California · San Francisco Bay Area, California
south napa 2014
- mainshock
- M6.0 mw · nc72282711
- origin (UTC)
- 2014-08-24 10:20:44
- epicentre
- 38.215°, -122.312° depth 11.1 km
- catalog
- USGS ComCat network nc
- zone radius
- 53.2 km Gardner–Knopoff window
- completeness Mc
- 1.2 protocol v3, max over time bins
- aftershocks ≥ Mc
- 607 largest M4.1
- window
- 0.5–365 daysfull year
rate decay
Observed rate in log-spaced bins against Omori–Utsu fits made with the first 3, 30 and 120 days only, drawn across the whole window. Where a curve leaves the dots, the early fit extrapolated badly.
- observed rate
- Omori fitted on first 3 d (p = 5.00)
- Omori fitted on first 30 d (p = 0.79)
- Omori fitted on first 120 d (p = 0.63)
Table view
| days since mainshock | observed rate | Omori fitted on first 3 d (p = 5.00) | Omori fitted on first 30 d (p = 0.79) | Omori fitted on first 120 d (p = 0.63) |
|---|---|---|---|---|
| 0.5 | — | 27.04 | 32.03 | 35.51 |
| 0.56 | 22.6 | — | — | — |
| 0.59 | — | 26.57 | 30.31 | 32.45 |
| 0.7 | — | 26.02 | 28.52 | 29.58 |
| 0.71 | 29.76 | — | — | — |
| 0.83 | — | 25.38 | 26.69 | 26.92 |
| 0.9 | 23.52 | — | — | — |
| 0.98 | — | 24.66 | 24.84 | 24.45 |
| 1.14 | 11.15 | — | — | — |
| 1.16 | — | 23.83 | 22.99 | 22.17 |
| 1.38 | — | 22.89 | 21.16 | 20.08 |
| 1.44 | 35.25 | — | — | — |
| 1.63 | — | 21.84 | 19.38 | 18.17 |
| 1.83 | 11.6 | — | — | — |
| 1.93 | — | 20.67 | 17.66 | 16.42 |
| 2.29 | — | 19.37 | 16.01 | 14.82 |
| 2.31 | 27.51 | — | — | — |
| 2.71 | — | 17.97 | 14.46 | 13.37 |
| 2.92 | 13.04 | — | — | — |
| 3.21 | — | 16.45 | 13.01 | 12.06 |
| 3.7 | 10.31 | — | — | — |
| 3.8 | — | 14.86 | 11.66 | 10.87 |
| 4.5 | — | 13.2 | 10.42 | 9.79 |
| 4.68 | 8.14 | — | — | — |
| 5.33 | — | 11.51 | 9.29 | 8.81 |
| 5.93 | 7.87 | — | — | — |
| 6.31 | — | 9.84 | 8.26 | 7.93 |
| 7.48 | — | 8.22 | 7.32 | 7.14 |
| 7.5 | 11.87 | — | — | — |
| 8.85 | — | 6.7 | 6.48 | 6.42 |
| 9.49 | 2.23 | — | — | — |
| 10.48 | — | 5.31 | 5.73 | 5.78 |
| 12.01 | 5.65 | — | — | — |
| 12.41 | — | 4.09 | 5.06 | 5.19 |
| 14.7 | — | 3.05 | 4.46 | 4.67 |
| 15.2 | 4.46 | — | — | — |
| 17.41 | — | 2.2 | 3.92 | 4.2 |
| 19.23 | 3.08 | — | — | — |
| 20.61 | — | 1.53 | 3.45 | 3.78 |
| 24.34 | 2.96 | — | — | — |
| 24.41 | — | 1.03 | 3.03 | 3.39 |
| 28.91 | — | 0.67 | 2.67 | 3.05 |
| 30.8 | 3.3 | — | — | — |
| 34.23 | — | 0.42 | 2.34 | 2.74 |
| 38.98 | 1.96 | — | — | — |
| 40.54 | — | 0.25 | 2.05 | 2.46 |
| 48 | — | 0.15 | 1.8 | 2.21 |
| 49.33 | 1.46 | — | — | — |
| 56.84 | — | 0.084 | 1.58 | 1.99 |
| 62.42 | 3.05 | — | — | — |
| 67.31 | — | 0.046 | 1.38 | 1.79 |
| 78.99 | 1.29 | — | — | — |
| 79.71 | — | 0.025 | 1.21 | 1.61 |
| 94.39 | — | 0.013 | 1.06 | 1.44 |
| 99.97 | 1.4 | — | — | — |
| 111.78 | — | 0.0065 | 0.93 | 1.3 |
| 126.5 | 1.31 | — | — | — |
| 132.37 | — | 0.0032 | 0.82 | 1.17 |
| 156.75 | — | 0.0016 | 0.71 | 1.05 |
| 160.1 | 0.98 | — | — | — |
| 185.62 | — | 0.00076 | 0.62 | 0.94 |
| 202.6 | 0.82 | — | — | — |
| 219.8 | — | 0.00036 | 0.55 | 0.85 |
| 256.4 | 1.32 | — | — | — |
| 260.29 | — | 0.00017 | 0.48 | 0.76 |
| 308.23 | — | 0.000077 | 0.42 | 0.68 |
| 324.5 | 0.99 | — | — | — |
| 365 | — | 0.000035 | 0.37 | 0.61 |
7-day forecasts
Each point is a forecast issued at that origin for the next 7 days, with its 90% predictive interval, against the count that followed.
- observed
- Omori–Utsu
- ETAS (fixed μ, subcritical)
- GBM-hybrid · cross/pooled
Table view
| forecast origin (days) | observed | Omori–Utsu | ETAS (fixed μ, subcritical) | GBM-hybrid · cross/pooled |
|---|---|---|---|---|
| 1 | 90 | 44.66 (34–56) | — | 179.73 (158–202) |
| 2 | 75 | 76.03 (62–91) | 109.63 (90–130) | 155.76 (136–177) |
| 3 | 56 | 71.05 (57–85) | 88.93 (4–271) | 95.31 (80–112) |
| 5 | 47 | 27.42 (19–36) | 66.42 (3–198) | 45.86 (35–57) |
| 7 | 35 | 44.52 (34–56) | 57.92 (12–131) | 54.09 (42–66) |
| 10 | 34 | 18.35 (12–26) | 47.47 (8–111) | 18 (11–25) |
| 14 | 29 | 18.52 (12–26) | 34.63 (10–70) | 24.52 (17–33) |
| 21 | 18 | 18.71 (12–26) | 26.77 (7–55) | 35.95 (26–46) |
| 30 | 20 | 16.7 (10–24) | 21.61 (9–37) | 26.38 (18–35) |
| 45 | 12 | 12.75 (7–19) | 18.15 (8–31) | 14.25 (8–21) |
| 60 | 27 | 9.85 (5–15) | 15.86 (2–39) | 12.6 (7–19) |
| 90 | 15 | 9.64 (5–15) | 14.88 (5–29) | 10.63 (6–16) |
| 120 | 8 | 8.52 (4–14) | 13.57 (2–33) | 8.34 (4–13) |
| 180 | 6 | 6.58 (3–11) | 11.35 (1–31) | 7.05 (3–12) |
| 240 | 6 | 5.34 (2–9) | 9.79 (1–25) | 6.14 (2–10) |
30-day forecasts
Each point is a forecast issued at that origin for the next 30 days, with its 90% predictive interval, against the count that followed.
- observed
- Omori–Utsu
- ETAS (fixed μ, subcritical)
- GBM-hybrid · cross/pooled
Table view
| forecast origin (days) | observed | Omori–Utsu | ETAS (fixed μ, subcritical) | GBM-hybrid · cross/pooled |
|---|---|---|---|---|
| 1 | 173 | 49.3 (38–61) | — | 213.47 (190–238) |
| 2 | 154 | 118.4 (101–137) | 378.56 (324–435) | 285.38 (258–313) |
| 3 | 134 | 114.6 (97–132) | 279.13 (32–727) | 162.17 (142–183) |
| 5 | 126 | 37.73 (28–48) | 209.08 (32–512) | 65.64 (53–79) |
| 7 | 112 | 120.81 (103–139) | 207.51 (55–439) | 153.54 (133–174) |
| 10 | 99 | 30.7 (22–40) | 191.33 (45–420) | 31.51 (23–41) |
| 14 | 90 | 46.05 (35–57) | 137.44 (51–256) | 60.39 (48–73) |
| 21 | 71 | 59.24 (47–72) | 102.97 (54–165) | 114.65 (97–133) |
| 30 | 57 | 58.33 (46–71) | 90.69 (51–139) | 92.87 (77–109) |
| 45 | 64 | 47.03 (36–59) | 77.26 (40–124) | 53.46 (42–66) |
| 60 | 61 | 37.29 (28–48) | 71.79 (27–134) | 48.52 (37–60) |
| 90 | 45 | 38.4 (29–49) | 67.99 (30–117) | 42.37 (32–53) |
| 120 | 35 | 34.6 (25–45) | 65.98 (15–144) | 34.42 (25–44) |
| 180 | 30 | 27.14 (19–36) | 52.42 (15–108) | 29.11 (21–38) |
| 240 | 40 | 22.23 (15–30) | 45.96 (11–98) | 25.54 (18–34) |
information gain
Per-event log-score difference from the Omori–Utsu law. Above zero: the model assigned more probability to what actually happened.
every window, classical models
modelestimate [95% interval]
ETAS (free)+0.074 [+0.006, +0.151]
ETAS (fixed μ, subcritical)+0.061 [−0.015, +0.160]
Omori–Utsu + NB spread+0.041 [−0.002, +0.111]
windows where learned models forecast too
modelestimate [95% interval]
Poisson GLM · cross/chrono + NB+0.100 [−0.001, +0.171]
Poisson GLM · cross/chrono+0.098 [−0.004, +0.172]
GBM-hybrid · cross/other_region + NB+0.095 [−0.012, +0.164]
Poisson GLM · cross/pooled + NB+0.094 [−0.008, +0.165]
Poisson GLM · cross/pooled+0.093 [−0.011, +0.167]
GBM-hybrid · cross/chrono + NB+0.091 [−0.011, +0.158]
ETAS (fixed μ, subcritical)+0.091 [−0.018, +0.163]
GBM-hybrid · cross/pooled + NB+0.087 [−0.015, +0.155]
GBM-hybrid · cross/pooled+within + NB+0.087 [−0.013, +0.153]
ETAS (free)+0.087 [−0.027, +0.160]
Poisson GLM · within + NB+0.085 [−0.007, +0.149]
GBM-hybrid · cross/other_region+0.083 [−0.018, +0.146]
Omori–Utsu + NB spread+0.082 [−0.011, +0.142]
Poisson GLM · within+0.081 [−0.004, +0.145]
Poisson MLP · cross/pooled + NB+0.081 [−0.028, +0.153]
Poisson MLP · cross/chrono + NB+0.073 [−0.036, +0.146]
Poisson MLP · cross/other_region + NB+0.066 [−0.049, +0.139]
GBM · cross/chrono + NB+0.064 [−0.058, +0.144]
GBM · cross/pooled + NB+0.064 [−0.059, +0.142]
GBM · cross/other_region + NB+0.062 [−0.060, +0.140]
Poisson GLM · cross/other_region + NB+0.062 [−0.055, +0.137]
GBM · within + NB+0.049 [−0.038, +0.106]
GBM · cross/chrono+0.036 [−0.099, +0.127]
Poisson MLP · cross/pooled+0.034 [−0.108, +0.129]
GBM-hybrid · cross/chrono+0.033 [−0.019, +0.067]
GBM · cross/pooled+0.024 [−0.126, +0.119]
GBM · within+0.007 [−0.096, +0.086]
GBM-hybrid · cross/pooled+within+0.006 [−0.006, +0.018]
GBM-hybrid · cross/pooled+0.002 [−0.064, +0.047]
Poisson MLP · cross/chrono+0.002 [−0.144, +0.112]
GBM · cross/other_region−0.001 [−0.150, +0.093]
GBM-hybrid · within + NB−0.035 [−0.102, +0.052]
GBM-hybrid · within−0.035 [−0.097, +0.038]
Poisson MLP · cross/other_region−0.053 [−0.150, +0.053]
Poisson GLM · cross/other_region−0.707 [−0.932, −0.440]
calibration
Randomised probability integral transform over all windows. Flat at 1 is calibrated; a U means intervals too narrow, a hump means too wide.
Omori–Utsu
90% coverage 64% · 45 windows
Omori–Utsu + NB spread
90% coverage 73% · 45 windows
ETAS (fixed μ, subcritical)
90% coverage 95% · 42 windows
GBM-hybrid · within
90% coverage 73% · 30 windows
GBM-hybrid · cross/pooled
90% coverage 51% · 45 windows
where
Forecast density at day 30 for the next 7 days on the 2 km benchmark grid; dots are the 20 epicentres that followed.
KDE (adaptive)
ETAS kernel
Cell GBM
modelestimate [95% interval]
Cell GBM−0.094 [−0.202, +0.098]
ETAS kernel−0.245 [−0.362, −0.030]
KDE (fixed bandwidth)−0.347 [−0.446, −0.152]
fitted parameters
Refitted at every origin on data up to that origin. A parameter on its search bound is flagged (Omori with an asterisk, ETAS by name): early in a sequence the catalog is still incomplete, the rate looks flat, and neither likelihood identifies its decay parameters — the optimum sits on a bound.
| origin (d) | events | Omori p | Omori c (d) | ETAS α | ETAS p | ETAS n₃₆₅ | on bound | free ETAS μ/day | free n₃₆₅ |
|---|---|---|---|---|---|---|---|---|---|
| 1 | 13 | 5.00* | 7.818 | — | — | — | — | — | — |
| 2 | 33 | 5.00* | 24.238 | 4.45 | 0.26 | 0.23 | — | 0.02 | 0.02 |
| 3 | 54 | 5.00* | 25.447 | 1.75 | 0.88 | 0.99 | — | 13.91 | 0.45 |
| 5 | 73 | 5.00* | 14.314 | 1.79 | 0.86 | 0.93 | — | 6.81 | 0.50 |
| 7 | 93 | 0.83 | 1.268 | 1.75 | 0.80 | 0.99 | — | 7.92 | 0.43 |
| 10 | 110 | 5.00* | 20.906 | 1.67 | 0.83 | 0.99 | — | 1.90 | 0.83 |
| 14 | 128 | 1.64 | 4.666 | 1.68 | 0.83 | 0.83 | — | 0.40 | 0.92 |
| 21 | 157 | 0.96 | 1.578 | 1.69 | 0.81 | 0.64 | — | 1.38 | 0.53 |
| 30 | 185 | 0.79 | 0.773 | 1.66 | 0.81 | 0.58 | — | 1.33 | 0.46 |
| 45 | 219 | 0.78 | 0.724 | 1.64 | 0.85 | 0.58 | — | 0.51 | 0.67 |
| 60 | 242 | 0.81 | 0.883 | 1.59 | 0.92 | 0.62 | — | 0.00 | 0.88 |
| 90 | 303 | 0.66 | 0.212 | 1.50 | 0.94 | 0.68 | — | 0.00 | 0.99 |
| 120 | 348 | 0.63 | 0.103 | 1.54 | 0.96 | 0.67 | — | 0.11 | 0.96 |
| 180 | 412 | 0.64 | 0.120 | 1.66 | 0.96 | 0.58 | — | 0.16 | 0.88 |
| 240 | 460 | 0.65 | 0.179 | 1.74 | 0.97 | 0.50 | — | 0.09 | 0.84 |
completeness
Mc per log-spaced time bin (bootstrap median of 200 resamples). The sequence Mc is the largest bin value.
| from (d) | to (d) | events, all M | Mc | bootstrap sd | estimator |
|---|---|---|---|---|---|
| 0.50 | 13.5 | 160 | 1.10 | 0.22 | gft90 |
| 13.51 | 70.2 | 191 | 1.20 | 0.31 | gft90 |
| 70.22 | 160.1 | 139 | 1.10 | 0.17 | gft95 |
| 160.09 | 365.0 | 281 | 1.20 | 0.12 | gft90 |