Observation of diffusion processes in earthquake populations and implications for the predictability of seismicity systems
Bibliographic record
Abstract
Scale invariance, either in space or in time, has been shown in many papers to characterize earthquake distributions. Unfortunately, little work has been dedicated to looking at the general space‐time scaling invariance of seismicity systems, even though a better understanding of how the two domains (spatial and temporal) link together could help the development of the stochastic dynamical modeling of earthquake populations. In this paper we report the observation of diffusion processes of temporally correlated seismic activity for three different data sets: a mine (Creighton Mine, Canada), the Long Valley Caldera in eastern California, and a 7‐year period of recorded seismic activity in southern California. The observed subdiffusion processes are indicative of the general space‐time scaling of the system, taking the form of a slow power law growth R ( t ) ∼ t H of the mean distance R ( t ) between the main event and the temporally correlated afterevents occuring after a delay t . H is found on average to be small (0.1 for Creighton Mine, 0.22 for the Long Valley Caldera, and 0.22 for the southern California main events with magnitude ≥1.5) but fluctuates significantly from one main event to the other: the diffusion is found to be intermittent (non‐Gaussian) and multiscaling, and except for the Long Valley Caldera, a systematic correlation between the sizes of the main event and subsequent afterevents and the growth exponent H is observed. While classical viscous relaxation models (e.g., elastic listhosphere‐plastic asthenosphere coupling, or fluid flow triggered by sudden changes in pore pressure) have been proposed to characterize this relaxation by homogeneous (i.e., nonintermittent) normal ( H = 0.5) diffusion processes, the direct implication of the reported results is that seismicity systems, at spatial scales from meters to hundreds of kilometers and small (microearthquakes in a mine) to intermediate magnitudes, relax spatiotemporally in a nonelastic way, revealing the stochastic space‐time scale‐invariant nature of such systems. Since these diffusion processes correspond to a loss of information with time on the location of the main event, they can be used to investigate the limits of predictability, at all spatial scales, of seismicity systems in terms of the spatiotemporal clustering of temporally correlated earthquakes.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".