Spatial gradients in the primary geomagnetic fields directly contribute to both the amplitudes and phases of inter-station transfer functions (IS-TFs). This suggests that, for the analysis of subsurface resistivity structures, IS-TFs should be carefully treated by checking the establishment of the plane-wave assumption. Geomagnetic time-series data include various and complicated characteristics and accordingly, time–frequency domain analysis is suitable for the discussion of spatial gradients of time-varying geomagnetic fields. However, such evaluations are complicated by the huge amount of information contained in the spectrograms from several stations. Therefore, we propose a Multi-Channel Nonnegative Matrix Factorization (MC-NMF) method that can decompose raw spectrograms into several components, allowing the spatial gradient of each geomagnetic temporal variation to be identified. We confirm that such components actually affect the estimation of IS-TFs using data acquired at the Kakioka and Memambetsu magnetic observatories in Japan. We derive the year-to-year changes in IS-TFs from each set of paired stations among Kakioka, Kanoya, and Memambetsu observatories. Although the IS-TFs should exhibit opposite polarities (a negative correlation) when the input and output observatories are swapped; surprisingly, some of them have “identical” polarities. The application of MC-NMF shows that the analyzed geomagnetic data include several components that have various spatial gradients. Although IS-TFs sometimes fail to give the expected implication regarding the spatial gradients of geomagnetic temporal variations, MC-NMF can verify whether the IS-TFs exhibit any spatial gradients. Thus, the use of IS-TFs with MC-NMF can yield better implications regarding subsurface resistivity information.

中文翻译：

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引起站间传递函数不稳定的地磁时间变化的空间梯度

主地磁场中的空间梯度直接影响站间传递函数 (IS-TF) 的幅度和相位。这表明，对于地下电阻率结构的分析，应该通过检查平面波假设的建立来仔细处理 IS-TF。地磁时间序列数据具有多种复杂的特征，因此时频域分析适合于讨论时变地磁场的空间梯度。然而，由于来自多个站点的频谱图中包含的大量信息，这种评估变得复杂。因此，我们提出了一种多通道非负矩阵分解 (MC-NMF) 方法，该方法可以将原始频谱图分解为几个分量，允许识别每个地磁时间变化的空间梯度。我们使用在日本 Kakioka 和 Memambetsu 磁天文台获得的数据确认这些组件实际上影响了 IS-TF 的估计。我们从 Kakioka、Kanoya 和 Memambetsu 天文台之间的每组配对站中推导出 IS-TF 的逐年变化。尽管当输入和输出天文台交换时，IS-TF 应该表现出相反的极性（负相关）；令人惊讶的是，其中一些具有“相同”的极性。MC-NMF 的应用表明，分析的地磁数据包括几个具有不同空间梯度的分量。尽管 IS-TF 有时无法给出关于地磁时间变化的空间梯度的预期含义，MC-NMF 可以验证 IS-TF 是否表现出任何空间梯度。因此，将 IS-TF 与 MC-NMF 结合使用可以对地下电阻率信息产生更好的影响。