On the relationship between levels of seismicity and pump parameters in a hydraulic fracturing job
Bibliographic record
Abstract
The McGarr equation gives a means of estimating the amount of seismicity associated with a fluid injection/hydrofrac job. McGarr's formula seems however to be little used: most examples in the literature contradict it. Here we analyse a number of hydrofrac datasets from gas shales to assess whether they satisfy the McGarr equation. In agreement with other authors we find that moment is proportional to injected volume but the equality is not satisfied. Combining McGarr's formula with the Gutenberg-Richter Law allows estimates to be made of the number of events expected above a given magnitude. We show that the requirement of a finite moment budget implies that the Gutenberg-Richter b-value must be less than 1.5: b=1.5 corresponds to a fractal dimension for the underlying fault network of 3. Almost all of the datasets we analysed are characterized by b values greater than 1.5 implying that in these cases the Gutenberg-Richter Law is not consistent with the assumption of a finite moment budget. Based on the data analysed, we conclude that McGarr's formula may well be valid for injection/fraccing but that most of the moment budget is lost in undetectably small events on length scales down to the grain-size.
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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 | 0.015 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".