Summary and research objective

The project asks whether medium- and long-term local variation that may be missing from the direct background component of ETAS can be converted into forecast skill using only information available before forecast issuance, while ETAS continues to model short-term aftershock triggering.

CH-008 is not an independent earthquake-generation model or a replacement physical law for ETAS. It is a controlled challenger that preserves ETAS triggering, magnitude model, and total daily expected event count. Its sole intervention is the spatial allocation of ETAS direct-background mass.

Development logic

The project first reproduced a published ETAS application and aligned an independent native implementation with it. Early challengers examined spatial residuals and latent fault-network states. CH-004 introduced a magnitude-marked renewal clock measured in expected ETAS root-hazard units. CH-006 added frailty, but frailty did not contribute skill in its initially selected regime; that result was retained as a negative mechanism finding. CH-007 validated a stronger renewal-only regime. CH-008 widened only two search upper bounds and selected an interior parameter point at which renewal and frailty both made separately measurable contributions.

ETAS baseline

The Epidemic-Type Aftershock Sequence model treats earthquakes as a marked space-time point process. Conditional intensity at a place and time is the sum of direct background seismicity and triggering contributions from prior events:

μ(x) is direct background intensity. The kernel g includes magnitude-dependent productivity, modified Omori temporal decay, and a magnitude-dependent spatial kernel. Events are not assigned a certain “mainshock” or “aftershock” label; the background share at the event is represented probabilistically:

The baseline in this project is not a simple historical-rate map. It is locked at commit level to the EarthquakeNPP ComCat_25 experiment and the Mizrahi–Nandan–Wiemer space-time implementation. Native conditional intensity, kernel integrals, likelihood, and catalog-continuation tests were aligned with reference outputs.

CH-008 approach

Decomposing ETAS intensity into background and triggering, CH-008 modifies only the former:

This mass-preservation contract provides three controls: ETAS aftershock triggering remains unchanged, the models have identical total expected daily counts, and any gain must come from assigning direct-background events to more appropriate spatial cells.

From latent score to background distribution

The renewal and frailty states are combined into a cell or fault score. ETAS background probability is exponentially tilted by this score, but both the log tilt and the mass allowed to depart from ETAS are bounded:

Approximately 72.4% of background mass therefore remains in the direct ETAS distribution under all conditions. CH-008 cannot diverge without limit when a latent state is noisy or wrong.

Two causal latent states

1. Magnitude-marked renewal age

The degree to which an event resets local state is weighted by both its ETAS background posterior and its magnitude. In a dense aftershock sequence, p_bg is small, so aftershocks have less influence on the long-memory clock. The magnitude mark is:

Normalized hazard age increases with expected background hazard and decreases with observed, softly classified, magnitude-marked root-event mass:

Local age is blended with neighboring age and passed to a unit-mean Brownian Passage Time (BPT) hazard. Only positive log excess above the memoryless unit hazard is retained:

This clock is not elapsed physical time since a known major fault rupture. It is a dimensionless statistical age measured in the direct-event hazard expected by ETAS.

2. Discounted Gamma–Poisson frailty

Frailty measures whether the softly observed direct-event mass of a cell or fault neighborhood remains persistently above the mass expected by ETAS. Expected exposure X and observed posterior root mass Y exponentially discount old history:

Negative or negligible log frailty is set to zero, and the local value is blended with neighbors to a limited degree. Frailty is not physical fault strength. It is a regularized, dimensionless local-susceptibility indicator inferred from the catalog relative to ETAS expectation.

Regional exposure normalization

Because cell areas, catalog durations, and activity rates differ, the renewal clock outside California is normalized using pre-evaluation history only:

The same constant scales expected and observed reset mass. The target period cannot determine this scale, CH-008 parameters are not refitted, and exactly one candidate is evaluated per external region.

Locked CH-008 parameters

Selection used an unscored warm-up beginning in 2007 followed by the 2014–2018 California development period. Sixty-four scrambled Sobol points and the exact ETAS control were compared under an annual-risk-sensitive rule. No outcome from 2019 onward entered parameter selection. The selected renewal weight is interior to the expanded 4.0 bound, and the mixture fraction is interior to the expanded 0.5 bound.

Data sources and geographic contract

Each event retains source identity, UTC origin time, location, magnitude, depth, source update time, and a raw-payload hash where available. Forecast issue time is exclusive: an event at or after issue time cannot enter forecast history. Magnitude completeness is a predeclared experiment parameter for each region.

In California, CH-008 state is computed on UCERF3 fault branches and transferred to the forecast grid through proximity weights and a branch-consensus filter. New Zealand and Chile use the same renewal–frailty mechanism on 0.5° latent cell-neighborhood graphs. The same model family and parameter values are used, but the geometric adapters are not identical.

The New Zealand retrospective fit period is 1987–2007 and its evaluation period is 2008–2025. Chile uses 2000–2014 for fit and 2015–2025 for evaluation. Region, threshold, period, normalization, and admission gates were recorded before target-catalog scores were opened.

Leakage-free daily workflow

Each target window is one UTC day. Events observed during that day cannot alter its already published forecast; they enter only the next state. Forecast backfill is forbidden. The California ETAS grid uses 10,000 native catalog continuations with analytical background roots. New Zealand and Chile are scored with native sequential conditional intensity, in which only strictly earlier events may trigger a target event.

Success metric and uncertainty

Information gain for a target event is the log conditional-rate ratio against ETAS. The primary metric is its event-wise mean:

IGPE > 0 means that CH-008 assigned a higher geometric-mean conditional intensity than ETAS to the observed events. Because CH-008 preserves total mass, triggering, and magnitude distribution, the ideal paired compensator difference is zero. The test therefore primarily compares conditional spatial background allocation.

Retrospective uncertainty was measured with 10,000 stationary daily block-bootstrap replicates, using mean block lengths of 30 and 90 days to partly retain earthquake-sequence dependence. The prospective system records a provisional score from the first observed catalog and a final score after a seven-day revision window. Event-free days remain recorded but do not contribute to event-wise IGPE.

Retrospective evidence

In California 2019–2022, full CH-008 gained an additional +0.000802 IGPE over its renewal-only ablation; in 2023–2026 the increment was +0.001816. Paired 30- and 90-day bootstrap lower bounds were positive in both periods, supporting a measurable frailty contribution in the selected combined regime.

For low-ETAS events, IGPE was +0.022916 in 2019–2022 and +0.028800 in 2023–2026. For M4+ events, the corresponding values were +0.008580 and +0.013505. All six three-year New Zealand intervals and all eleven annual Chile scores from 2015 through 2025 were positive. These are supportive findings consistent with the model design, not independent prospective evidence.

Live prospective protocol

The current study is a 14-day operational dry run identified as ch008-three-region-dry-run-v1. California, New Zealand, and Chile share the same daily issue clock. Forecasts are permanently published at least 1,425 minutes before the target day begins; every grid, state, and manifest is identified by SHA-256.

• Dry-run scores do not count toward a scientific prospective-superiority claim.
• After the dry run, a separate activation manifest is required without model or feature changes.
• The planned primary test lasts 365 days and requires at least 500 combined target events across the three regions.
• Any change to parameters, features, catalog thresholds, or geometry requires a new model and protocol identity.
• Forecast backfill is prohibited; only artifacts published before their target window count.
• Regional results are reported separately, while the primary decision uses a predeclared combined paired IGPE.

The live dashboard reports pipeline health, region publication, catalog cutoffs, provisional and final daily scores, and 14-day progress. Once 14 common target days have been scored, the seven-day catalog-settlement period is tracked separately.

Reproducibility and audit trail

Reference dependencies are locked by commit, and model and experiment artifacts by SHA-256. The recorded EarthquakeNPP commit is 26d18048…, the compatible ETAS commit is 51e0c8e4…, and the SeismoStats commit is 4d617d6b…. The CH-008 model hash is 72e030a4….

Forecast grids, states, and manifests are stored under deterministic keys in Hetzner Object Storage. PostgreSQL stores catalog snapshot identities, forecast runs, artifact hashes, daily scores, and incidents. Raw rolling-catalog responses are retained. The service health endpoint checks the database and, when required, object-storage access.

Source code, locked configuration, model files, migrations, and the scientific wiki are public in the GitHub repository. Native formulas and operational contracts are covered by automated tests. Failed experiments remain in the experiment index, preventing the history from being rewritten around positive outcomes alone.

Limitations and responsible use

1. The strongest current results are retrospective; the live dry run is not scientific superiority evidence.
2. CH-008 primarily improves conditional spatial background allocation. It does not change the magnitude distribution or total daily rate.
3. California uses fault-network geometry, while New Zealand and Chile use cell-neighborhood geometry. This adapter difference must remain explicit.
4. Catalog locations, magnitudes, and event identities can be revised. Provisional and final scores are therefore distinct.
5. Network coverage and magnitude completeness vary in space and time; a fixed Mc does not eliminate all such heterogeneity.
6. Short-term incompleteness after major events may affect ETAS posteriors and therefore the CH-008 state.
7. A single year may not provide adequate power in every region; this is why the duration gate is paired with a minimum-event gate.
8. This system is not a public earthquake alert, early-warning service, or tool for individual safety decisions.

Core references and project records

1. Ogata, Y. (1988). Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes. DOI
2. Mizrahi, L., Nandan, S., and Wiemer, S. (2021). Embracing Data Incompleteness for Better Earthquake Forecasting. DOI
3. Matthews, M. V., Ellsworth, W. L., and Reasenberg, P. A. (2002). A Brownian Model for Recurrent Earthquakes. DOI
4. Field, E. H., et al. (2013). Uniform California Earthquake Rupture Forecast, Version 3. USGS OFR 2013-1165
5. Politis, D. N., and Romano, J. P. (1994). The Stationary Bootstrap. DOI
6. Rhoades, D. A., et al. (2010). New Zealand CSEP Testing Centre. DOI
7. CSEP and pyCSEP test theory
8. EarthquakeNPP reference software and the ETAS reference implementation
9. CH-008 scientific review dossier
10. Locked three-region dry-run protocol