On estimation of stopping criteria for iterative solutions of gravity downward continuation
Bibliographic record
Abstract
This article discusses methods for selecting criteria used for stopping iterative regularization methods applied to solving continuation of gravity observed at or outside the Earth’s surface down to the geoid. This computational step is required for determination of the gravimetric geoid by the Stokes approach. For surface gravity data measured with spatial resolutions at the kilometer level and higher, their downward continuation becomes ill posed and its solution numerically unstable. Two iterative methods often used for solving this problem, namely the Landweber and conjugate gradient least-squares (CGLS) methods, are investigated using a sample of surface gravity data synthesized from a global gravitational model over a mountainous test area in Colorado, USA. Five different commonly used stopping criteria are applied to both iterative methods and neither of them, except L-curve, succeed to stop the iterative process at the reasonable solution. A simple approach is proposed to stop the iterative methods exploiting stochastic properties of surface gravity data. Results of numerical tests suggest that a rather simple stopping criterion based on stochastics parameters of surface gravity data estimated using a leave-one-out cross-validation procedure yields results superior to those based on the L-curve approach which is best performing among the five standard methods for selecting the stopping criterion. Results based on the Landweber method outperform those based on the CGLS method. Iterative methods based on optimum numbers of iterations represent an alternative to commonly used regularization techniques for solving ill-posed inverse problems, such as Tikhonov, that require optimal estimates of regularization parameters.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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) | 0.000 | 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 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".