3D magnetotelluric modeling using the T-Ω Ω finite-element method
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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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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 | 0.000 | 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 |
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