HIGH-ORDER PSEUDO-ANALYTICAL METHOD FOR ACOUSTIC WAVE MODELING
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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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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.003 | 0.005 |
| Science and technology studies | 0.002 | 0.012 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.001 |
| 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