Ill‐Posed Resistivity Inverse Problems and its Application to Geoengineering Solutions
Bibliographic record
Abstract
The most important physical properties to study ill-posed inverse problems in physical sciences are electrical conductivity, magnetic permeability, density, wave-velocity, elasticity parameters/modulus, and dielectric permittivity. This paper attempts electrical conductivity of the earth materials and describes some innovative approaches which have been used to solve ill-posed resistivity inverse problems encountered in mapping and monitoring geo-environmental problems. The paper begins with an overview of the present state of knowledge about electrical resistivity methods for mapping and monitoring in-situ processes that cannot be accessed directly. The current study indicates that a generalized mathematical approach has not been developed to investigate the sensitivity of resistivity measurements to changes in resistivity at depth. Therefore, the paper also presents a generalized mathematical formulation for sensitivity analysis and describes sensitivity of resistivity measurements. Reciprocity and perturbation analysis form the basis for the mathematical formulation, which has been extended further towards introducing multi-dimensional resistivity inversion useful for mapping and monitoring in-situ processes. A generalized multi-dimensional mathematical technique is described herein for computing numerical response over the one-dimensional (1-D), two-dimensional (2-D) and three-dimensional (3-D) resistivity models excited by a three-dimensional (3-D) point source. These problems also described as 1-D/3-D, 2-D/3-D and 3-D/3-D inverse problems in the scientific literature.
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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 | 0.001 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".