Interpolation of geophysical data using continuous global surfaces
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Bibliographic record
Abstract
Abstract A wide class of interpolation methods, including thin-plate and tension splines, kriging, sinc functions, equivalent-source, and radial basis functions, can be encompassed in a common mathematical framework involving continuous global surfaces (CGSs). The difficulty in applying these techniques to geophysical data sets has been the computational and memory requirements involved in solving the large, dense matrix equations that arise. We outline a three-step process for reducing the computational requirements: (1) replace the direct inversion techniques with iterative methods such as conjugate gradients; (2) use preconditioning to cluster the eigenvalues of the interpolation matrix and hence speed convergence; and (3) compute the matrix–vector product required at each iteration with a fast multipole or fast moment method. We apply the new methodology to a regional gravity compilation with a highly heterogeneous sampling density. The industry standard minimum-curvature algorithms and several scale-dependent CGS methods are unable to adapt to the varying data density without introducing spurious artifacts. In contrast, the thin-plate spline is scale independent and produces an excellent fit. When applied to an aeromagnetic data set with relatively uniform sampling, the thin-plate spline does not significantly improve results over a standard minimum-curvature algorithm.
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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 | 0.000 | 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 | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it