Table 1 Mathematical symbols related to magnitude and number of events
Symbol | Section first used | Description |
|---|---|---|
\(M\) | \({{b}}\) | Magnitude of an earthquake |
\({M}_{\mathrm{c}}\) | \({{b}}\) | Magnitude of completeness, the minimum magnitude above which all earthquakes within an analysis window are reliably detected |
\({M}_{i}\) | \({{b}}\) | Magnitude of the \(i\)-th earthquake out of \(N\) |
\({M}_{\mathrm{min}}\) | Deviation of the FMD from the GR law | Lower limit of magnitude used to estimate \({b}^{+}\) |
\({M}_{\mathrm{ref}}\) | Deviation of the FMD from the GR law | \({M}_{\mathrm{min}}\) used to calculate the reference value of \({b}^{+}\) when comparing the differences between the mean estimated values of \({b}^{+}\) for different \({M}_{\mathrm{min}}\) in Fig. 8 |
\({M}_{\mathrm{th}}\) | Hypocenter data and analysis window | Lower threshold magnitude used to estimate each index value (1.95 for area A and 3.45 for are B) |
\({M}_{\mathrm{z}}\) | Estimation of Mc | Lower limit of the magnitude range used to estimate MAXC |
\(m\) | Deviation of the FMD from the GR law | Difference in magnitude between each earthquake and that which proceeded it |
\({m}_{\mathrm{i}}\) | Deviation of the FMD from the GR law | Magnitude difference between the \(i\)-th and \(i-1\)-th earthquakes within an analysis window |
\({m}_{\mathrm{th}}\) | Deviation of the FMD from the GR law | Arbitrary positive constant representing a lower threshold of \(m\) used to estimate \({b}^{+}\) with Eq. (6) (set to 0.2 in the analysis in this paper) |
\(N\) | Hypocenter data and analysis window | Number of events satisfying \({M\ge M}_{\mathrm{th}}\) used to estimate each index value |
\({N}{^{\prime}}\) | Tidal correlation | Number of earthquakes out of \(N\) which are uncorrelated with the tide and occur at intervals sufficiently longer than the tidal period |
\({N}_{\mathrm{th}}\) | Deviation of the FMD from the GR law | Number of earthquakes satisfying \(M\ge {M}_{\mathrm{min}}\) and \({m\ge m}_{\mathrm{th}}\) within an analysis window |
\({n}_{\mathrm{all}}\) | Statistical test to distinguish anomalous index values | Number of \(p\) estimated by the statistical tests with the same region center coordinates |
\({n}_{j}\) | Brunner-Munzel test | Number of \(j\)-th set of samples to which BM test is applied (\(j=1, 2\)) |
\({n}_{\mathrm{similarEQ}}\) | Anomalous b-values of all earthquakes in and around Japan (area B) | Number of similar earthquakes in an analysis window |
\({n}_{1}\), \({n}_{2}\) | Kolmogorov-Smirnov test | Numbers of two sets of samples to which the KS test and BM test are applied |