Efficient and Stable Finite Difference Modelling of Acoustic Wave Propagation in Variable-density Media
Bibliographic record
Abstract
In this paper, we consider the development and analysis of a new explicit compact high-order finite difference scheme for acoustic wave equation formulated in divergence form, which is widely used to describe seismic wave propagation through a heterogeneous media with variable media density and acoustic velocity. The new scheme is compact and of fourth-order accuracy in space and second-order accuracy in time. The compactness of the scheme is obtained by the so-called combined finite difference method, which utilizes the boundary values of the spatial derivatives and those boundary values are obtained by one-sided finite difference approximation. An empirical stability analysis has been conducted to obtain the Currant-Friedrichs-Lewy (CFL) condition, which confirmed the conditional stability of the new scheme. Four numerical examples have been conducted to validate the convergence and effectiveness of the new scheme. The application of the new scheme to a realistic wave propagation problem with Perfect Matched Layer boundary condition is also validated in this paper as well.
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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) | 0.000 | 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".