PyInvGeo: An open-source Python package for regularized linear inversion in geophysics
Bibliographic record
Abstract
We developed several algorithms to solve the generalized linear inversion problem. In real-world problems, the datasets are huge and direct inversion of data matrix is not possible. Iterative algorithms can provide the desired solution by iteratively updating the solution along the opposite direction of the gradient. Hence, we develop steepest descent with ℓ 2 , Huber, Cauchy, and hybrid ℓ 1 / ℓ 2 norms regularization, conjugate gradient with smoothness and sparsity constraints, FISTA, and alternating minimization algorithms. L-curve for the ℓ 2 − ℓ 2 minimization and Generalized Cross Validation function for the ℓ 2 − ℓ 1 minimization are used to provide the optimum regularization parameter. The numerical seismic deconvolution tests on synthetic single-channel data show the performances of the different algorithms and the parameter selections. Then, based on the performances of the algorithms on single channel data, we select the conjugate gradient with sparsity constraint and FISTA for deconvolution of Teapot dome 2D real data. We find that on 2D data, the FISTA method provides sparser solutions. However, through deconvolution of 3D seismic data, by increasing the dimensions and complexity of signals of interest, we show that the FISTA algorithm struggles to provide continuous and interpretable results. To address this issue, we introduce the Hoyer-squared norm to promote sparsity. Hoyer-squared norm is almost everywhere differentiable, scale-invariant, and contrary to ℓ 1 norm it does not equally shrink all the coefficients. The 3D deconvolution shows that the Hoyer-squared method outperforms FISTA and provides a continuous and interpretable solution. Finally, we develop a Hoyer-squared-based multiple suppression in the Radon domain and successfully test the algorithm on synthetic and real marine Gulf of Mexico data. The multiple suppression algorithm is based on the parabolic Radon transform. The Python package for the algorithms and numerical testes is included for reproducibility purposes and to facilitate the use of the algorithms on different problems.
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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 | 0.005 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.004 | 0.002 |
| Research integrity | 0.001 | 0.004 |
| Insufficient payload (model declined to judge) | 0.076 | 0.037 |
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".