Mitigating Non-linearity in Full Waveform Inversion by Scaled Sobolev Pre-conditioning
Bibliographic record
Abstract
Summary Seismic full waveform inversion (FWI) can be linearized by implementing a first-order Born approximation. However, this requires good a-priori knowledge of the background velocity. The problem of updating the background velocity in FWI can be handled by spatial scale separation of the velocity variations. Still, it is the Born approximation that decides which velocity scales can be considered as reflectivity which scale is the background. We propose a new scale separation technique based on spatial derivatives of the velocity functions. Its incorporation into FWI results in a pre-conditioning scheme that is a scaled version of the Sobolev gradient. The per-iteration computational cost in applying this scaled Sobolev pre-conditioner is negligible. Sobolev gradients have been used in image processing to help convergence in non-linear problems. In our scaled version, the scaling parameters allow switching between different scales of velocity updates and thereby mitigating the non-linearity in FWI by initially switching to very low-wavenumber (background velocity) updates; small scale updates are included naturally during the later iterations. Numerical examples on the Marmousi models show the potential of the scaled Sobolev preconditioning.
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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 | 0.001 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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 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".