Temporal Dispersion Correction and Prediction by Using Spectral Mapping
Bibliographic record
Abstract
Summary Time-domain finite difference (FD) modeling for wave propagation has been widely used for illumination studies and advanced imaging techniques such as RTM and FWI in complex geology. Any finite-order approximation of the time and space derivatives using FD methods suffer from some degree of numerical dispersion. The temporal and spatial dispersion are independent of each other. Spatial dispersion can be reduced with higher-order finite difference operators and optimized coefficients. The time derivatives are usually approximated to 2nd order. Thus, FD-based simulations and imaging methods often suffer from numerical temporal dispersion error. In this paper, we show that the numerical temporal dispersion from 2nd-order time FD can be corrected via a trace-by-trace spectral mapping operation. For RTM, this spectral mapping operation is to add the predicted temporal dispersion into each gather before backward propagation. This approach eliminates the temporal dispersion at only small cost. One clear benefit of the temporal dispersion correction is a significant speed up because a larger time step can be used.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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".