Improving the use of the randomized singular value decomposition for the\n inversion of gravity and magnetic data
Bibliographic record
Abstract
The large-scale focusing inversion of gravity and magnetic potential field\ndata using $L_1$-norm regularization is considered. The use of the randomized\nsingular value decomposition methodology facilitates tackling the computational\nchallenge that arises in the solution of these large-scale inverse problems. As\nsuch the powerful randomized singular value decomposition is used for the\nnumerical solution of all linear systems required in the algorithm. A\ncomprehensive comparison of the developed methodology for the inversion of\nmagnetic and gravity data is presented. These results indicate that there is\ngenerally an important difference between the gravity and magnetic inversion\nproblems. Specifically, the randomized singular value decomposition is\ndependent on the generation of a rank $q$ approximation to the underlying model\nmatrix, and the results demonstrate that $q$ needs to be larger, for equivalent\nproblem sizes, for the magnetic problem as compared to the gravity problem.\nWithout a relatively large $q$ the dominant singular values of the magnetic\nmodel matrix are not well-approximated. The comparison also shows how the use\nof the power iteration embedded within the randomized algorithm is used to\nimprove the quality of the resulting dominant subspace approximation,\nespecially in magnetic inversion, yielding acceptable approximations for\nsmaller choices of $q$. The price to pay is the trade-off between approximation\naccuracy and computational cost. The algorithm is applied for the inversion of\nmagnetic data obtained over a portion of the Wuskwatim Lake region in Manitoba,\nCanada\n
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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 | 0.002 | 0.007 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| 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".