Reconstruction of seismic data using adaptive regularization
Bibliographic record
Abstract
In seismic data processing, we often need to interpolate/extrapolate missing spatial locations in a domain of interest. The reconstruction problem can be posed as an inverse problem where from inadequate and incomplete data one attempts to recover the complete band-limited seismic wavefield. However, the problem is often ill posed due to factors such as inaccurate knowledge of bandwidth and noise. In this case, regularization can be used to help to obtain a unique and stable solution. In this paper, we formulate band-limited data reconstruction as a minimum norm least squares type problem where an adaptive DFT-weighted norm regularization term is used to constrain solutions. In particular, the regularization term is updated iteratively through using the modified periodogram of the estimated data. The technique allows for adaptive incorporation of prior knowledge of the data such as the spectrum support and the shape of the spectrum. The adaptive regularization can be accelerated using FFTs and an iterative solver like preconditioned conjugate gradient algorithm. Examples on synthetic and real seismic data illustrate improvement of the new method over damped least squares estimation.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 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".