Poisson Downward Continuation Solution by the Jacobi Method
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Bibliographic record
Abstract
Poisson Downward Continuation Solution by the Jacobi Method Downward continuation is a continuing problem in geodesy and geophysics. Inversion of the discrete form of the Poisson integration process provides a numerical solution to the problem, but because the B matrix that defines the discrete Poisson integration is not always well conditioned the solution may be noisy in situations where the discretization step is small and in areas containing large heights. We provide two remedies, both in the context of the Jacobi iterative solution to the Poisson downward continuation problem. First, we suggest testing according to the upward continued result from each solution, rather then testing between successive solutions on the geoid, so that choice of a tolerance for the convergence of the iterative method is more meaningful and intuitive. Second, we show how a tolerance that reflects the conditioning of the B matrix can regularize the solution, and suggest an approximate way of choosing such a tolerance. Using these methods, we are able to calculate a solution that appears regular in an area of Papua New Guinea having heights over 3200 m, over a grid with 1 arc-minute spacing, based on a very poorly conditioned B matrix.
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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 | 0.003 | 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 | 0.000 |
| 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