A decade- long prospective evaluation of earthquake forecasting models in California, tested against nearly 600 quakes (exactly 597 of magnitude Mw ≥ 3.95), shows that select models, especially certain versions of well- established operational ones, can reliably describe next- day patterns of earthquake numbers, locations, and magnitudes.

This comes from a University of Bristol-led study published in Nature Communications (August 2026; press coverage around October 14- 15, 2026). Researchers assessed 27 time- varying seismicity models (focusing on 21 for Mw ≥ 3.95) operated fully prospectively by the Collaboratory for the Study of Earthquake Predictability (CSEP) from August 2007 to August 2018.

These generated 51,625 automated next- day forecasts for California, using only data available before each forecast day. The forecasts were compared to the 597 observed earthquakes (depths ≤ 30 km in the CSEP- California test region), which included major sequences such as the 2010 Mw 7.2 El Mayor- Cucapah, the 2012 Brawley swarm, and the 2014 Mw 6.0 South Napa event.

Key Findings

• Roughly 95% of the models produced forecasts statistically consistent with the number of observed earthquakes (using a Negative Binomial Distribution test that better handles clustering variability; a stricter Poisson test was less favorable overall).
• About two- thirds were consistent with the spatial locations (epicenters) of the quakes.
• About 95% matched the magnitude distributions.⁠

Individually, select versions of the Epidemic- Type Aftershock Sequence (ETAS) and Short- Term Earthquake Probability (STEP) models, widely used types for operational earthquake forecasting (OEF) by agencies in places like Italy, New Zealand, and the US, showed sustained consistency with the prospective data.

Some newer models and those incorporating smaller earthquakes as inputs performed relatively better, indicating progress in forecasting skill over time. Many models slightly overestimated rates but stayed within statistical bounds cumulatively; daily performance was stronger in quieter periods or certain aftershock sequences and weaker right after the largest mainshocks (as expected, since these models struggle to anticipate the exact timing of large events themselves).

Context and Implications

These are probabilistic forecasts of rates and likelihoods (where, when, how large activity is more likely over the next day), not deterministic predictions of exact events. No method currently predicts the precise time, place, and size of the next earthquake. The California test stands out for its scale (number of models, decade- long duration, and volume of prospective observations) compared to earlier CSEP efforts in Japan, New Zealand, and Italy.⁠

The results provide strong evidence supporting the use of these model types in public OEF systems for situational awareness, especially during elevated activity periods. The team offers recommendations (“model recipes”), open- source software (including pyCSEP tools and reproducibility packages), and benchmarking data to aid development of operational systems worldwide. Funding came from the Leverhulme Trust, USGS, and Statewide California Earthquake Center.

In short, the nearly 600 California earthquakes supplied rigorous, bias- resistant validation that certain next- day seismic risk models work as intended over long periods, bolstering confidence in their practical value for preparedness without overclaiming predictive power.

ETAS (Epidemic-Type Aftershock Sequence) and STEP (Short- Term Earthquake Probability) are two leading statistical models used for short- term earthquake forecasting, particularly for aftershock sequences and clustered seismicity.

Both are widely applied in operational earthquake forecasting (OEF) systems by agencies such as the USGS, Italy’s INGV, and New Zealand’s Earth Sciences agencies. They rely on well- established empirical laws of seismicity rather than deterministic physical prediction of individual events.

Core Shared Principles

Both models describe seismicity as a combination of:

• A background (or spontaneous and long- term) rate of earthquakes.
• Triggered (clustered) seismicity, where past earthquakes increase the likelihood of future ones.

They incorporate classic empirical relations:

• Omori- Utsu law: Aftershock rates decay as a power law with time after a triggering event (roughly rate ∝ 1/(t + c)^p).
• Gutenberg- Richter law: Earthquake frequency decreases exponentially with magnitude (more small events than large ones).
• Productivity scaling: Larger earthquakes trigger more aftershocks.

These enable probabilistic forecasts of the expected rate (or probability) of earthquakes of certain magnitudes in space and time, often for the next day, week, or other short windows, without claiming to predict exact times or locations of individual shocks.

ETAS Model

Introduced by Yosihiko Ogata in the late 1980s, ETAS is a self- exciting point process (a type of Hawkes process). It treats every earthquake as a potential “parent” that can trigger its own “offspring” aftershocks, which can in turn trigger further events, forming a cascading, epidemic-like branching process.

The conditional intensity (expected rate) at a given time t, location, and above a magnitude threshold is typically expressed as:$$\lambda (x,y,t\mid H_t)=\mu (x,y)+\sum _{i:t_i<t}K\cdot {10}^{\alpha (m_i-m_c)}\cdot \nu (t-t_i)\cdot s(x-x_i,y-y_i)$$Where:

• $\mu (x,y)$ is the background rate (spatially varying, often from long-term seismicity).
• The sum is over past events i.
• $K$K and $\alpha$α control productivity (how many aftershocks a magnitude $m_i$mi​ event produces).
• ν(t– ti​) is the temporal decay (Omori- Utsu form).
• s(⋅) is a spatial kernel (often isotropic or anisotropic, decaying with distance).
• $m_c$ is a completeness magnitude threshold.

Key features:

• Fully recursive: secondary and higher- order aftershocks are naturally included.
• Parameters are usually estimated by maximum likelihood from a catalog (sometimes Bayesian methods are used for robustness).
• Flexible spatial kernels and variants exist (e.g., adaptive smoothing, incorporation of smaller events, or slow- slip effects).
• Strengths: Captures cascading triggering well; widely tested and extended; strong theoretical foundation.
• Limitations: Can be computationally intensive; sensitive to catalog incompleteness; spatial kernels are often simplified (isotropic by default).

ETAS and its variants performed well in the long- term California CSEP tests referenced in recent studies.

STEP Model

Developed by Gerstenberger and colleagues (around 2004- 2005), STEP builds on the simpler Reasenberg- Jones (1989) aftershock model and was designed for practical, real- time use (including early USGS aftershock forecasts).

It also has background and clustered components, but differs in structure:

• Background: Often taken from a long- term seismic hazard model (e.g., Frankel et al. smoothed seismicity or national hazard maps).
• Clustering: Uses the Reasenberg- Jones formulation for aftershock rates after a mainshock, extended to multiple sequences. Parameters can be generic (from past sequences in similar settings) or sequence- specific (updated as new events occur).
• Combination rule: Rates from background and aftershock components are typically combined by taking the maximum (rather than summing), which helps avoid double- counting in active areas.
• Spatial component: Empirically derived decay with distance; earthquakes are classified into primary and secondary events or clusters, with zone- specific adjustments.
• Variants such as STEPJAVA (a Java reimplementation) appear in CSEP experiments.

Key features:

• More modular and heuristic: Combines distinct model pieces rather than a single unified branching process.
• Computationally efficient and analytic in many implementations.
• Easily integrates with official long- term hazard maps for consistency.
• Strengths: Practical for operational use; adapts parameters per sequence; often produces focused “hot spots”.
• Limitations: Less fully recursive than classic ETAS in some formulations; spatial rules can be more empirical.

Main Differences

Aspect	ETAS	STEP
Triggering style	Fully recursive branching (every event can trigger others equally)	Cluster and sequence- oriented; primary vs. secondary events
Rate combination	Background and sum of all triggers	Often max(background, clustered rates)
Parameter handling	Global or regionally fitted; fixed during forecast windows	Generic and sequence- specific; updated as events accrue
Spatial treatment	Continuous kernels	Empirical zones and distance decay
Computational style	Point-process intensity	More modular, often faster for real- time use

In prospective tests (including California CSEP experiments spanning ~2007- 2018), select versions of both models showed good consistency with observed numbers, locations, and magnitudes of moderate earthquakes, supporting their use in public OEF.

Performance is often comparable, with results depending on the specific variant, catalog, and evaluation metric; neither perfectly forecasts the occurrence of large mainshocks themselves (a known limitation of pure clustering models).

Practical Use

Both generate probabilistic rate maps or expected counts for short time windows. They are routinely updated with new catalog data. Modern research continues to refine them (e.g., better handling of incompleteness, anisotropy, swarms, or hybrid deep- learning combinations).

In short, ETAS emphasizes a unified, cascading statistical process, while STEP emphasizes practical, adaptive combination of background hazard and aftershock sequences. Together they form the backbone of many current short- term seismic risk forecasts.

Select earthquake forecasting models demonstrate consistency with prospective decadal observations in California

Abstract Summary

Earthquake forecasting systems are operational in several countries.

To validate them rigorously, the authors prospectively tested 27 forecasting models (including types used for operational earthquake forecasting) operated by the Collaboratory for the Study of Earthquake Predictability (CSEP).

From August 2007 to August 2018 these models produced 51,625 next- day Mw ≥ 3.95 seismicity forecasts for California. The forecasts were evaluated against 597 observed Mw ≥ 3.95 earthquakes (depths ≤ 30 km) using community- vetted statistical methods.

Background and Methods

CSEP ran fully automated, prospective experiments to avoid retrospective bias.

Models included variants of:

• Epidemic- Type Aftershock Sequence (ETAS)
• Short- Term Earthquake Probability (STEP)
• Alternatives (e.g., PPE, EEPAS)
• Nonparametric and ensemble models

Forecasts were issued daily at midnight UTC for the next 24 hours on a spatial grid, using only prior data.

Evaluation used CSEP tests for number (Poisson and Negative Binomial Distribution), spatial distribution, and magnitude distribution, plus comparisons against a time- invariant smoothed seismicity benchmark (HKJ-ADAPTIVE-M2).

Focus was primarily on the 21 models targeting Mw ≥ 3.95 (results for a smaller set of Mw ≥ 4.95 models appear in supplementary material). The catalog included sequences such as the 2010 Mw 7.2 El Mayor–Cucapah, 2012 Brawley swarm, and 2014 Mw 6.0 South Napa.

Key Results Highlights

• Number consistency: Nearly all models (20/21 under the NBD test) matched cumulative observed counts statistically, despite fixed productivity parameters and fully automated operation. About half differed by ≤20% from observations; strong performers included STEPJAVA and certain ETAS versions.
• Daily performance: Models often under -predicted rates on the day of large mainshocks (inherent limitation of clustering models) but performed better in subsequent days or quiet periods.
• Spatial and magnitude: Over two- thirds consistent spatially; 95% matched magnitude distributions. Nonparametric and adaptive- smoothing components helped spatial skill.
• Overall, time- varying clustering models added value over purely time- invariant ones. Newer models and those using smaller earthquakes as inputs tended to perform relatively better.

Discussion and Implications

The study supports use of ETAS- and STEP- type models in public OEF for situational awareness.

Limitations remain (e.g., forecasting the exact occurrence of large events themselves and handling certain swarms). The authors offer “model recipes”, open- source reproducibility tools (Code Ocean capsule and GitHub), forecast data via CSEP, and the USGS earthquake catalog.

Data and Code Availability: Forecasts at cseptesting.org; catalog via USGS; software packages cited in the paper (including a peer- reviewed Code Ocean version).

This paper provides one of the most extensive prospective validations of next- day seismic forecasting models to date and underpins recent coverage about nearly 600 California earthquakes validating such models. The full article (including figures, methods, and supplementary material) is freely available at the linked URL.

Journal: Nature Communications, (volume 17, Article number: 9444

Published: 06 August 2026, Open access paper

DOI: 10.1038/s41467-026-76243-7

Provided: University of Bristol

Authors: José A. Bayona,
Francesco Serafini,
Fábio Silva,
Pablo Iturrieta,
William H. Savran,
Marcus Herrmann,
Warner Marzocchi,
Philip J. Maechling &
Maximilian J. Werner