Regularized 2D Savitzky–Golay derivative filter in estimating the second vertical derivative of potential field data
Bibliographic record
Abstract
ABSTRACT A robust method of estimating the second vertical derivative of two‐dimensional (2D) potential field data is proposed. The proposed method uses a 2D variant of Savitzky–Golay derivative filtering. The design of the 2D Savitzky–Golay derivative filter, unlike its one‐dimensional (1D) counterpart, is a non‐trivial exercise. This is due to the inherent complexity associated with 2D polynomial regression, which increases with the increase in the degree of the polynomial and the dimension of the filter window. The measure of complexity increases manifold, as the polynomial order increases from cubic to quintic. A larger polynomial order demands a larger dimension of the filter window patch as a minimum requirement. The large window patch which, in turn, poses computational challenges, becomes an ill‐posed problem and is computationally inefficient. To alleviate such a problem, an appropriate set of filter parameters is proposed, which ensures computational efficiency while maintaining sufficient robustness. The computational issue arising from the ill‐posed condition of the system matrix is addressed via shrinkage ‐based regularization. A numerical experiment was conducted on a synthetically generated 2D dataset without and with a moderate amount of Gaussian random noise in order to check the applicability of the proposed method. The performance in terms of robustness was also compared with the other, usually considered as a benchmark, method. The proposed method is then successfully applied to determine the second vertical derivative of the high‐resolution Bouguer gravity anomaly data over an impact crater in Lake Wanapitaei, Canada. A qualitative interpretation of the second vertical derivative map over Lake Wanapitei is given.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 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 teacher head, 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".