Estimation of paleomagnetic directions plays a crucial role in magnetostratigaphy, paleogeographic reconstruction, and constraining past geomagnetic field behavior. While analysis and aggregation of paleomagnetic directional data are performed in a hierarchical fashion, the standard statistical framework employed by paleomagnetists does not consider uncertainty propagation through each level of the hierarchy. With this limitation, inferences drawn from paleomagnetic data will be affected by underestimated uncertainties. We provide here an approximate directional uncertainty propagation scheme that applies to Fisher distributions and, thus, to a number of paleomagnetic data processing tasks. The scheme is a straightforward addition to the existing paleomagnetic statistical framework and is demonstrated using case studies to show how uncertainties can be propagated through different stages of the paleomagnetic data processing chain. Furthermore, we discuss situations, such as the transformation into virtual geomagnetic poles, where this simple form of uncertainty propagation cannot be employed because the data are not Fisher distributed.

中文翻译：

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分层古磁重构中的不确定性传播

古磁方向的估计在磁成影，古地理重建和限制过去的地磁场行为中起着至关重要的作用。尽管古电磁定向数据的分析和汇总是以分层方式进行的，但古磁性学家所采用的标准统计框架并未考虑不确定性在整个分层结构中的传播。受此限制，从古磁数据得出的推论将受到低估的不确定性的影响。在这里，我们提供了一种近似的方向不确定性传播方案，该方案适用于Fisher分布，因此适用于许多古磁数据处理任务。该方案是对现有古磁统计框架的直接补充，并通过案例研究进行了演示，以显示如何通过古磁数据处理链的不同阶段传播不确定性。此外，我们讨论了诸如转换为虚拟地磁极这样的情况，由于数据不是费舍尔分布的，因此无法采用这种简单形式的不确定性传播。