Modeling topographical density for geoid determinationThis article is one of a series of papers published in this Special Issue on the theme<i>GEODESY</i>.
Bibliographic record
Abstract
In geoid computation, effects of real three-dimensional topographic masses on the Earth’s gravity field must be accurately quantified and, in the Stokes–Helmert scheme, replaced with effects of those masses condensed on the geoid. The most comprehensive modern schemes for evaluation of topographical effects account for terrain effects, use a spherical model of topography, and incorporate two-dimensionally varying models of topographical mass density. In this contribution, we employ a three-dimensionally varying model of topographical density. We use Newton’s integration to determine the direct topographical effect (DTE) on gravity and primary indirect topographical effect (PITE) on gravity potential. Lastly, we apply Stokes’ integration to calculate the DTE, PITE, and secondary indirect topographical effect (SITE) on geoidal height. We focus here on validation of our results and demonstration of our software’s capabilities. We present results for the simple geometrical shape of a disc under various rotations and for the anomalous density of lake waters. Effects on geoidal height for these simulations reach centimetre level, up to 2.2 cm in magnitude. For a simulation of the effects of neglected mass anomalies of the lakes, we find results reaching 0.8 cm in magnitude. We examine the behavior of our results as calculated using various step sizes for numerical integration and by comparing numerical results with analytical results for the specific case of a disc. These results suggest that the maximum percent error of our results is about 23.5% for the DTE on gravity and 7.6% for the PITE on gravity potential.
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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 | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.002 | 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".