Stress inversion of shear-tensile focal mechanisms with application to hydraulic fracture monitoring
Bibliographic record
Abstract
Stress inversion methods used to evaluate the state of stress from multiple earthquake focal mechanisms are based on the Bott hypothesis, which assumes that the slip vector lies in the fault plane and is parallel to the maximum resolved shear stress in that plane. This assumption does not consider non-double-couple source components, which may be significant in some scenarios such as hydraulic fracturing, where a large fluid volume is injected to induce tensile rock failure. With the introduction of a modified Bott hypothesis that allows for out-of-plane slip, we develop a stress inversion algorithm that accounts for tensile components of the source mechanism. The composite Griffith Mohr–Coulomb criterion is utilized for fault stability characterization. Synthetic tests are used to quantify the error in stress determination that arises when conventional stress inversion is applied in the presence of non-double-couple sources. A statistical approach is applied to analyse the minimum number of focal mechanisms required for reliable inversion results. We find that at least 30 focal mechanisms with diverse orientations are required in the presence of typical noise levels. We evaluate our method using microseismic data collected from Barnett Shale in the Fort Worth Basin, Texas. The inferred effective stress state is characterized by a subhorizontal maximum principal stress, with intermediate and minimum principal stresses deviating from the vertical and horizontal planes, respectively.
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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 | 0.002 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| 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 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".