the tensor product of the closed-form spatial correlation kernel with a squared exponential kernel in time. Dating uncertainties are incorporated into the modeling concept using a noisy input Gaussian process. All but one modeling hyperparameters are marginalized, to reduce their influence on the outcome and to translate their variability to the posterior variance. The resulting distribution incorporates uncertainties related to dating, measurement and modeling process. Results from application to archeomagnetic data show less variation in the dipole than comparable models, but are in general agreement with previous findings.

中文翻译：

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基于相关性的古地磁场时间演化

在之前的一项研究中，引入了一种新的古地磁场快照建模概念（Mauerberger 等，2020，https://doi.org/10.1093/gji/ggaa336）。通过假设地磁势的高斯过程，提出了一种基于相关的算法，该算法结合了封闭形式的空间相关函数。这项工作将建议的建模策略扩展到时域。时空相关核由封闭形式的空间相关核与时间平方指数核的张量积构造而成。使用噪声输入高斯过程将测年不确定性纳入建模概念。除了一个建模超参数之外，所有建模超参数都被边缘化，以减少它们对结果的影响并将它们的可变性转化为后验方差。由此产生的分布包含与测年、测量和建模过程相关的不确定性。应用到古地磁数据的结果显示偶极子的变化比可比模型小，但与以前的发现大体一致。