The use of Mohr circles in the interpretation of magnetotelluric data
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Bibliographic record
Abstract
One of Ted Lilley’s many original contributions to electromagnetic geophysics was his introduction of the Mohr circle as an aid in the analysis of the magnetotelluric (MT) impedance tensor. Although well known as a representation of the stress tensor in elasticity theory, the usefulness of Mohr circles was virtually unrecognised by the MT community until the pioneer paper of Lilley (1976). An important difference between the stress tensor and the MT tensor is that the former is real while the latter is complex, which means that the MT tensor must be represented by two Mohr circles rather than one. In his early treatments of MT data, Lilley bypassed this complication by concentrating solely on the real part of the MT tensor, and was able to identify various invariants of the real tensor geometrically on the Mohr circle diagram. In later discussions of the physical interpretation of the seven independent invariants of the complex MT tensor, however, it became necessary to consider both real and imaginary Mohr circles together when seeking a geometrical representation of all the invariants. A significant advance was made with the introduction of the (real) phase tensor by Caldwell, Bibby and Brown (2002). Although the phase tensor has only three independent invariants, they retain the important physical properties of the seven invariants of the MT tensor, and can be displayed graphically in a single Mohr circle diagram. In particular, identification of the dimensionality of the regional conductivity structure becomes a straightforward matter whether or not the data are distorted by near-surface conductivity anomalies. An analysis of MT field data with error bars will be presented using the phase tensor and its Mohr circle representation in order to show when a two- or one-dimensional interpretation of the regional conductivity structure is appropriate and strike angles are calculated for two-dimensional structures.
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Full frame distilled prediction
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 | 0.001 | 0.001 |
| 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 |
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 it