The relationship between the magnetotelluric tensor invariants and the phase tensor of Caldwell, Bibby and Brown
Bibliographic record
Abstract
We examine the relationship between the seven invariants of the complex MT tensor, which we previously proposed as a vehicle for testing the dimensionality of the regional conductivity structure prior to an analysis of MT data, and the three invariants of the real ‘phase tensor', recently introduced as an innovative aid in the treatment of MT data. It is found that the relevant invariants, and the necessary conditions on them for galvanically distorted data to be consistent with ID, 2D or 3D regional structures, agree in almost every detail for the two approaches. The new method does lead, however, to an improved normalisation of the eighth (dependent) invariant previously introduced. It is shown that the phase tensor can be expressed as a sum of three simple matrices, clearly associated with ID, 2D and 3D regional conductivity structures respectively. It is further shown that it can be depicted graphically as a single Mohr circle that retains the principal properties of the separate real and imaginary Mohr circles associated with the MT tensor. The simplicity and elegance of the phase tensor method is achieved by dispensing with the capability of distinguishing between galvanically distorted and undistorted data in ID and 2D regions, a distinction that is ultimately unimportant and unnecessary with real data. The paper concludes with a simple illustrative example of the theory applied to a real MT dataset from NE Australia. A shallow ID regional conductivity structure associated with a sedimentary basin is revealed, and a 2D anomaly with calculated strike angle is also identified.
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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 | 0.002 | 0.011 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 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".