California · Santa Cruz Mountains, California

loma prieta 1989

mainshock: M6.9 mw · nc216859
origin (UTC): 1989-10-18 00:04:15
epicentre: 37.036°, -121.880° depth 17.2 km
catalog: USGS ComCat network nc
zone radius: 68.7 km Gardner–Knopoff window
completeness Mc: 1.3 protocol v3, max over time bins
aftershocks ≥ Mc: 4,140 largest M5.4
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 = 1.49)
Omori fitted on first 30 d (p = 1.04)
Omori fitted on first 120 d (p = 0.93)

Table view

days since mainshock	observed rate	Omori fitted on first 3 d (p = 1.49)	Omori fitted on first 30 d (p = 1.04)	Omori fitted on first 120 d (p = 0.93)
0.5	—	612.64	657.45	729.81
0.56	693.04	—	—	—
0.59	—	569.88	596.4	639.8
0.7	—	525.35	537.1	559
0.71	464.3	—	—	—
0.83	—	479.69	480.31	486.95
0.9	385.71	—	—	—
0.98	—	433.64	426.65	423.08
1.14	356.82	—	—	—
1.16	—	387.97	376.6	366.74
1.38	—	343.46	330.46	317.27
1.44	420.01	—	—	—
1.63	—	300.85	288.41	274
1.83	252.98	—	—	—
1.93	—	260.77	250.46	236.27
2.29	—	223.71	216.54	203.48
2.31	221.91	—	—	—
2.71	—	190.03	186.46	175.05
2.92	168.11	—	—	—
3.21	—	159.91	159.99	150.44
3.7	144.29	—	—	—
3.8	—	133.38	136.84	129.19
4.5	—	110.33	116.73	110.87
4.68	105.88	—	—	—
5.33	—	90.59	99.33	95.09
5.93	78.66	—	—	—
6.31	—	73.87	84.35	81.51
7.48	—	59.87	71.5	69.84
7.5	72.33	—	—	—
8.85	—	48.25	60.51	59.83
9.49	49.56	—	—	—
10.48	—	38.7	51.14	51.23
12.01	50.1	—	—	—
12.41	—	30.91	43.18	43.86
14.7	—	24.59	36.42	37.54
15.2	39.87	—	—	—
17.41	—	19.5	30.69	32.12
19.23	26.22	—	—	—
20.61	—	15.42	25.84	27.48
24.34	20.54	—	—	—
24.41	—	12.16	21.75	23.51
28.91	—	9.58	18.29	20.11
30.8	15.96	—	—	—
34.23	—	7.52	15.38	17.2
38.98	10.22	—	—	—
40.54	—	5.9	12.93	14.71
48	—	4.62	10.86	12.58
49.33	10.82	—	—	—
56.84	—	3.62	9.12	10.76
62.42	9.91	—	—	—
67.31	—	2.83	7.66	9.2
78.99	9.06	—	—	—
79.71	—	2.21	6.43	7.87
94.39	—	1.73	5.4	6.73
99.97	7.67	—	—	—
111.78	—	1.35	4.53	5.75
126.5	5.49	—	—	—
132.37	—	1.05	3.8	4.92
156.75	—	0.82	3.19	4.2
160.1	5.32	—	—	—
185.62	—	0.64	2.68	3.59
202.6	7.01	—	—	—
219.8	—	0.5	2.25	3.07
256.4	4.13	—	—	—
260.29	—	0.39	1.89	2.63
308.23	—	0.3	1.58	2.25
324.5	5.31	—	—	—
365	—	0.23	1.33	1.92

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	1,048	606.49 (566–647)	716.13 (219–1,445)	836.37 (789–884)
2	777	1,056.74 (1,004–1,110)	1,424.19 (252–3,380)	1,908.84 (1,837–1,981)
3	607	571.56 (533–611)	960.46 (359–1,796)	720.63 (677–765)
5	443	408.02 (375–442)	665.96 (237–1,271)	464 (429–500)
7	377	306.21 (278–335)	505.26 (185–953)	349.6 (319–381)
10	311	242.63 (217–269)	383.13 (97–823)	277.01 (250–305)
14	223	214.48 (191–239)	303.03 (58–705)	245.88 (220–272)
21	146	154.04 (134–175)	235.39 (24–629)	162.79 (142–184)
30	93	110.5 (94–128)	169.19 (14–469)	124.69 (107–143)
45	66	70.77 (57–85)	124.5 (14–326)	82.7 (68–98)
60	88	52.77 (41–65)	90.07 (1–315)	60.64 (48–74)
90	48	42 (32–53)	74.66 (1–260)	43.96 (33–55)
120	41	36.71 (27–47)	62.92 (1–212)	34.49 (25–44)
180	146	27 (19–36)	52.32 (0.5–191)	35.44 (26–45)
240	41	24.72 (17–33)	52.12 (0.5–290)	30.73 (22–40)

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	1,766	909.54 (860–959)	1,156.2 (329–2,390)	935.98 (886–987)
2	1,446	2,507.45 (2,425–2,590)	4,358.7 (435–11.717k)	5,115.34 (4,998–5,233)
3	1,248	971.45 (920–1,023)	2,861.72 (999–5,500)	1,221.84 (1,165–1,280)
5	1,022	803.39 (757–850)	2,022.38 (685–3,931)	940.74 (891–991)
7	880	649.76 (608–692)	1,566.46 (575–2,952)	757.93 (713–803)
10	722	585.43 (546–626)	1,269.38 (306–2,766)	684.77 (642–728)
14	569	599.96 (560–641)	1,085.27 (241–2,423)	718.2 (674–763)
21	431	472.4 (437–508)	824.78 (199–1,798)	499.24 (463–536)
30	326	362.69 (332–394)	617.13 (130–1,398)	409.26 (376–443)
45	299	246.98 (221–273)	501.88 (94–1,173)	288.61 (261–317)
60	277	191.86 (169–215)	376.91 (25–1,084)	220.47 (196–245)
90	238	161.54 (141–183)	334.47 (39–869)	169.1 (148–191)
120	138	145.35 (126–165)	353.44 (0.5–1,474)	136.59 (118–156)
180	253	109.7 (93–127)	278.23 (0.5–1,141)	144 (125–164)
240	134	101.92 (86–119)	249.42 (0.5–1,059)	126.68 (108–145)

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)+0.070 [+0.010, +0.102]

ETAS (free)+0.068 [+0.009, +0.100]

Omori–Utsu + NB spread+0.017 [+0.002, +0.052]

45 windows · 15,244 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]

GBM-hybrid · cross/pooled + NB+0.049 [+0.005, +0.156]

GBM-hybrid · cross/other_region + NB+0.049 [+0.004, +0.155]

Poisson MLP · cross/pooled + NB+0.047 [+0.003, +0.152]

GBM-hybrid · cross/pooled+within + NB+0.047 [+0.005, +0.148]

ETAS (fixed μ, subcritical)+0.046 [−0.001, +0.160]

Omori–Utsu + NB spread+0.046 [+0.005, +0.143]

ETAS (free)+0.045 [−0.001, +0.158]

Poisson GLM · within + NB+0.044 [+0.004, +0.140]

Poisson MLP · cross/other_region + NB+0.044 [−0.003, +0.158]

Poisson GLM · cross/pooled + NB+0.043 [+0.004, +0.136]

GBM · cross/other_region + NB+0.041 [+0.005, +0.126]

GBM · cross/pooled + NB+0.040 [+0.006, +0.119]

Poisson GLM · cross/other_region + NB+0.040 [−0.007, +0.155]

GBM · within + NB+0.034 [−0.013, +0.147]

GBM-hybrid · within + NB+0.034 [−0.015, +0.132]

Poisson MLP · cross/pooled+0.019 [−0.006, +0.062]

GBM-hybrid · cross/pooled+0.018 [−0.007, +0.058]

GBM · cross/pooled+0.015 [+0.002, +0.033]

GBM · cross/other_region+0.012 [−0.010, +0.042]

Poisson GLM · cross/pooled+0.011 [−0.011, +0.040]

Poisson GLM · within+0.009 [−0.013, +0.036]

GBM-hybrid · cross/other_region+0.007 [−0.032, +0.062]

GBM-hybrid · cross/pooled+within+0.001 [−0.009, +0.011]

GBM-hybrid · within−0.001 [−0.026, +0.024]

GBM · within−0.028 [−0.054, −0.018]

Poisson MLP · cross/other_region−0.147 [−0.231, −0.041]

Poisson GLM · cross/other_region−6.140 [−7.414, −4.612]

30 windows · 4,769 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 42% · 45 windows

Omori–Utsu + NB spread

90% coverage 73% · 45 windows

ETAS (fixed μ, subcritical)

90% coverage 100% · 45 windows

GBM-hybrid · within

90% coverage 57% · 30 windows

GBM-hybrid · cross/pooled

90% coverage 49% · 45 windows

where

Forecast density at day 30 for the next 7 days on the 2 km benchmark grid; dots are the 93 epicentres that followed.

KDE (adaptive)

ETAS kernel

Cell GBM

modelestimate [95% interval]

Cell GBM+0.161 [+0.092, +0.243]

KDE (fixed bandwidth)−0.114 [−0.151, −0.060]

ETAS kernel−0.518 [−0.567, −0.410]

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	249	1.15	0.000	4.31	1.19	0.20	—	0.05	0.19
2	583	0.65	0.000	1.52	1.35	0.99	—	0.50	1.28
3	792	1.49	1.348	1.69	1.08	0.99	—	101.30	0.55
5	1,050	1.35	1.078	1.78	1.00	0.87	—	0.00	0.90
7	1,215	1.37	1.111	1.82	1.00	0.78	—	0.00	0.80
10	1,399	1.25	0.892	2.02	0.99	0.66	—	0.00	0.69
14	1,592	1.05	0.444	2.00	0.97	0.65	—	0.48	0.68
21	1,815	1.03	0.422	2.04	1.00	0.59	—	0.00	0.63
30	2,002	1.04	0.437	2.03	1.01	0.57	—	0.00	0.61
45	2,190	1.08	0.534	1.88	1.08	0.63	—	0.00	0.67
60	2,328	1.08	0.542	1.98	1.07	0.56	—	0.00	0.60
90	2,605	0.99	0.273	1.97	1.07	0.59	—	0.37	0.67
120	2,843	0.93	0.104	1.99	1.07	0.65	—	0.94	0.74
180	3,148	0.90	0.040	2.04	1.08	0.66	—	0.99	0.76
240	3,525	0.86	0.000	2.42	1.04	0.54	—	0.75	0.64

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	398	1.30	0.20	gft90
1.14	2.6	680	1.00	0.21	gft95
2.60	5.9	728	1.20	0.17	gft95
5.93	13.5	805	1.20	0.12	gft95
13.51	30.8	795	1.20	0.11	gft95
30.80	70.2	751	1.20	0.15	gft95
70.22	160.1	1,004	1.20	0.14	gft95
160.09	365.0	1,774	1.20	0.23	gft95