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.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 |
| 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) | 0.003 | 0.001 |
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".