temporal decay
How forecast skill changes with how much of the sequence a model has seen, and with how far ahead it looks. The zero line is the Omori–Utsu law refitted at every origin.
skill by forecast origin
Pooled across sequences and horizons. The hypothesis that learned models help most early — when a single sequence offers little data and other sequences can lend it — is read off the left end of this chart.
- ETAS (fixed μ, subcritical)
- Omori–Utsu + NB spread
- GBM-hybrid · cross/pooled
Table view
| forecast origin (days since mainshock) | ETAS (fixed μ, subcritical) | Omori–Utsu + NB spread | GBM-hybrid · cross/pooled |
|---|---|---|---|
| 1 | 0.36 | 0.00 | -0.05 |
| 2 | 0.21 | 0.00 | -0.03 |
| 3 | 0.27 | 0.00 | 0.06 |
| 5 | 0.05 | 0.00 | 0.01 |
| 7 | 0.05 | 0.06 | 0.01 |
| 10 | 0.07 | 0.08 | 0.00 |
| 14 | 0.03 | 0.03 | -0.02 |
| 21 | 0.01 | 0.02 | -0.01 |
| 30 | 0.01 | 0.02 | -0.03 |
| 45 | 0.01 | 0.02 | 0.01 |
| 60 | 0.11 | 0.12 | 0.02 |
| 90 | -0.00 | 0.02 | 0.01 |
| 120 | 0.01 | 0.03 | 0.03 |
| 180 | 0.15 | 0.15 | -0.03 |
| 240 | 0.02 | 0.06 | 0.01 |
skill by horizon
The same pooling, split by forecast length.
- ETAS (fixed μ, subcritical)
- Omori–Utsu + NB spread
- GBM-hybrid · cross/pooled
Table view
| forecast horizon (days) | ETAS (fixed μ, subcritical) | Omori–Utsu + NB spread | GBM-hybrid · cross/pooled |
|---|---|---|---|
| 1 | 0.02 | 0.01 | -0.02 |
| 7 | 0.10 | 0.01 | -0.00 |
| 30 | 0.22 | 0.02 | -0.01 |
decay exponents
Omori p and ETAS parameters as refitted at three origins. ETAS values on a search bound are marked with an asterisk; see failures.
| sequence | Omori p · 7 d | · 30 d | · 120 d | ETAS α · 30 d | ETAS p · 30 d | ETAS n₃₆₅ · 30 d | ETAS α · 120 d | ETAS n₃₆₅ · 120 d |
|---|---|---|---|---|---|---|---|---|
| Landers 1992 | 5.00 | 1.63 | 1.44 | 1.16 | 1.37 | 0.99 | 1.35 | 0.96 |
| Hector Mine 1999 | 0.89 | 1.34 | 1.24 | 2.34 | 1.15 | 0.60 | 2.38 | 0.55 |
| Ridgecrest 2019 | 0.96 | 1.04 | 1.22 | 2.44 | 1.10 | 0.99 | 2.46 | 0.95 |
| Northridge 1994 | 1.31 | 1.27 | 1.28 | 2.33 | 1.18 | 0.95 | 2.30 | 0.79 |
| El Mayor–Cucapah 2010 | 1.13 | 1.17 | 1.03 | 2.43 | 1.09 | 0.83 | 2.40 | 0.92 |
| Loma Prieta 1989 | 1.37 | 1.04 | 0.93 | 2.03 | 1.01 | 0.57 | 1.99 | 0.65 |
| San Simeon 2003 | 0.85 | 1.22 | 1.00 | 2.13 | 1.00 | 0.99 | 2.06 | 0.90 |
| South Napa 2014 | 0.83 | 0.79 | 0.63 | 1.66 | 0.81 | 0.58 | 1.54 | 0.67 |
| Parkfield 2004 | 0.82 | 0.79 | 0.66 | 4.19 | 0.81 | 0.15 | 1.13 | 0.91 |
| L’Aquila 2009 | 0.92 | 1.22 | 1.18 | 1.21 | 1.49 | 0.90 | 1.44 | 0.85 |
| Amatrice 2016 | 1.00 | 0.85 | — | 1.30 | 1.28 | 0.98 | — | — |
| Norcia 2016 | 1.01 | 0.94 | 0.79 | 2.44 | 1.08 | 0.63 | 2.42 | 0.61 |
| Darfield 2010 | 5.00 | 1.06 | 1.08 | 0.88 | 1.67 | 0.99 | 1.50 | 0.99 |
| Kaikōura 2016 | 2.18 | 1.41 | 1.24 | 1.83 | 1.31 | 0.57 | 2.15 | 0.44 |
a year from one month
One forecast issued at day 30 for the rest of the window. Omori extrapolates a curve; ETAS simulates a cascade, and near-critical cascades grow long tails.
| sequence | observed | Omori mean | Omori 90% | ETAS mean | ETAS 90% | free ETAS mean |
|---|---|---|---|---|---|---|
| Landers 1992 | 1,176 | 793 | 747–840 | 9,381 | 4,010–16,576 | 33,874 |
| Hector Mine 1999 | 285 | 224 | 199–248 | 729 | 40–2,156 | 597 |
| Ridgecrest 2019 | 1,393 | 1,833 | 1,763–1,904 | 14,501 | 55–55,801 | 12,426 |
| Northridge 1994 | 254 | 224 | 199–248 | 3,486 | 0–18,511 | 2,876 |
| El Mayor–Cucapah 2010 | 389 | 278 | 251–306 | 1,585 | 5–6,172 | 1,544 |
| Loma Prieta 1989 | 2,138 | 1,268 | 1,210–1,327 | 4,173 | 1,610–7,705 | 2,820 |
| San Simeon 2003 | 847 | 601 | 561–642 | 4,586 | 162–14,427 | 7,722 |
| South Napa 2014 | 422 | 259 | 233–286 | 848 | 532–1,224 | 945 |
| Parkfield 2004 | 1,856 | 960 | 910–1,012 | 1,347 | 779–2,042 | 1,311 |
| L’Aquila 2009 | 584 | 635 | 594–677 | 1,744 | 1,048–2,583 | 5,497 |
| Amatrice 2016 | 726 | 838 | 791–886 | 1,525 | 974–2,176 | 1,462 |
| Norcia 2016 | 1,841 | 1,429 | 1,367–1,492 | 2,341 | 856–4,417 | 4,930 |
| Darfield 2010 | 3,122 | 1,076 | 1,023–1,131 | 4,806 | 1,057–10,766 | 11,868 |
| Kaikōura 2016 | 233 | 156 | 136–177 | 383 | 95–825 | 336 |