Magnitude‐Frequency Distributions and Slip‐History Predictions for Earthquakes Using Cellular Automata and Absorbing Markov Chains
Bibliographic record
Abstract
Abstract Cellular automata have proven effective in obtaining statistical insights into expected time series, magnitude‐frequency distributions, and average slip histories of earthquakes by confirming, for instance, the Gutenberg‐Richter magnitude‐frequency distribution and the existence of scaling functions for slip histories. Yet, exhaustive modeling is often required to obtain such insights since the model behavior is generally difficult to predict from fixed input parameters, such as the dissipation and long‐range stress interaction distance. We demonstrate that the temporal dynamics of a cellular automaton (CA), representing discretized equations of motion, can be simplified and modeled as an absorbing Markov chain with transition matrices that are fully determined by CA parameters. Time series, frequency‐size distributions, and slip histories of the Markov chain Monte Carlo (MCMC) and CA models are stochastically equivalent. The proposed method is a mean‐field approximation that replicates temporal CA statistics by ignoring spatial components. Fundamentally, the temporal portion of CA can be represented as a memoryless process in which the current outcome only depends on the immediate past. We believe the transparency of the statistical model may provide pertinent insights into the mean‐field behavior of a variety of physical applications near a critical state, including earthquake and avalanche patterns. For instance, the average slip histories display a typical but asymmetric shape due to a preferred path through probability space with initial acceleration of slip rate to peak size followed by slower deceleration toward rupture arrest.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".