On “3-D inversion of gravity and magnetic data with depth resolution” (Maurizio Fedi and Antonio Rapolla, <scp>Geophysics</scp> , 64, 452-461).
Bibliographic record
Abstract
We have read with great interest the paper entitled “3D inversion of gravity and magnetic data with depth resolution” by Fedi and Rapolla. We realize that many discussions we had with one of the authors had not resolved our differences and, therefore, we are writing this comment to document out concerns regarding the authors’ conclusion that the upward-continued gravity or magnetic data contain extra information and provide depth resolution. As is well known in potential-field theory, the fields produced by the subsurface source at any two nonintersecting observational surfaces are linearly related to each other and one contains no more information than does the other. Furthermore, the field on the observational surface above the source can be reproduced by an infinite number of equivalent sources below that surface. As a consequence, gravity or magnetic data do not provide any information about the subsurface structure unless the source is assumed to have certain restrictive properties. No amount of upward continuation will create any new information and, consequently, the addition of upward-continued data will not resolve the depth distribution of the source. In practical applications, when the data are available in a small area and/or when the data are coursely sampled, then exact numerical continuation is not possible to perform. In such circumstances, independently-measured data at a different level will provide extra information that is not contained in the data at the original level. The maximum amount of additional information that any upper-level data can supply is that which is contained in the missing portion of the data map at the lower level. Fedi and Rapolla provide two examples which they claim support their hypothesis that data along the vertical direction are needed to obtain depth resolution and, furthermore, that upward-continued data serve this purpose. As is shown below, both results arise …
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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 | 0.004 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.003 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.003 | 0.004 |
| Insufficient payload (model declined to judge) | 0.009 | 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".