Fig. 3

Examples of temporal changes in the difference in the cAIC and comparison of clock error estimation results from different methods. a Temporal changes in clock errors (top) and those for differences in cAIC (\(\mathrm{\Delta cAIC}\)) from two different models for line fitting (\(y=ax+b\) and \(y=ax\)) (bottom). Values of \(\mathrm{\Delta cAIC}\) were calculated between SCCF on the day indicated by the black vertical dashed line and an SCCF on another day. b Temporal changes in clock errors estimated using three different methods. Here, WCC–LAD windowed cross-correlation and least absolute deviation regression, WCC–OLS windowed cross-correlation and ordinary linear least-squares regression, CC cross-correlation without dividing into short time windows. The enlarged results for the period indicated by the black rectangle are shown in the small panels on the right side of the figure. c (Top) Waveforms of the stacked cross-correlation functions (SCCF) in January 3, 2017 (blue line) and SCCF in July 27, 2020 (orange line), for the station pair N.NSOV–N.NSSV at the Nasu volcano. (bottom left) Estimated delay times between the two SCCFs for each lag time and the fitted straight line with the least absolute deviation (LAD) regression (red line). (bottom right) The cross-correlation function was calculated using the − 25 to + 25 s lag time portion of the two SCCFs. The horizontal dashed red line represents the delay time that maximizes the cross-correlation function. d Similar to the panel b, but for the station pair N.FJHV–V.FUJ2 at Mt. Fuji