A New Finite Difference Eikonal Equation Solver for Anisotropic Medium
Bibliographic record
Abstract
Summary The fast sweeping method has been proved very efficient in calculating the first arrivals in isotropic media. In this study, we extend the fast sweeping method to heterogeneous anisotropic medium by adapting the Lax-Friedrichs local scheme. The new fast sweeping method is able to solve the first arrival traveltime field for both qP and qS waves. By comparing the traveltime field to the full-waveform solution, we demonstrate that the iso-surfaces of the time field follow the constant phase of the wave and form a continuous envelope wrapping the wavefront. The iso-surfaces for the shear wave identify two continuous wavefronts one ahead of the other even in the directions where the triplication of qS-wave is developed. The rays for both qP and qS wave can be traced using the slowness vector from the traveltime field and we compared its accuracy with a two-point ray tracing method in a layered model. We show that rays from the traveltime field is nearly identical to the two-point ray tracing results. This new fast sweeping method not only avoids the multipath and shadow zone issues in complex heterogeneous media but also circumvent the multiple shear branch problems due to anisotropy.
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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 | 0.000 | 0.001 |
| 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 | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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 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".