Analytic continuation: A tool for aeromagnetic data interpretation
Bibliographic record
Abstract
Abstract Extending potential-field data to vertical complex-plane slices provides opportunities, unique to analytic functions, for subsurface imaging. We begin with an existing numerical method for differentiation by integration using Cauchy's integral formula. An example from data over northern Ontario, Canada, illustrates better conditioning compared to derivatives computed using finite differences. Next, these quantities are used for analytic continuation using rational complex-series expansion (Padé approximation). This method provides stable downward continuation to distances that are significantly greater than are achievable by Taylor series and spectral methods. A synthetic test confirms that the rational approximant faithfully reproduces the magnetic response of a thin sheet. A sign reversal of the total field, coincident with the origin of the sheet, features prominently on this example. We also provide synthetic results for sheets with finite depth extent, point sources, thin slabs, and contacts. These also exhibit polarity flips near the source location. Further, these provide a template for interpreting the source geometry using the shape of the approximating function. Additional synthetic tests illustrate an automatic method for locating closely spaced random assemblages of isolated poles. We apply our methods to a deposit-scale heliborne survey over a recently discovered volcanogenic massive sulphide ore deposit in a Canadian greenstone belt. The analytically continued profile over the deposit suggests the presence of a subvertical thin sheet of unknown depth extent. This interpretation coincides with a sulphide ore body that has been previously delimited by several drill holes. Some known prospects near this deposit are also imaged on maps and profiles of the Padé approximant.
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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 | 0.005 | 0.016 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.004 | 0.003 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.015 | 0.004 |
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".