A hexagonal finite difference mesh for 2D TTI RTM
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Bibliographic record
Abstract
A common finite difference implementation of reverse time migration with tilted transverse isotropy (TTI) follows the formulation of Alkhalifah (2000), Fletcher et. al. (2008) and Zhou et. al. (2006). The finite difference implementation of these equations in Cartesian coordinates necessitates the computation of mixed partial derivatives of the acoustic pressure in the spatial domain. Different methods exist for the computation of these mixed derivatives including sequentially computing centered first derivatives in each direction, computing staggered first derivatives with interpolation or the pseudospectral method. The computation of centered first derivatives causes ringing in the output but using staggered derivatives requires interpolation of the staggered points back to the original grid. The pseudospectral method necessitates the computation of a 2D FFT in a 2D simulation. In this paper, we propose a hexagonal mesh for the finite difference implementation of 2D TTI RTM. The implementation eliminates the need for mixed partial derivatives and reduces grid dispersion in wave simulations.
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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