aftershocks, forecast one window at a time

36,622 aftershocks. 14 real sequences from California, Central Italy, New Zealand. Every model sees only the past; every forecast is scored against what happened next. The question is whether modern machine learning characterises how a sequence evolves better than the statistical laws seismology already has.

Read the benchmark →

the answer, so far

Across 14 held-out sequences, measured as per-event information gain over the Omori–Utsu law: trained across other sequences, GBM · cross/pooled beats Omori overall (+0.130 nats per event), but the gain lives in the first three days (+0.243), when a young sequence cannot yet fit its own decay law; by three weeks it is −0.008. ETAS, the classical cascade model, is the strongest overall (+0.171, above Omori on 14 of 14 sequences).

modelestimate [95% interval]

ETAS (fixed μ, subcritical)14 of 14 sequences above Omori · 612 windows+0.171 [+0.096, +0.307]

ETAS (free)14 of 14 sequences above Omori · 612 windows+0.138 [+0.073, +0.253]

GBM · cross/pooled13 of 14 sequences above Omori · 615 windows+0.130 [+0.055, +0.256]

Poisson GLM · cross/pooled13 of 14 sequences above Omori · 615 windows+0.129 [+0.048, +0.270]

GBM · cross/chrono12 of 13 sequences above Omori · 570 windows+0.116 [+0.010, +0.272]

GBM · cross/other_region13 of 14 sequences above Omori · 615 windows+0.115 [+0.035, +0.261]

Poisson MLP · cross/pooled8 of 14 sequences above Omori · 615 windows+0.059 [−0.061, +0.201]

Omori–Utsu + NB spread14 of 14 sequences above Omori · 615 windows+0.019 [+0.012, +0.030]

GBM-hybrid · cross/pooled9 of 14 sequences above Omori · 615 windows−0.007 [−0.043, +0.024]

GBM-hybrid · within2 of 14 sequences above Omori · 405 windows−0.056 [−0.078, −0.030]

Point estimate and 95% cluster-bootstrap interval, resampling whole sequences. Squares are learned models, circles classical. Zero is the Omori–Utsu law with a Poisson count distribution.

the sequences

Each mainshock resolved against its catalog’s live service; completeness set by one pre-registered rule.

sequence	region	catalog	Mw	Mc	aftershocks ≥ Mc	window (days)
Landers 1992	California	USGS ComCat	7.3	2.5	3,679	0.5–365
Hector Mine 1999	California	USGS ComCat	7.1	2.6	1,069	0.5–365
Ridgecrest 2019	California	USGS ComCat	7.1	2.0	4,729	0.5–365
Northridge 1994	California	USGS ComCat	6.7	2.4	1,051	0.5–365
El Mayor–Cucapah 2010	California	USGS ComCat	7.2	3.0	1,076	0.5–365
Loma Prieta 1989	California	USGS ComCat	6.9	1.3	4,140	0.5–365
San Simeon 2003	California	USGS ComCat	6.5	2.1	2,150	0.5–280.9
South Napa 2014	California	USGS ComCat	6.0	1.2	607	0.5–365
Parkfield 2004	California	USGS ComCat	6.0	1.2	2,666	0.5–365
L’Aquila 2009	Central Italy	INGV	6.1	2.1	2,183	0.5–365
Amatrice 2016	Central Italy	INGV	6.0	1.8	3,912	0.5–63.7
Norcia 2016	Central Italy	INGV	6.5	2.3	3,778	0.5–365
Darfield 2010	New Zealand	GeoNet	7.2	2.8	4,641	0.5–365
Kaikōura 2016	New Zealand	GeoNet	7.8	3.2	941	0.5–365

this is not earthquake prediction

QuakeCast describes how aftershock sequences that have already begun go on to evolve: how many events above a completeness magnitude follow in the next one, seven or thirty days, and where. It does not say when or where a future mainshock will happen, and no forecast here is fit for warnings or safety decisions.

Does ML improve aftershock-rate forecasts?models →
Does it improve spatial density forecasts?space →
How does it compare with Omori–Utsu and ETAS?time →
How stable are the results across sequences?per sequence →
Does generalisation fail across tectonic regimes?regions →