Gradient and smoothness regularization operators for geophysical inversion on unstructured meshes
Bibliographic record
Abstract
Abstract The non-uniqueness of the underdetermined inverse problem requires that any available geological information be incorporated to constrain the results. Such information commonly comes in the form of a geological model comprising unstructured wireframe surfaces. Hence, we perform geophysical modelling on unstructured meshes, which provide the flexibility required to efficiently incorporate complicated geological information. Designing spatial matrix operators for unstructured meshes is a non-trivial task. Gradient operators are required for powerful inversion regularization schemes that allow for the incorporation of geological information. Other authors have developed simple regularization schemes for unstructured meshes but those approaches do not use true gradient operators and do not allow for the incorporation of structural information. In this paper we develop new methods for generating spatial gradient operators on unstructured meshes. Our approach is essentially to fit a linear trend in a small neighbourhood around each cell. This results in a small linear system of equations to solve for each cell. Solving for the linear trend parameters yields the required information to construct the stationary gradient operators. Care must be taken when setting up the linear systems to avoid potential numerical issues. We test and compare our methods against the rectilinear mesh equivalents using some simple illustrative 2-D synthetic examples. Our methods are then applied to more complicated 2-D and 3-D examples, including real earth scenarios. This work provides a new method for regularizing inversions on unstructured meshes while allowing for the incorporation of structural orientation information.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 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 source (direct Gemma or distilled Codex), 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".