Scaling relations and spectral characteristics of tensile microseisms: evidence for opening/closing cracks during hydraulic fracturing
Bibliographic record
Abstract
Using formulae for both tensile and shear sources, we investigate spectral characteristics of microearthquakes induced by hydraulic fracturing, with application to passive-seismic data recorded during a multistage treatment programme in western Canada. For small moment magnitudes (Mw < 0), reliable determination of corner frequency requires accurate knowledge of QP and QS, although spectral estimates of magnitude are relatively unaffected by uncertainty in seismic attenuation. Here, we estimate QP and QS using spectral ratios derived from perforation shots. Of the microseismic events analysed during the hydraulic-fracture treatment, 17 of 20 exhibit an S/P spectral ratio <5, which is consistent with tensile failure. In addition, four microseismic events are characterized by a modulating source spectrum containing quasi-periodic notches. We interpret this spectral character to reflect a complex rupture pattern that involves rapid (5−8 ms) opening and closing of tensile cracks. In general, for tensile rupture on a penny-shaped crack, our model predicts that source radius (a) is related to moment magnitude (Mw) and internal fluid pressure within the fracture (Pi) by a simple empirical scaling relation: log10(a) = [9 − log102]/3 + 0.5Mw − log10(Pi)/3.
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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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".