3D magnetotelluric modeling using the T-Ω Ω finite-element method
Bibliographic record
Abstract
Abstract We present a finite-element algorithm for computing MT responses for 3D conductivity structures. The governing differential equations in the finite-element method are derived from the T–Ω Helmholtz decomposition of the magnetic field H in Maxwell's equations, in which T is the electric vector potential and Ω is the magnetic scalar potential. The Coulomb gauge condition on T necessary to obtain a unique solution for T is incorporated into the magnetic flux density conservation equation. This decomposition has two important benefits. First, the only unknown variable in the air is the scalar value of Ω. Second, the curl–curl equation describing T is only defined in the earth. By comparison, the system of curl–curl equations for H and the electric field E are singular in the air, where the conductivity σ is zero. Although the use of a small but nonzero value of σ in the air and application of a divergence correction are usually necessary in the E or H formulation, the T–Ω method avoids this necessity. In the finite-element approximation, T and Ω are represented by the edge-element and nodal-element interpolation functions within each brick element, respectively. The validity of this modeling approach is investigated and confirmed by comparing modeling results with those of other numerical techniques for two 3D models.
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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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 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 | 0.000 |
| Research integrity | 0.001 | 0.000 |
| 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".