Table 4 Parameters of linear relationships between logarithmic frequency and VEI or eruption magnitude categories (equation 19). MA: window size, 2n, of the moving average calculation (equation 1). M: eruption magnitude. The linear relationships were obtained for the discrete points in the VEI range and M range. The intervals of points were 1 and 0.5 for VEI and eruption magnitude, respectively. Values in the parentheses show the range of 95 percentile confidence interval estimated by the bootstrap method (Efron 1979) with 10,000 replicates
VEI | ||||
|---|---|---|---|---|
MA | VEI range | a | b | R2 |
8 | 4 to 6 (3 points) | 4.757 (4.358–5.257) | 0.8534 (0.7648–0.9449) | 0.9999 (0.9887–1.0000) |
6 | 4 to 6 (3 points) | 4.815 (4.442–5.364) | 0.8627 (0.7748–0.9604) | 0.9998 (0.9861–1.0000) |
4 | 4 to 6 (3 points) | 4.900 (4.566–5.474) | 0.8747 (0.7908–0.9716) | 0.9995 (0.9836–1.0000) |
Eruption magnitude | ||||
MA | M range | a | b | R2 |
8 | ≥4.0 to ≥6.0 (5 points) | 4.603 (4.228 - 5.451) | 0.8202 (0.7398 - 0.9642) | 0.9798 (0.9708 - 0.9989) |
6 | ≥4.5 to ≥6.0 (4 points) | 3.882 (3.432 - 6.009) | 0.6819 (0.5838 - 1.055) | 0.9880 (0.9630 - 0.9994) |