Solid angles and the impact of receiver-array geometry on microseismic moment-tensor inversion
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Bibliographic record
Abstract
ABSTRACT Seismic moment tensors provide a concise mathematical representation of point sources that can be used to characterize microseismic focal mechanisms. After correction for propagation effects, the six independent components of a moment tensor can be found by least-squares inversion based on P- and/or S-waveform (or spectral) amplitudes observed at different directions from the source. Using synthetic waveform data, we investigated geometrical factors that affect the reliability of such inversions. We demonstrated that the solid angle subtended by the receiver array, as viewed from the source location, plays a fundamental role in the stability of the inversion. In particular, the condition number of the generalized inverse scales approximately inversely with the solid angle, implying that for a solid angle of zero (as is the case for a single vertical borehole) the inversion is ill-conditioned. The presence of random noise alsohas a significant effect on the inversion results; our results showed that the signal-to-noise ratio (S/N) for reliable inversion scales approximately as the square root of the condition number. Taken together with geometrical considerations, we found that a S/N>10 is generally needed to obtain reliable inversion results for the full moment tensor under certain microseismic acquisition scenarios that include dual observation wells or surface star pattern. Our numerical tests indicated that least-squares moment-tensor solutions obtained under nonideal conditions are biased toward limited regions of the full parameter space. In particular, random noise introduces a bias toward volumetric source types, whereas ill-conditioned inversions may exhibit bias toward poorly resolved eigenvector(s) of the inversion matrix. Possible strategies to improve the reliability of moment-tensor inversion include ensuring a nonzero solid-angle aperture by using multiple observation wells, and/or incorporating other types of data such as a priori knowledge of fracture orientation.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it