An accurate and robust multigrid algorithm for 2D forward resistivity modelling
Bibliographic record
Abstract
ABSTRACT We present an adaptation of the full multigrid algorithm in DC resistivity modelling in an effort to increase its accuracy. There is a great difficulty with conventional multigrid solvers in representing the physics of an arbitrary distribution of electrical conductivity on a very coarse grid. In general, conventional rectangular finite‐difference or 5‐point approximations of Poisson's equation cannot represent, at a coarse grid level, the effective anisotropy on a coarse scale which results from fine structure in the model. An exception to this generalization occurs when the principal axes of structural anisotropy are aligned with the coordinate axis. Additional and similarly generated problems arise when a coarse cell is obliged to represent fine structure containing very high conductivity contrasts. We have developed an adaptation of the usual resistive‐network representation of the continuum, which avoids some of these problems, and have compared it with the traditional resistive network currently used. The network adaptation consists of replacing the usual 5‐point Laplacian operator stencil used on the finite‐difference grid with a 9‐point stencil, and the conductivity scalar with a 6‐parameter conductivity parametrization. This parametrization permits representation of arbitrarily orientated anisotropy as well as more complex behaviour related to high conductivity contrasts. The importance of multigrid solvers does not lie in their speed at forward modelling (which is comparable with other methods), but rather in their potential for inverse modelling. Inverse solvers which proceed by refinement of an initially very coarse solution can, in principle, take time only linearly proportional to the number of gridpoints in the final desired model.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".