HIGH-ORDER PSEUDO-ANALYTICAL METHOD FOR ACOUSTIC WAVE MODELING
Bibliographic record
Abstract
For the time evolution of acoustic wavefields we present an alternative derivation of the pseudo-analytical method, which enables us to generalize the method to high-order formulations. Within the same derivation framework, we compare the second-order pseudo-analytical method, the Fourier finite difference method, and the fourth-order Lax-Wendroff time integration method. We demonstrate that the pseudo-analytical method can be regarded as a modified Lax-Wendroff method. Different from the fourth-order time stepping method, both the second-order pseudo-analytical method and the Fourier finite difference method use pseudo-Laplacians to compensate for time stepping errors. The pseudo-Laplacians need to be solved in the wavenumber domain with constant compensation velocities for computational simplicity and efficiency. Low-order pseudo-Laplacians are more sensitive to the choice of compensation velocities than high-order ones. As a result, we need to use the combination of several pseudo-Laplacians to achieve the required accuracy for low-order pseudo-analytical methods. When using the pseudospectral method to evaluate all spatial derivatives, the computation cost for the second-order pseudo-analytical method, the Fourier finite difference method, and the fourth-order Lax-Wendroff time integration method is approximately the same. Both the second-order pseudo-analytical method and the Fourier finite difference method have less restrictive stability conditions than the fourth-order time stepping method. We demonstrate with numerical examples that the second-order pseudo-analytical method, greatly improves the original pseudo-analytical method and as a modified version of the Lax-Wendroff method, is well suited for imaging seismic data in subsalt areas where reverse-time migration plays a crucial role.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.003 |
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".