Constrained electrical resistivity tomography Bayesian inversion using inverse Matérn covariance matrix
Bibliographic record
Abstract
Bayesian inversion using maximum a posteriori estimator is a quantitative approach that has been successfully applied to the electrical resistivity tomography inverse problem. In most approaches, model covariance parameters are generally chosen as stationary and isotropic, which assumes a statistical homogeneity of the studied field. However, the statistical properties of resistivity within the earth are, in reality, location dependent due to spatially varying processes that control the bulk resistivity of rocks, such as water content, porosity, clay content, etc. Taking into account the spatial variability of the resistivity field, we use the nonstationary Matérn covariance family, which is defined through linear stochastic partial differential equations. Two types of prior information are considered: structure orientation and spatially increasing the range with increasing depth. The latter is applied successfully on the first synthetic model, which aims at retrieving the depth of bedrock and the shape of the conductive lens. In the second synthetic example, a conductive dike model embedded into four layers is used to study the performance of structure orientation. Finally, the proposed approach is used to invert real data measured over an extensively characterized sandy-to-silty aquifer. First, the structure orientation of this aquifer was determined by applying a structure tensor calculated using gradients of the ground penetrating radar image. The introduction of this information gives a resistivity model that is more compatible with the aquifer structure.
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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 | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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".