California · Mojave, California
hector mine 1999
- mainshock
- M7.1 mw · ci9108652
- origin (UTC)
- 1999-10-16 09:46:44
- epicentre
- 34.603°, -116.265° depth 13.7 km
- catalog
- USGS ComCat network ci
- zone radius
- 72.8 km Gardner–Knopoff window
- completeness Mc
- 2.6 protocol v3, max over time bins
- aftershocks ≥ Mc
- 1,069 largest M5.0
- 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 = 1.06)
- Omori fitted on first 30 d (p = 1.34)
- Omori fitted on first 120 d (p = 1.24)
Table view
| days since mainshock | observed rate | Omori fitted on first 3 d (p = 1.06) | Omori fitted on first 30 d (p = 1.34) | Omori fitted on first 120 d (p = 1.24) |
|---|---|---|---|---|
| 0.5 | — | 378.17 | 333.83 | 354.06 |
| 0.56 | 338.99 | — | — | — |
| 0.59 | — | 327.43 | 302.12 | 315.41 |
| 0.7 | — | 282.22 | 270.83 | 278.55 |
| 0.71 | 273.82 | — | — | — |
| 0.83 | — | 242.27 | 240.49 | 243.93 |
| 0.9 | 230.48 | — | — | — |
| 0.98 | — | 207.24 | 211.53 | 211.89 |
| 1.14 | 185.85 | — | — | — |
| 1.16 | — | 176.71 | 184.35 | 182.65 |
| 1.38 | — | 150.26 | 159.24 | 156.34 |
| 1.44 | 161.54 | — | — | — |
| 1.63 | — | 127.46 | 136.39 | 132.94 |
| 1.83 | 88.2 | — | — | — |
| 1.93 | — | 107.9 | 115.9 | 112.36 |
| 2.29 | — | 91.17 | 97.75 | 94.46 |
| 2.31 | 88.03 | — | — | — |
| 2.71 | — | 76.92 | 81.9 | 79.02 |
| 2.92 | 68.11 | — | — | — |
| 3.21 | — | 64.81 | 68.19 | 65.82 |
| 3.7 | 50.39 | — | — | — |
| 3.8 | — | 54.54 | 56.46 | 54.62 |
| 4.5 | — | 45.85 | 46.52 | 45.17 |
| 4.68 | 57.01 | — | — | — |
| 5.33 | — | 38.52 | 38.16 | 37.25 |
| 5.93 | 47.91 | — | — | — |
| 6.31 | — | 32.33 | 31.19 | 30.64 |
| 7.48 | — | 27.12 | 25.4 | 25.15 |
| 7.5 | 24.3 | — | — | — |
| 8.85 | — | 22.74 | 20.62 | 20.6 |
| 9.49 | 17.86 | — | — | — |
| 10.48 | — | 19.06 | 16.7 | 16.85 |
| 12.01 | 12.7 | — | — | — |
| 12.41 | — | 15.97 | 13.5 | 13.76 |
| 14.7 | — | 13.38 | 10.89 | 11.22 |
| 15.2 | 10.59 | — | — | — |
| 17.41 | — | 11.2 | 8.77 | 9.15 |
| 19.23 | 6.17 | — | — | — |
| 20.61 | — | 9.38 | 7.05 | 7.45 |
| 24.34 | 6.27 | — | — | — |
| 24.41 | — | 7.85 | 5.66 | 6.06 |
| 28.91 | — | 6.57 | 4.55 | 4.93 |
| 30.8 | 4.26 | — | — | — |
| 34.23 | — | 5.49 | 3.64 | 4 |
| 38.98 | 2.39 | — | — | — |
| 40.54 | — | 4.6 | 2.92 | 3.25 |
| 48 | — | 3.85 | 2.34 | 2.64 |
| 49.33 | 1.72 | — | — | — |
| 56.84 | — | 3.22 | 1.87 | 2.14 |
| 62.42 | 2.38 | — | — | — |
| 67.31 | — | 2.69 | 1.5 | 1.74 |
| 78.99 | 1.98 | — | — | — |
| 79.71 | — | 2.25 | 1.2 | 1.41 |
| 94.39 | — | 1.88 | 0.96 | 1.14 |
| 99.97 | 1.02 | — | — | — |
| 111.78 | — | 1.57 | 0.76 | 0.93 |
| 126.5 | 0.67 | — | — | — |
| 132.37 | — | 1.32 | 0.61 | 0.75 |
| 156.75 | — | 1.1 | 0.49 | 0.61 |
| 160.1 | 0.69 | — | — | — |
| 185.62 | — | 0.92 | 0.39 | 0.49 |
| 202.6 | 0.5 | — | — | — |
| 219.8 | — | 0.77 | 0.31 | 0.4 |
| 256.4 | 0.45 | — | — | — |
| 260.29 | — | 0.64 | 0.25 | 0.32 |
| 308.23 | — | 0.54 | 0.2 | 0.26 |
| 324.5 | 0.39 | — | — | — |
| 365 | — | 0.45 | 0.16 | 0.21 |
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 | 445 | 668.13 (626–711) | 709.03 (530–909) | 648.62 (607–691) |
| 2 | 329 | 124.96 (107–144) | 349.53 (129–657) | 140.57 (121–160) |
| 3 | 264 | 246.65 (221–273) | 296.48 (167–455) | 274.36 (247–302) |
| 5 | 184 | 194.19 (172–217) | 242.78 (70–498) | 227.54 (203–253) |
| 7 | 116 | 175.3 (154–197) | 222.74 (17–624) | 192.81 (170–216) |
| 10 | 78 | 121.41 (104–140) | 156.15 (2–531) | 143.16 (124–163) |
| 14 | 57 | 69.28 (56–83) | 112.36 (0.5–448) | 83.47 (69–99) |
| 21 | 41 | 39.54 (29–50) | 70.33 (0.5–296) | 48.23 (37–60) |
| 30 | 22 | 26.39 (18–35) | 44.34 (1–146) | 31.93 (23–41) |
| 45 | 14 | 14.73 (9–21) | 38.76 (0.5–212) | 17.75 (11–25) |
| 60 | 14 | 11.07 (6–17) | 33.23 (0.5–178) | 16.2 (10–23) |
| 90 | 6 | 8.05 (4–13) | 16.52 (0.5–94) | 9.78 (5–15) |
| 120 | 9 | 5.74 (2–10) | 18.39 (0.5–103) | 7.71 (3–13) |
| 180 | 5 | 3.44 (1–7) | 6.7 (0.5–32) | 5.31 (2–9) |
| 240 | 0.5 | 2.56 (0.5–5) | 5.93 (0.5–33) | 3.44 (1–7) |
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 | 651 | 1,429.7 (1,368–1,492) | 1,593.92 (1,124–2,131) | 1,255.55 (1,198–1,314) |
| 2 | 514 | 130.95 (112–150) | 660.18 (319–1,100) | 155.93 (136–177) |
| 3 | 433 | 478.85 (443–515) | 636.25 (390–930) | 542.98 (505–582) |
| 5 | 332 | 443.47 (409–478) | 607.52 (187–1,223) | 523.07 (486–561) |
| 7 | 245 | 443.82 (409–479) | 589.97 (77–1,501) | 488.16 (452–525) |
| 10 | 187 | 323.52 (294–353) | 450.68 (19–1,388) | 381.47 (350–414) |
| 14 | 149 | 182.89 (161–205) | 342.61 (12–1,074) | 225.52 (201–250) |
| 21 | 104 | 111.38 (94–129) | 248.27 (3–866) | 135.88 (117–155) |
| 30 | 77 | 80.99 (66–96) | 194.87 (0.5–847) | 98.02 (82–115) |
| 45 | 73 | 48.63 (37–60) | 125.29 (0.5–602) | 58.59 (46–71) |
| 60 | 59 | 38.74 (29–49) | 100.74 (0.5–529) | 56.73 (45–69) |
| 90 | 31 | 30.15 (21–39) | 74.41 (0.5–384) | 36.6 (27–47) |
| 120 | 19 | 22.15 (15–30) | 67.56 (0.5–374) | 29.75 (21–39) |
| 180 | 15 | 13.72 (8–20) | 31.57 (0.5–120) | 21.17 (14–29) |
| 240 | 12 | 10.39 (5–16) | 23.56 (0.5–81) | 13.97 (8–20) |
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 (fixed μ, subcritical)+0.165 [−0.013, +0.255]
ETAS (free)+0.055 [−0.095, +0.135]
Omori–Utsu + NB spread+0.020 [−0.001, +0.079]
windows where learned models forecast too
modelestimate [95% interval]
Omori–Utsu + NB spread+0.038 [−0.014, +0.068]
GBM-hybrid · cross/chrono + NB+0.036 [−0.017, +0.067]
GBM-hybrid · cross/pooled + NB+0.035 [−0.017, +0.065]
GBM-hybrid · cross/pooled+within + NB+0.034 [−0.018, +0.065]
Poisson GLM · cross/pooled + NB+0.032 [−0.021, +0.063]
GBM-hybrid · cross/other_region + NB+0.026 [−0.029, +0.058]
GBM-hybrid · within + NB+0.022 [−0.010, +0.040]
Poisson GLM · cross/chrono + NB+0.019 [−0.047, +0.053]
GBM-hybrid · within+0.018 [−0.018, +0.037]
Poisson MLP · cross/other_region + NB+0.013 [−0.067, +0.048]
Poisson GLM · cross/other_region + NB+0.011 [−0.065, +0.046]
Poisson MLP · cross/pooled + NB+0.007 [−0.078, +0.041]
GBM · cross/other_region + NB+0.006 [−0.095, +0.042]
Poisson MLP · cross/chrono + NB+0.005 [−0.077, +0.041]
GBM · cross/pooled + NB+0.004 [−0.098, +0.041]
ETAS (fixed μ, subcritical)+0.004 [−0.091, +0.042]
ETAS (free)+0.002 [−0.083, +0.042]
GBM · cross/chrono + NB+0.001 [−0.107, +0.039]
GBM-hybrid · cross/chrono−0.016 [−0.029, +0.018]
GBM · within + NB−0.024 [−0.061, −0.004]
GBM · within−0.040 [−0.089, −0.012]
Poisson GLM · cross/pooled−0.043 [−0.060, −0.016]
GBM-hybrid · cross/pooled+within−0.057 [−0.087, +0.014]
GBM-hybrid · cross/pooled−0.057 [−0.088, +0.014]
GBM · cross/chrono−0.061 [−0.192, −0.016]
Poisson GLM · within + NB−0.061 [−0.095, +0.005]
Poisson GLM · within−0.065 [−0.098, −0.011]
GBM · cross/pooled−0.121 [−0.267, −0.064]
GBM · cross/other_region−0.139 [−0.282, −0.078]
Poisson GLM · cross/chrono−0.216 [−0.283, −0.136]
GBM-hybrid · cross/other_region−0.232 [−0.315, −0.037]
Poisson MLP · cross/other_region−0.354 [−0.456, −0.271]
Poisson MLP · cross/pooled−0.360 [−0.533, −0.231]
Poisson GLM · cross/other_region−0.479 [−0.656, −0.355]
Poisson MLP · cross/chrono−0.591 [−0.748, −0.392]
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 80% · 45 windows
ETAS (fixed μ, subcritical)
90% coverage 96% · 45 windows
GBM-hybrid · within
90% coverage 83% · 30 windows
GBM-hybrid · cross/pooled
90% coverage 44% · 45 windows
where
Forecast density at day 30 for the next 7 days on the 2 km benchmark grid; dots are the 22 epicentres that followed.
KDE (adaptive)
ETAS kernel
Cell GBM
modelestimate [95% interval]
Cell GBM−0.020 [−0.051, +0.091]
KDE (fixed bandwidth)−0.197 [−0.370, −0.091]
ETAS kernel−0.756 [−0.850, −0.538]
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 | 138 | 0.67 | 0.000 | 3.32 | 0.67 | 0.31 | — | 180.33 | 1.91 |
| 2 | 277 | 5.00* | 4.068 | 2.63 | 1.02 | 0.28 | — | 0.00 | 0.01 |
| 3 | 365 | 1.06 | 0.132 | 2.72 | 0.96 | 0.25 | — | 53.67 | 0.03 |
| 5 | 472 | 0.95 | 0.000 | 2.46 | 1.00 | 0.49 | — | 0.00 | 0.49 |
| 7 | 561 | 0.89 | 0.000 | 2.28 | 1.07 | 0.67 | — | 0.00 | 0.67 |
| 10 | 629 | 0.95 | 0.014 | 2.32 | 1.07 | 0.61 | — | 0.00 | 0.61 |
| 14 | 677 | 1.21 | 0.425 | 2.32 | 1.12 | 0.61 | — | 0.00 | 0.61 |
| 21 | 734 | 1.34 | 0.696 | 2.35 | 1.14 | 0.61 | — | 0.00 | 0.62 |
| 30 | 784 | 1.34 | 0.687 | 2.34 | 1.15 | 0.60 | — | 0.00 | 0.61 |
| 45 | 826 | 1.40 | 0.846 | 2.33 | 1.17 | 0.61 | — | 0.00 | 0.61 |
| 60 | 861 | 1.35 | 0.703 | 2.38 | 1.17 | 0.58 | — | 0.00 | 0.59 |
| 90 | 920 | 1.25 | 0.455 | 2.39 | 1.15 | 0.57 | — | 0.00 | 0.57 |
| 120 | 951 | 1.24 | 0.446 | 2.38 | 1.16 | 0.55 | — | 0.00 | 0.56 |
| 180 | 988 | 1.25 | 0.466 | 2.40 | 1.18 | 0.55 | — | 0.00 | 0.55 |
| 240 | 1,020 | 1.23 | 0.408 | 2.43 | 1.19 | 0.53 | — | 0.00 | 0.53 |
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 | 1.1 | 315 | 2.60 | 0.17 | gft95 |
| 1.14 | 2.6 | 549 | 2.40 | 0.10 | gft90 |
| 2.60 | 5.9 | 1,022 | 2.20 | 0.16 | gft95 |
| 5.93 | 13.5 | 1,514 | 2.10 | 0.16 | gft95 |
| 13.51 | 30.8 | 2,350 | 1.70 | 0.28 | gft95 |
| 30.80 | 70.2 | 2,793 | 1.70 | 0.15 | gft95 |
| 70.22 | 160.1 | 3,437 | 1.60 | 0.15 | gft95 |
| 160.09 | 365.0 | 4,114 | 1.40 | 0.08 | gft95 |