Stabilizing explicit frequency‐space migration using local WKBJ operators
Bibliographic record
Abstract
We introduce a new operator for explicit wavefield extrapolation. We modify the commonly used locally homogeneous wavefield extrapolator to include a local vertical gradient, whose purpose is simply to enhance operator stability when spatially localized. The locally homogeneous operator assumes that wavefield extrapolation across a single depth step can be done with straight raypaths using the assumed constant velocity at the output point. Such operators can produce excellent seismic images but the straight ray assumption means that their spatial aperture is infinite, which leads to instability when the operator is localized by spatial windowing. Adjusting the operator to accommodate a suitably chosen positive vertical velocity gradient causes raypath curvature which naturally limits the operator within a finite aperture. The required modification to the locally homogeneous operator is essentially a WKBJ-style integrated phase. The resulting operator has a finite aperture and is sufficiently stable when localized to be used in an explicit depth migration scheme. We demonstrate operator fidelity with excellent images of the Marmousi model.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 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) | 0.002 | 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 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".