A regularized approach for estimation of a composite focal mechanism from a set of microearthquakes
Bibliographic record
Abstract
ABSTRACT We have developed a novel regularized approach to estimate a composite focal mechanism for microseismic events that share a similar source mechanism. The method operates by minimizing the weighted misfits of the SH/P amplitude ratios (in absolute sense and logarithmic scale) and P-wave polarities, using a regularization parameter determined from the trade-off curve for these values. This approach overcomes the low signal-to-noise ratio (S/N) and single-event azimuthal gaps that may otherwise limit the effectiveness of sparse surface arrays. Compared with focal mechanisms derived from P-wave polarity or amplitude-based methods, our regularized approach reduces the multiplicity of solutions and avoids the use of signed amplitude ratios, which may be ambiguous for data with low S/N. We apply our method to a set of 13 microseismic events recorded during hydraulic-fracture stimulation of the Marcellus Shale in West Virginia and Pennsylvania, USA, yielding a strike-slip focal mechanism accompanied by a minor normal component. Our solution is similar to previously reported focal mechanisms in this area. Jackknife analysis, which tests stability of the inversion based on random sampling of the observation, indicates 95% confidence intervals of 1° and 2°, respectively, for the plunge and azimuth of the P and T axes. By analyzing the event subsets, outliers are identified and the assumption of a single dominant focal mechanism is validated. Numerical modeling demonstrates that our approach is robust in the presence of variations of up to 0°–10° and 0°–35°, respectively, for the plunge and azimuth of P and T axes of the focal mechanisms of these events. Sensitivity analysis using synthetic data also indicates that the algorithm is tolerant to mispicks as well as errors in polarity and amplitude ratio. In the presence of some dissimilar focal mechanisms, the dominant focal mechanism can be reliably estimated if at least 70% of the events have similar source mechanisms.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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".