Event locations: speeding up grid searches using quadratic interpolation
Bibliographic record
Abstract
SUMMARY The grid search method is a common approach to estimate the three spatial coordinates of event hypocentres. However, locating events in large search spaces with small grid spacings is computationally prohibitive. This study accelerates the grid searches over large search spaces using a quadratic interpolation technique. We start with the coarse-grid-estimated location, where we have the minimum value of the difference in the traveltimes between S and P waves summed over all receivers. Then, we select the neighbouring grid points and build a 3D quadratic function. The unknown coefficients of the 3D quadratic function are computed by solving a system of linear equations. After that, we interpolate the location by solving partial derivatives of the quadratic function. The quadratic interpolation technique performs well on both synthetic and real microseismic data examples, typically leading to similar event locations as those obtained using 10 times smaller grid spacings in all three directions, at a minor additional computational expense, and without the need to generate traveltimes at new spatial positions.
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How this classification was reachedexpand
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 | 0.001 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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 teacher head, 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".