Combining Ray-Tracing Techniques and Finite-Element Modelling in Deformable Media
Bibliographic record
Abstract
We propose a numerical ray-tracing algorithm for isotropic media discretized by finite elements. This algorithm, which is based on tetrahedral elements, combines the flexibility of finite-element modelling with the calculation of rays through a three-dimensional (3D) speed field, given a direction of a ray at its initial point. We implement this algorithm and investigate the sensitivity of rays (namely, their shape and the signal travel time along them) to (i) deformations of the medium and subsequent changes of its speed field and (ii) perturbations of initial direction in the presence of first- and second-order discontinuities. We consider several scenarios analytically, and use them to verify the finite-element scheme. The ray-tracing scheme accounts for Snell’s law at interfaces of velocity discontinuities and intrinsically handles discontinuous velocity gradients. It accommodates objects of arbitrary 3D shape and arbitrary speed fields. Furthermore, this finite-element technique accounts for deformations of a discretized medium on the level of each node by moving the node location and associated value of velocity. For several numerical experiments, we deform different models to observe deviations of rays from their initial shape. This study shows how the computation of rays can be combined with finite-element calculations of static elastic deformations, with implications to seismic and optical studies.
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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 | 0.002 | 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 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".