Linear traveltime perturbation interpolation: a novel method to compute 3-D traveltimes
Bibliographic record
Abstract
Abstract The linear traveltime interpolation has been a routine method to compute first arrivals of seismic waves and trace rays in complex media. The method assumes that traveltimes follow a linear distribution on each boundary of cells. The linearity assumption of traveltimes facilitates the numerical implementation but its violation may result in large computational errors. In this paper, we propose a new way to mitigate the potential shortcoming hidden in the linear traveltime interpolation. We use the vertex traveltimes in a calculated cell to introduce an equivalent homogeneous medium that is specific to the cell boundary from a source. Therefore, we can decompose the traveltime at a point on the cell boundary into two parts: (1) a reference traveltime propagating in the equivalent homogeneous medium and (2) a perturbation traveltime that is defined as the difference between the original and reference traveltimes. We now treat that the traveltime perturbation is linear along each boundary of cells instead of the traveltime. With the new assumption, we carry out the bilinear interpolation over traveltime perturbation to complete traveltime computation in a 3-D heterogeneous model. The numerical experiments show that the new method, the linear traveltime perturbation interpolation, is able to achieve much higher accuracy than that based on the linear traveltime interpolation.
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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 | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".