A Model Based Data Driven Dictionary Learning for Seismic Data Representation
Bibliographic record
Abstract
Summary In this work, we consider a space-time variable signal cone to model seismic data. The signal cone variability is obtained through scaling, slanting and translation of the kernel for cone-limited (C-limited) functions (functions whose Fourier transform lives within a cone) or for C-Gaussian function (a multivariate function whose Fourier transform decays exponentially with respect to slowness and frequency), which constitutes our dictionary. We find a discrete number of scaling, slanting, and translation parameters from a continuum by optimally matching the data. This is a nonlinear optimization problem which we address by a fixed point method that utilizes a variable projection method with $ell_{1}$ constraints on the linear parameters and other constraints on the nonlinear parameters. We observe that slow decay and oscillatory behavior of the kernel for C-limited functions constitute bottlenecks for the optimization problem which we partially overcome by the C-Gaussian function. We demonstrate our method through an interpolation example. We present the interpolation result using the estimated parameters obtained from the proposed method and compare it with those obtained using sparsity promoting curvelet decomposition, matching pursuit Fourier interpolation and sparsity promoting plane wave decomposition methods.
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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) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| 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 | 0.001 |
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".