Mitigating Cycle Skipping in Full Waveform Inversion by Using a Scaled-Sobolev Objective Function
Bibliographic record
Abstract
Summary Cycle skipping in the conventional full waveform inversion (FWI) objective function depends on the frequency content of the data, and on the error in the background velocity. The error in background velocity that can be tolerated without skipping cycles is determined by the half cycle criterion. However, the half cycle criterion is offset dependant so that far offsets in the data are more prone to cycle skipping than near offsets. This offset dependence of the half cycle criterion implies that the differentials of residuals with offset can be used as additional constraints in the objective function. In this study we introduce the scaled-Sobolev objective (SSO) that seeks to minimize a smooth version of the data residuals in addition to their derivatives in all data domain dimensions. The smoothing of the data is done using the scaled-Sobolev inner product (SSIP) in the data domain, resulting in an edge-preserving smoothing operator. In the absence of low frequencies, increasing the maximum order of derivatives in SSO is more important than the zeroth order scale factor. Initial results with synthetic data using the Marmousi model show that SSO can overcome a bulk shift in velocity of 30%, with a lowest frequency of 8 Hz.
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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 | 0.003 |
| 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 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".