California · Eastern California Shear Zone

ridgecrest 2019

mainshock: M7.1 mw · ci38457511
origin (UTC): 2019-07-06 03:19:53
epicentre: 35.770°, -117.599° depth 8 km
catalog: USGS ComCat network ci
zone radius: 72.8 km Gardner–Knopoff window
completeness Mc: 2.0 protocol v3, max over time bins
aftershocks ≥ Mc: 4,729 largest M5.5
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 = 1.13)
Omori fitted on first 30 d (p = 1.04)
Omori fitted on first 120 d (p = 1.22)

Table view

days since mainshock	observed rate	Omori fitted on first 3 d (p = 1.13)	Omori fitted on first 30 d (p = 1.04)	Omori fitted on first 120 d (p = 1.22)
0.5	—	1,790.34	1,660.77	1,420.86
0.56	1,574.4	—	—	—
0.59	—	1,478.04	1,409.6	1,269.5
0.7	—	1,220.21	1,194.42	1,124.65
0.71	1,208.38	—	—	—
0.83	—	1,007.35	1,010.63	988.14
0.9	1,030.12	—	—	—
0.98	—	831.63	854.06	861.37
1.14	672.76	—	—	—
1.16	—	686.56	720.99	745.27
1.38	—	566.8	608.1	640.35
1.44	431.76	—	—	—
1.63	—	467.93	512.49	546.67
1.83	382.95	—	—	—
1.93	—	386.3	431.63	463.96
2.29	—	318.91	363.33	391.68
2.31	352.13	—	—	—
2.71	—	263.28	305.69	329.09
2.92	262.31	—	—	—
3.21	—	217.36	257.09	275.33
3.7	209.57	—	—	—
3.8	—	179.44	216.14	229.5
4.5	—	148.14	181.67	190.67
4.68	216.28	—	—	—
5.33	—	122.3	152.65	157.96
5.93	170.19	—	—	—
6.31	—	100.96	128.24	130.53
7.48	—	83.35	107.72	107.63
7.5	107.93	—	—	—
8.85	—	68.81	90.47	88.59
9.49	93.32	—	—	—
10.48	—	56.81	75.97	72.8
12.01	86.8	—	—	—
12.41	—	46.9	63.79	59.74
14.7	—	38.72	53.55	48.96
15.2	43.22	—	—	—
17.41	—	31.96	44.96	40.09
19.23	39	—	—	—
20.61	—	26.39	37.74	32.8
24.34	25.94	—	—	—
24.41	—	21.78	31.68	26.82
28.91	—	17.98	26.59	21.91
30.8	17.06	—	—	—
34.23	—	14.85	22.32	17.89
38.98	16.2	—	—	—
40.54	—	12.26	18.73	14.61
48	—	10.12	15.72	11.92
49.33	13.31	—	—	—
56.84	—	8.35	13.19	9.72
62.42	7.06	—	—	—
67.31	—	6.9	11.07	7.93
78.99	5.79	—	—	—
79.71	—	5.69	9.29	6.46
94.39	—	4.7	7.8	5.27
99.97	4.2	—	—	—
111.78	—	3.88	6.54	4.29
126.5	3.99	—	—	—
132.37	—	3.2	5.49	3.5
156.75	—	2.64	4.61	2.85
160.1	4.26	—	—	—
185.62	—	2.18	3.87	2.32
202.6	2.15	—	—	—
219.8	—	1.8	3.25	1.89
256.4	2.35	—	—	—
260.29	—	1.49	2.72	1.54
308.23	—	1.23	2.29	1.26
324.5	2.36	—	—	—
365	—	1.01	1.92	1.02

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	1,689	1,920.14 (1,848–1,993)	2,357.54 (785–4,613)	2,467.65 (2,386–2,550)
2	1,311	568.34 (529–608)	707.31 (182–1,511)	1,145.12 (1,090–1,201)
3	1,070	783 (737–829)	619.11 (431–834)	914.69 (865–965)
5	812	687.89 (645–731)	907.32 (658–1,189)	753.49 (709–799)
7	639	619.31 (579–661)	1,035.68 (781–1,319)	657.82 (616–700)
10	460	466.04 (431–502)	1,247.82 (0.5–5,956)	524.88 (487–563)
14	283	382.76 (351–415)	947.96 (0.5–5,027)	438.82 (405–474)
21	179	246.59 (221–273)	747.98 (0.5–4,272)	282.94 (256–311)
30	108	160.38 (140–181)	375.34 (0.5–2,178)	186.04 (164–209)
45	122	94.01 (78–110)	410.79 (0.5–1,964)	109.05 (92–127)
60	48	69.41 (56–83)	216.1 (0.5–270)	80.37 (66–95)
90	30	38.81 (29–49)	144.68 (0.5–362)	45.04 (34–56)
120	33	26.65 (18–35)	71.87 (0.5–415)	31.49 (23–41)
180	25	18.78 (12–26)	52.72 (0.5–224)	21.48 (14–29)
240	23	13.41 (8–20)	46.8 (0.5–42)	13.67 (8–20)

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	2,730	3,223.58 (3,130–3,317)	4,168.14 (1,346–8,250)	5,870.9 (5,745–5,997)
2	2,269	731.83 (688–777)	937.61 (280–1,906)	1,750.59 (1,682–1,820)
3	1,958	1,444.27 (1,382–1,507)	895.28 (637–1,189)	1,769.19 (1,700–1,839)
5	1,553	1,514.06 (1,450–1,578)	1,995.5 (1,475–2,579)	1,666.38 (1,600–1,734)
7	1,246	1,518.92 (1,455–1,583)	3,395.96 (2,626–4,247)	1,592.47 (1,527–1,658)
10	999	1,233.38 (1,176–1,291)	4,101.01 (2–17.68k)	1,395.98 (1,335–1,458)
14	722	1,103.79 (1,049–1,159)	3,919.57 (1–17.482k)	1,271.72 (1,213–1,331)
21	551	763.59 (718–809)	3,374.48 (0.5–17.733k)	875.97 (828–925)
30	417	525.44 (488–563)	2,106.43 (0.5–11.648k)	609.53 (569–650)
45	277	325.13 (296–355)	1,910.94 (0.5–11.125k)	377.16 (346–409)
60	174	250.61 (225–277)	1,471.94 (0.5–8,440)	290.17 (262–318)
90	125	146.09 (127–166)	991.73 (0.5–5,118)	169.56 (148–191)
120	124	103.05 (87–120)	494.19 (0.5–1,827)	121.8 (104–140)
180	69	75.19 (61–90)	211.41 (0.5–1,136)	85.97 (71–101)
240	68	54.55 (43–67)	279.41 (0.5–1,359)	55.6 (44–68)

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)+0.078 [+0.006, +0.156]

ETAS (free)+0.061 [−0.023, +0.136]

Omori–Utsu + NB spread+0.009 [+0.002, +0.039]

45 windows · 21,677 events · moving-block bootstrap. Naive references (constant rate, persistence, uniform density) score far lower and are left out of the plot; they appear in the tables.

windows where learned models forecast too

modelestimate [95% interval]

Poisson MLP · cross/chrono + NB+0.037 [+0.018, +0.061]

Poisson MLP · cross/pooled + NB+0.037 [+0.018, +0.061]

Omori–Utsu + NB spread+0.036 [+0.017, +0.060]

Poisson GLM · cross/chrono + NB+0.036 [+0.018, +0.058]

Poisson GLM · cross/pooled + NB+0.036 [+0.018, +0.058]

GBM · cross/chrono + NB+0.035 [+0.013, +0.059]

GBM · cross/pooled + NB+0.035 [+0.013, +0.059]

GBM-hybrid · cross/chrono + NB+0.035 [+0.017, +0.057]

GBM-hybrid · cross/pooled + NB+0.035 [+0.017, +0.057]

GBM-hybrid · cross/pooled+within + NB+0.035 [+0.017, +0.057]

GBM-hybrid · cross/other_region + NB+0.034 [+0.015, +0.057]

GBM · cross/other_region + NB+0.034 [+0.008, +0.059]

Poisson MLP · cross/chrono+0.032 [+0.009, +0.062]

Poisson MLP · cross/pooled+0.032 [+0.009, +0.062]

Poisson MLP · cross/other_region + NB+0.031 [+0.007, +0.055]

Poisson GLM · cross/other_region + NB+0.030 [+0.005, +0.054]

ETAS (fixed μ, subcritical)+0.021 [−0.015, +0.049]

ETAS (free)+0.020 [−0.021, +0.048]

GBM · within + NB+0.013 [−0.003, +0.042]

GBM · cross/chrono+0.003 [−0.052, +0.027]

GBM · cross/pooled+0.003 [−0.052, +0.027]

Poisson GLM · within + NB−0.002 [−0.026, +0.040]

GBM · cross/other_region−0.004 [−0.144, +0.047]

Poisson GLM · within−0.012 [−0.031, +0.018]

GBM · within−0.014 [−0.047, +0.005]

Poisson GLM · cross/chrono−0.019 [−0.033, +0.006]

Poisson GLM · cross/pooled−0.019 [−0.033, +0.006]

GBM-hybrid · cross/chrono−0.048 [−0.068, −0.030]

GBM-hybrid · cross/pooled−0.048 [−0.068, −0.030]

GBM-hybrid · cross/pooled+within−0.052 [−0.075, −0.030]

GBM-hybrid · within + NB−0.059 [−0.120, +0.036]

GBM-hybrid · within−0.092 [−0.138, −0.018]

Poisson MLP · cross/other_region−0.113 [−0.203, −0.063]

GBM-hybrid · cross/other_region−0.136 [−0.221, −0.085]

Poisson GLM · cross/other_region−1.212 [−1.486, −1.084]

30 windows · 5,061 events. Within-sequence models abstain until 24 training windows have closed.

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 29% · 45 windows

Omori–Utsu + NB spread

90% coverage 73% · 45 windows

ETAS (fixed μ, subcritical)

90% coverage 87% · 45 windows

GBM-hybrid · within

90% coverage 37% · 30 windows

GBM-hybrid · cross/pooled

90% coverage 29% · 45 windows

where

Forecast density at day 30 for the next 7 days on the 2 km benchmark grid; dots are the 108 epicentres that followed.

KDE (adaptive)

ETAS kernel

Cell GBM

modelestimate [95% interval]

KDE (fixed bandwidth)−0.051 [−0.061, +0.005]

Cell GBM−0.070 [−0.101, +0.010]

ETAS kernel−1.263 [−1.317, −1.072]

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	619	0.98	0.000	4.62	0.98	0.25	—	0.30	0.24
2	1,097	1.88	0.414	3.09	1.90	0.21	—	0.50	0.21
3	1,426	1.13	0.000	0.26	1.86	0.83	—	72.47	0.72
5	1,863	1.02	0.000	0.82	1.47	0.88	—	0.10	0.97
7	2,198	0.96	0.000	0.90	1.16	0.99	—	92.90	1.03
10	2,496	0.97	0.000	2.52	1.05	0.92	—	28.04	0.86
14	2,837	0.94	0.000	2.47	1.04	0.99	—	19.29	0.99
21	3,120	0.99	0.000	2.46	1.08	0.99	—	0.00	1.02
30	3,336	1.04	0.038	2.44	1.10	0.99	—	0.00	0.99
45	3,566	1.12	0.204	2.46	1.11	0.99	—	0.00	1.00
60	3,753	1.12	0.210	2.45	1.12	0.99	—	0.00	1.00
90	3,927	1.19	0.390	2.46	1.14	0.97	—	0.00	0.97
120	4,052	1.22	0.448	2.46	1.15	0.95	—	0.00	0.95
180	4,303	1.16	0.295	2.46	1.14	0.96	—	0.00	0.95
240	4,437	1.17	0.304	2.48	1.14	0.94	—	0.00	0.93

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	1,919	2.00	0.19	gft95
1.14	2.6	1,864	1.70	0.15	gft95
2.60	5.9	4,805	1.30	0.04	gft95
5.93	13.5	4,925	1.40	0.08	gft95
13.51	30.8	4,530	1.30	0.10	gft95
30.80	70.2	4,391	1.20	0.00	gft95
70.22	160.1	3,693	1.20	0.01	gft95
160.09	365.0	4,771	1.20	0.00	gft95