Long wavelength solutions to the surface consistent equations
Bibliographic record
Abstract
The surface consistent equations always have one or more singular values, depending on the configuration of the seismic survey. These singular values slow convergence, add uncertainty, and make it difficult to resolve the long wavelengths in the solution. Multigrid methods possess a greater ability to resolve long wavelength terms than Gauss‐Seidel methods that are currently in use. These improved solutions are calculated at little or no additional computational cost. While total convergence is not guaranteed, multigrid methods seem to be able to universally improve the quality of surface consistent decomposition. There are some limitations we reach in solving the surface consistent equations. An attempt is made to further justify our previous conclusion (Millar and Bancroft, 2004) that some of the long wavelength drift that can plague Gauss‐Seidel solutions is theoretically avoidable. In more or less the same amount of computer time using multigrid techniques we are getting more accurate synthetic solutions. We see how the quality of our solution depends on the geometry of the survey, and the role singular values play in the solution. Lastly, we explore the challenges of including of a time variant term in the equations 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) | 0.001 | 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".