Spatial gradients of geomagnetic temporal variations causing the instability of inter-station transfer functions

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.