Decomposition of a Finite Temporal Correlation Scale in GNSS GEO Satellite Clocks via Phase-Based Temporal Response Analysis

In a previous study, we reported the presence of a finite temporal correlation scale of approximately 30–35 minutes in GNSS satellite clock data based on time-domain correlation analyses. However, the physical origin of this temporal scale—whether it reflects satellite-specific properties or a structure common to the satellite ensemble—remained unclear. In this study, we investigate the origin of this correlation scale by applying a frequency-domain, phase-based temporal response analysis to GNSS geostationary Earth orbit (GEO) satellite clock data. After reconstructing the clock bias time series on a common temporal grid, we define a temporal response function using cross-spectral phase and group delay, and systematically separate common-mode and satellite-specific components among the GEO satellites. We find that the previously reported 30–35 min temporal scale is not intrinsic to individual satellites but instead represents a temporal response structure shared by the GEO satellite ensemble. When this common-mode component is removed using a leave-one-out median reference, the residual temporal response converges to below 0.1 s and exhibits near-unity coherence across all satellites. These results demonstrate that temporal structures that are difficult to characterize using time-domain correlation metrics can be robustly identified as phase responses in the frequency domain. This study provides the first observational decomposition of the previously reported finite temporal correlation scale into common and residual components, and supports a framework in which time is treated as a responding structure rather than an instantaneous parameter.