Comparison of integral equation and physical scale modeling of the electromagnetic responses of models with large conductivity contrasts
Bibliographic record
Abstract
Abstract A comparison is made between the results from two different approaches to modeling geophysical electromagnetic responses: a numerical approach based upon the electric-field integral equation and the physical scale modeling approach. The particular implementation of the integral-equation solution was developed recently, and the comparison presented here is essentially a test of this new formulation. The implementation approximates the region of anomalous conductivity by a mesh of uniform cuboidal cells and approximates the total electric field within a cell by a linear combination of bilinear edge-element basis functions. These basis functions give a representation of the electric field that is divergence free but not curl free within a cell, and whose tangential component is continuous between cells. The charge density (which arises from the discontinuity of the normal com-ponent of the electric field across interfaces between cells of different conductivities and between cells and the background) is incorporated in a similar manner to integral equation solutions to dc resistivity modeling. The scenarios considered for the comparison comprise a graphite cube of 6.3×104S∕m conductivity and 14-cm length in free space and in brine (7.3S∕m conductivity). The transmitter and receiver were small horizontal loops; measurements and computations were made for various fixed transmitter-receiver separations and various heights of the transmitter-receiver pair for frequencies ranging from 1–400kHz. The agreement between the numerical results from the integral-equation implementation and the measurements from the physical scale modeling was very good, contributing to the verification of this particular implementation of the integral-equation solution to electromagnetic modeling.
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How this classification was reachedexpand
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 | 0.000 | 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 |
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 teacher head, 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".