California · Mojave, California
landers 1992
- mainshock
- M7.3 mw · ci3031111
- origin (UTC)
- 1992-06-28 11:57:34
- epicentre
- 34.200°, -116.437° depth -0.1 km
- catalog
- USGS ComCat network ci
- zone radius
- 77.0 km Gardner–Knopoff window
- completeness Mc
- 2.5 protocol v3, max over time bins
- aftershocks ≥ Mc
- 3,679 largest M5.7
- 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 = 0.43)
- Omori fitted on first 30 d (p = 1.63)
- Omori fitted on first 120 d (p = 1.44)
Table view
| days since mainshock | observed rate | Omori fitted on first 3 d (p = 0.43) | Omori fitted on first 30 d (p = 1.63) | Omori fitted on first 120 d (p = 1.44) |
|---|---|---|---|---|
| 0.5 | — | 473.08 | 464.46 | 484.59 |
| 0.56 | 444.45 | — | — | — |
| 0.59 | — | 451.91 | 450.2 | 467.56 |
| 0.7 | — | 430.49 | 434.2 | 448.67 |
| 0.71 | 422.63 | — | — | — |
| 0.83 | — | 409.02 | 416.42 | 427.92 |
| 0.9 | 423.34 | — | — | — |
| 0.98 | — | 387.67 | 396.83 | 405.38 |
| 1.14 | 405.14 | — | — | — |
| 1.16 | — | 366.6 | 375.5 | 381.17 |
| 1.38 | — | 345.97 | 352.54 | 355.53 |
| 1.44 | 293.71 | — | — | — |
| 1.63 | — | 325.89 | 328.15 | 328.74 |
| 1.83 | 266.91 | — | — | — |
| 1.93 | — | 306.47 | 302.62 | 301.17 |
| 2.29 | — | 287.77 | 276.3 | 273.27 |
| 2.31 | 331.95 | — | — | — |
| 2.71 | — | 269.87 | 249.63 | 245.48 |
| 2.92 | 231.88 | — | — | — |
| 3.21 | — | 252.79 | 223.05 | 218.28 |
| 3.7 | 213 | — | — | — |
| 3.8 | — | 236.55 | 197.05 | 192.11 |
| 4.5 | — | 221.16 | 172.08 | 167.37 |
| 4.68 | 151.12 | — | — | — |
| 5.33 | — | 206.62 | 148.54 | 144.37 |
| 5.93 | 125.14 | — | — | — |
| 6.31 | — | 192.91 | 126.76 | 123.34 |
| 7.48 | — | 180.01 | 106.97 | 104.42 |
| 7.5 | 118.1 | — | — | — |
| 8.85 | — | 167.89 | 89.31 | 87.65 |
| 9.49 | 87.07 | — | — | — |
| 10.48 | — | 156.52 | 73.8 | 72.99 |
| 12.01 | 67.74 | — | — | — |
| 12.41 | — | 145.87 | 60.41 | 60.34 |
| 14.7 | — | 135.91 | 49.02 | 49.55 |
| 15.2 | 38.48 | — | — | — |
| 17.41 | — | 126.59 | 39.45 | 40.45 |
| 19.23 | 30.62 | — | — | — |
| 20.61 | — | 117.89 | 31.52 | 32.84 |
| 24.34 | 27.68 | — | — | — |
| 24.41 | — | 109.77 | 25.02 | 26.54 |
| 28.91 | — | 102.19 | 19.74 | 21.36 |
| 30.8 | 18.02 | — | — | — |
| 34.23 | — | 95.12 | 15.5 | 17.12 |
| 38.98 | 11.63 | — | — | — |
| 40.54 | — | 88.53 | 12.11 | 13.69 |
| 48 | — | 82.39 | 9.42 | 10.91 |
| 49.33 | 12.2 | — | — | — |
| 56.84 | — | 76.66 | 7.31 | 8.67 |
| 62.42 | 8.15 | — | — | — |
| 67.31 | — | 71.34 | 5.65 | 6.88 |
| 78.99 | 6.54 | — | — | — |
| 79.71 | — | 66.37 | 4.36 | 5.45 |
| 94.39 | — | 61.75 | 3.35 | 4.31 |
| 99.97 | 4.11 | — | — | — |
| 111.78 | — | 57.45 | 2.58 | 3.41 |
| 126.5 | 2.71 | — | — | — |
| 132.37 | — | 53.45 | 1.97 | 2.69 |
| 156.75 | — | 49.72 | 1.51 | 2.12 |
| 160.1 | 6.59 | — | — | — |
| 185.62 | — | 46.26 | 1.16 | 1.67 |
| 202.6 | 1.48 | — | — | — |
| 219.8 | — | 43.03 | 0.88 | 1.31 |
| 256.4 | 0.86 | — | — | — |
| 260.29 | — | 40.03 | 0.67 | 1.03 |
| 308.23 | — | 37.23 | 0.51 | 0.81 |
| 324.5 | 0.81 | — | — | — |
| 365 | — | 34.64 | 0.39 | 0.64 |
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 | 1,362 | 1,705.37 (1,638–1,774) | 2,620.22 (1,794–3,574) | 2,193.1 (2,116–2,270) |
| 2 | 1,150 | 581.11 (542–621) | 647.7 (410–929) | 504.85 (468–542) |
| 3 | 920 | 1,374.91 (1,314–1,436) | 1,491.59 (911–2,188) | 1,229.3 (1,172–1,287) |
| 5 | 728 | 556.23 (518–595) | 1,041.34 (681–1,464) | 561.42 (523–601) |
| 7 | 586 | 386.36 (354–419) | 401.92 (291–527) | 437.88 (404–473) |
| 10 | 395 | 385.87 (354–418) | 571.61 (330–867) | 403.05 (370–436) |
| 14 | 242 | 309.79 (281–339) | 416.8 (219–666) | 318.93 (290–349) |
| 21 | 186 | 155.55 (135–176) | 256.01 (123–427) | 185.13 (163–208) |
| 30 | 100 | 112.6 (95–130) | 195.97 (86–342) | 126.37 (108–145) |
| 45 | 105 | 61.48 (49–75) | 126.42 (42–246) | 69 (56–83) |
| 60 | 59 | 48.83 (38–61) | 102.9 (25–223) | 54.99 (43–67) |
| 90 | 39 | 31.21 (22–41) | 65.37 (10–160) | 35.43 (26–45) |
| 120 | 23 | 20.75 (14–29) | 42.3 (3–118) | 23.82 (16–32) |
| 180 | 19 | 18.67 (12–26) | 43.12 (1–144) | 20.52 (13–28) |
| 240 | 8 | 11.83 (6–18) | 25.51 (0.5–95) | 12.83 (7–19) |
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 | 2,306 | 2,753.02 (2,667–2,840) | 9,952.98 (4,621–16.925k) | 3,695.52 (3,596–3,796) |
| 2 | 2,009 | 675.07 (633–718) | 796.32 (465–1,199) | 582.87 (543–623) |
| 3 | 1,721 | 4,124.63 (4,019–4,231) | 4,738.39 (2,022–8,379) | 3,652.44 (3,553–3,752) |
| 5 | 1,380 | 814.86 (768–862) | 3,654.95 (1,989–5,730) | 819.67 (773–867) |
| 7 | 1,155 | 588.27 (549–628) | 646.81 (403–936) | 674.09 (632–717) |
| 10 | 904 | 873.55 (825–922) | 2,194.96 (1,040–3,696) | 912.46 (863–962) |
| 14 | 650 | 804.68 (758–852) | 1,705.48 (815–2,860) | 828.41 (781–876) |
| 21 | 516 | 401.28 (369–435) | 1,198.58 (562–2,027) | 477.6 (442–514) |
| 30 | 363 | 333.53 (304–364) | 900.66 (446–1,483) | 374.34 (343–406) |
| 45 | 281 | 196.42 (174–220) | 650.69 (241–1,222) | 220.46 (196–245) |
| 60 | 204 | 168.55 (147–190) | 539.9 (188–1,037) | 189.79 (167–213) |
| 90 | 109 | 115.19 (98–133) | 372.32 (98–789) | 130.77 (112–150) |
| 120 | 85 | 78.99 (65–94) | 244.96 (52–552) | 90.69 (75–107) |
| 180 | 59 | 74.6 (61–89) | 209.4 (33–511) | 82.02 (67–97) |
| 240 | 28 | 47.93 (37–60) | 144.02 (14–388) | 51.98 (40–64) |
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)+0.135 [+0.012, +0.237]
ETAS (free)+0.071 [+0.001, +0.129]
Omori–Utsu + NB spread+0.016 [+0.001, +0.050]
windows where learned models forecast too
modelestimate [95% interval]
Poisson GLM · cross/pooled + NB+0.012 [+0.004, +0.026]
Omori–Utsu + NB spread+0.012 [+0.004, +0.024]
GBM-hybrid · cross/pooled + NB+0.012 [+0.003, +0.025]
GBM-hybrid · cross/pooled+within + NB+0.012 [+0.003, +0.025]
Poisson MLP · cross/pooled + NB+0.011 [+0.003, +0.024]
GBM-hybrid · cross/other_region + NB+0.011 [+0.002, +0.024]
GBM-hybrid · cross/chrono + NB+0.011 [+0.001, +0.024]
GBM · cross/pooled + NB+0.009 [−0.004, +0.025]
Poisson GLM · cross/pooled+0.009 [−0.002, +0.025]
GBM · cross/other_region + NB+0.008 [−0.005, +0.023]
GBM · cross/chrono + NB+0.007 [−0.012, +0.022]
ETAS (fixed μ, subcritical)+0.006 [−0.007, +0.019]
Poisson MLP · cross/other_region + NB+0.005 [−0.012, +0.018]
Poisson GLM · cross/chrono + NB+0.005 [−0.008, +0.016]
GBM-hybrid · cross/pooled+0.005 [−0.003, +0.016]
GBM-hybrid · cross/pooled+within+0.003 [−0.004, +0.017]
ETAS (free)+0.003 [−0.009, +0.016]
Poisson MLP · cross/chrono + NB+0.002 [−0.013, +0.015]
Poisson GLM · cross/other_region + NB+0.001 [−0.015, +0.017]
Poisson MLP · cross/pooled−0.001 [−0.018, +0.011]
GBM · cross/pooled−0.009 [−0.061, +0.020]
GBM-hybrid · within + NB−0.012 [−0.037, +0.023]
Poisson GLM · within + NB−0.015 [−0.043, +0.024]
GBM · cross/other_region−0.016 [−0.079, +0.022]
GBM-hybrid · cross/other_region−0.017 [−0.040, +0.014]
GBM-hybrid · within−0.019 [−0.040, +0.006]
Poisson GLM · within−0.020 [−0.044, +0.010]
GBM-hybrid · cross/chrono−0.026 [−0.061, +0.009]
GBM · cross/chrono−0.026 [−0.113, +0.012]
GBM · within + NB−0.029 [−0.060, +0.017]
GBM · within−0.051 [−0.084, −0.004]
Poisson MLP · cross/other_region−0.124 [−0.333, −0.044]
Poisson GLM · cross/other_region−0.130 [−0.252, −0.093]
Poisson GLM · cross/chrono−0.203 [−0.221, −0.154]
Poisson MLP · cross/chrono−0.552 [−0.632, −0.284]
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 42% · 45 windows
Omori–Utsu + NB spread
90% coverage 71% · 45 windows
ETAS (fixed μ, subcritical)
90% coverage 67% · 45 windows
GBM-hybrid · within
90% coverage 53% · 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 100 epicentres that followed.
KDE (adaptive)
ETAS kernel
Cell GBM
modelestimate [95% interval]
ETAS kernel−0.043 [−0.082, −0.005]
Cell GBM−0.062 [−0.097, +0.031]
KDE (fixed bandwidth)−0.067 [−0.098, −0.026]
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 | 214 | 5.00* | 27.504 | 2.16 | 4.50 | 0.99 | p | 0.09 | 0.14 |
| 2 | 526 | 5.00* | 9.226 | 3.01 | 4.50 | 0.15 | p | 0.10 | 1.92 |
| 3 | 830 | 0.43 | 0.317 | 0.15 | 2.04 | 0.99 | — | 122.35 | 0.63 |
| 5 | 1,201 | 5.00* | 17.669 | 0.56 | 1.98 | 0.99 | — | 31.61 | 0.91 |
| 7 | 1,448 | 5.00* | 17.880 | 7.50 | 4.50 | 0.02 | alpha, p | 0.00 | 1.25 |
| 10 | 1,750 | 1.69 | 4.571 | 0.64 | 1.77 | 0.99 | — | 0.00 | 1.02 |
| 14 | 2,034 | 1.42 | 3.431 | 0.68 | 1.64 | 0.99 | — | 0.00 | 1.07 |
| 21 | 2,276 | 1.96 | 6.070 | 0.97 | 1.53 | 0.99 | — | 0.00 | 1.05 |
| 30 | 2,503 | 1.63 | 4.256 | 1.16 | 1.37 | 0.99 | — | 0.00 | 1.05 |
| 45 | 2,697 | 1.70 | 4.663 | 1.16 | 1.35 | 0.99 | — | 0.00 | 1.02 |
| 60 | 2,866 | 1.50 | 3.531 | 1.22 | 1.32 | 0.99 | — | 0.00 | 1.01 |
| 90 | 3,070 | 1.42 | 3.049 | 1.31 | 1.29 | 0.98 | — | 0.00 | 0.99 |
| 120 | 3,179 | 1.44 | 3.156 | 1.35 | 1.29 | 0.96 | — | 0.00 | 0.97 |
| 180 | 3,494 | 1.20 | 1.704 | 1.46 | 1.24 | 0.94 | — | 0.00 | 0.95 |
| 240 | 3,576 | 1.25 | 2.030 | 1.43 | 1.27 | 0.93 | — | 0.00 | 0.94 |
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 | 431 | 2.50 | 0.23 | gft95 |
| 1.14 | 2.6 | 945 | 2.50 | 0.08 | gft95 |
| 2.60 | 5.9 | 1,474 | 2.50 | 0.22 | gft90 |
| 5.93 | 13.5 | 2,691 | 2.30 | 0.24 | gft95 |
| 13.51 | 30.8 | 4,009 | 2.10 | 0.10 | gft95 |
| 30.80 | 70.2 | 5,986 | 2.00 | 0.13 | gft95 |
| 70.22 | 160.1 | 7,469 | 2.00 | 0.07 | gft95 |
| 160.09 | 365.0 | 6,842 | 1.60 | 0.11 | gft95 |