Bibliographic record
Abstract
Explicit wavefield extrapolators are based on direct analytic mathematical formulae that express the output as an extrapolation operator acting on the input, while implicit methods usually require the calculation of the numerical inverse of a matrix to obtain the output.Typically, explicit methods are faster than implicit methods, and they often give more insight into the physics of the wave propagation, but they often suffer from instability.Four different explicit extrapolators based on Fourier theory are presented and analysed.They are: PS (ordinary phase shift), GPSPI (generalized phase shift plus interpolation), NSPS (non-stationary phase shift) and SNPS (symmetric non-stationary phase shift).A formal proof is given that NSPS in a direction orthogonal to the velocity gradient is the mathematical adjoint process to GPSPI in the opposite direction.This motivates the construction of SNPS that combines NSPS and GPSPI in a symmetric fashion.This symmetry (under interchange of input and output lateral coordinates) is required by reciprocity arguments.PS and SNPS are symmetric while NSPS and GPSPI are not.A numerical stability study using SVD (singular value decomposition) shows that all of these extrapolators can become unstable for strong lateral velocity gradients.Unstable operators allow amplitudes to grow non-physically in a recursion.Stability is enhanced by introducing a small (∼3 per cent) imaginary component to the velocities.This causes a numerical attenuation that tends to stabilize the operators but does not address the cause of the instability.For the velocity model studied (a very challenging case) GPSPI and NSPS have exactly the same instability while SNPS is always more stable.Instability manifests in a complicated way as a function of extrapolation step size, frequency, velocity gradient, and strength of numerical attenuation.The SNPS operator can be stabilized over a wide range of conditions with considerably less attenuation than is required for NSPS or GPSPI.
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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 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.004 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.016 | 0.004 |
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".