Fig. 3

Examples of estimates of corner frequency (f _c), attenuation term (\(t^{*}\)), and site amplification factors. a Map showing the locations of two earthquakes (red stars) and three stations (blue squares). EQ1 is an earthquake with M3.5 and a focal depth of 62 km, and EQ2 is an earthquake with M2.4 and a focal depth of 46 km. b S-coda spectral amplitude ratios for a pair of EQ1 and EQ2. Gray and blue lines denote spectral ratios for various common stations and the averaged spectral ratio, respectively. The red line denotes the theoretical spectral ratio that best fits the observations. Values of f _c estimated for the two earthquakes are indicated by green lines with f _c values. Inter-event distances (D) and the number of common stations (N) are shown in the panel. c Uncertainties in f _c estimates evaluated by a bootstrap method. Histograms of f _c for (left) EQ1 and (right) EQ2 are plotted from 1000 bootstrap samples, and standard errors of f _c are 0.27 Hz for EQ1 and 1.12 Hz for EQ2. d Spectral amplitudes of observed P waves (blue curves) and noise (dashed curves). Red line represents the theoretical spectral amplitude calculated from the optimal value of \(t_{0}^{*}\), site-amplification factors, and the ω ² source model. e Site amplification factors for the three stations