Additional file 1 of Statistical study on the regional characteristics of seismic activity in and around Japan: frequency-magnitude distribution and tidal correlation
Creators: name: Nagata, Kohei
name: Tamaribuchi, Koji
name: Hirose, Fuyuki
name: Noda, Akemi
Publisher: name: figshare
Year: 2024
Subjects: Cell Biology
Molecular Biology
Environmental Sciences not elsewhere classified
Biological Sciences not elsewhere classified
Mathematical Sciences not elsewhere classified
Computational Biology

description: Additional file 1: Fig. S1 Example analysis in a single spatial region. a Location of the spatial domain shown in the example. b The rectangular target region of the analysis, showing the cases of $$l=0.2^\circ$$ l = 0 . 2 ∘ (cyan) and $$l=0.4^\circ$$ l = 0 . 4 ∘ (magenta). c Time series of $$M$$ M and cumulative number of earthquakes of $$M\ge 2.0$$ M ≥ 2.0 in the target region. d FMD. Symbols and solid lines indicate non-integration and integration of larger magnitude earthquakes, respectively. e–g Time series of estimated $$b$$ b -, $$\eta$$ η -, and $$D$$ D -values, respectively. In c–g, symbol colors correspond to the rectangular regions shown in b. Fig. S2 Schematic of the analysis window. a Spatial window. When the spatial windows are shifted by half, there are four different patterns of non-overlapping windows for the same $$l$$ l as shown with red, blue, green, and orange solid lines for $$l=0.2^\circ$$ l = 0 . 2 ∘ . In the case of $$l=0.4^\circ$$ l = 0 . 4 ∘ , there are also four different patterns of non-overlapping windows though here only one pattern is plotted (red broken line). The center coordinates in the case of $$l=0.4^\circ$$ l = 0 . 4 ∘ (gray circle) are identical every other to that in the case of $$l=0.2^\circ$$ l = 0 . 2 ∘ (black cross). B Temporal window. The width of each window is the time it took for $$N$$ N earthquakes to occur (i.e., there is no analysis window in spatial windows where no more than 50 earthquakes occurred). The red and blue plots show the cases of $$N=50$$ N = 50 and $$N=100$$ N = 100 , respectively. There are two different patterns of non-overlapping windows (shown with circles and triangles) for the same $$N$$ N . In each spatiotemporal window, the index values ( $$b$$ b , $$\eta$$ η , $$D$$ D ), the parameters for criteria for use of index values ( $${M}_{\mathrm{c}}$$ M c , $$\mathrm{min}{T}_{N/4}$$ min T N / 4 ), and the parameter used in discussions ( $${b}^{+}$$ b + ) are calculated. Fig. S3 Probability density distributions of index values for the FMD expected from the GR law. One million $$M$$ M -series data were generated for each of the four different true $$b$$ b -values using random numbers. Each index value was calculated by extracting $$N$$ N values in order. A PDDs of observed $$b$$ b -values normalized by the true $$b$$ b -value. This distribution is independent of the true $$b$$ b -values and depends only on $$N$$ N . B PDDs of $$\eta$$ η -values. This index value is independent of $$b$$ b and depends only on $$N$$ N without normalization. Fig. S4 The expected relationship between $$D$$ D , normalized by $$N$$ N , and $$\mathrm{min}{T}_{N/4}$$ min T N / 4 in the case of a stationary Poisson distribution. The period of the tidal response is assumed to be constant at 12 h, and the mean occurrence interval and initial phase are randomly chosen to generate the occurrence time series following a stationary Poisson distribution. $$D$$ D and $$\mathrm{min}{T}_{N/4}$$ min T N / 4 were estimated 100,000 times each for $$N=50$$ N = 50 and $$N=100$$ N = 100 . The vertical dashed line marks 21,600 s (6 h). Fig. S5 An example of a FMD with which it is difficult to estimate $${M}_{\mathrm{c}}$$ M c . The inset shows the corresponding $$M-t$$ M - t plot. A large earthquake and its early aftershocks are included at the end of the analysis period, resulting in an unusually small $$b$$ b -value (0.34 with $${M}_{\mathrm{th}}=1.95)$$ M th = 1.95 ) due to the effect of reduced detectability. When the analysis period is set uniformly, as in this study, it is necessary to devise a method to discriminate such a partial decrease in detectability during the analysis period. Fig. S6 Same as Fig. 4, but using the EMR method to estimate $${M}_{\mathrm{c}}$$ M c . Fig. S7 Same as Fig. 14, but for the relationship between $${b}^{+}$$ b + and $$\mathrm{min}{T}_{N/4}$$ min T N / 4 . The relatively high $${b}^{+}$$ b + -value for very small values of $$\mathrm{min}{T}_{N/4}$$ min T N / 4 ( $$&lt;300 \mathrm{s}$$ &lt; 300 s ) in a is probably a result of the decrease in detectability (i.e., large $${M}_{\mathrm{c}}$$ M c ) with the upward convex FMD.