Triggering cascades and statistical properties of aftershocks
Bibliographic record
Abstract
Applying a simple general procedure for identifying aftershocks, we investigate their statistical properties for a high‐resolution earthquake catalog covering Southern California. We compare our results with those obtained by using other methods in order to show which features truly characterize aftershock sequences and which depend on the definition of aftershocks. Features robust across methods include the p value in the Omori‐Utsu law for large main shocks, Båth's law, and the productivity law with an exponent smaller than the b value in the Gutenberg‐Richter law. The identification of a typical aftershock distance with the rupture length is a feature we confirm as well as a power law decay in the spatial distribution of aftershocks with an exponent less than 2. Other results we obtain, but not common to all other works including Marsan and Lengliné (2008), Hainzl and Marsan (2008), and Zhuang et al. (2008), are (a) p values that do not increase with the main shock magnitude; (b) the duration of bare aftershock sequences that scales with the main shock magnitude; (c) an additional power law in the temporal variation, at intermediate times, in the rate of aftershocks for main shocks of small and intermediate magnitude; and (d) a b value for the Gutenberg‐Richter law of background events that is sensibly larger than that of aftershocks. Tests on synthetic catalogs generated by the epidemic‐type aftershock sequence model corroborate the validity of our approach.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.017 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.003 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".