Minimum entropy constrained cooperative inversion with application to electrical resistivity, seismic and magnetic field and synthetic data
Bibliographic record
Abstract
Interpreting independent geophysical data sets can be challenging due to ambiguity and non-uniqueness. To address this, joint inversion techniques have been developed to produce less ambiguous multi-physical subsurface images. Recently, a novel cooperative inversion approach that uses minimum entropy constraints has been proposed. The major feature of this approach is that it can produce sharper boundaries inside the model domain. We implemented this approach in an open-source software framework and systematically investigated its capabilities and applicability on electrical resistivity tomography (ERT), seismic refraction tomography (SRT), and magnetic data.First, we conducted a synthetic 2D ERT and SRT data study to demonstrate the approach and investigate the influence of the equations’ parameters that must be calibrated as well as to justify extensions of the method. The results show that the use of the joint minimum entropy (JME) stabilizer outclasses separate, conventional smoothness-constrained inversions and provides improved images.Next, we used the method to analyze 3D ERT and magnetic field data from Rockeskyller Kopf, Germany. Independent inversion of the magnetic field data already suggested a subsurface volcanic diatreme structure, but the joint inversion using JME not only confirmed the expected structure, but also provided improved details in the subsurface image. The multi-physical images of both methods are consistent in many regions of the model as they produce similar boundaries. Due to the sensitivity of the ERT measurements to hydrogeological conditions in the subsurface, some structures are only visible in the ERT data. These features seem not to be enforced on the magnetic susceptibility model, which highlights another advantage and the flexibility of the approach.However, the results of both the synthetic and field data use cases suggest that careful parameter tests are required prior to cooperative inversion to obtain a suitable hyperparameters and reference model. Our work implies that minimum entropy constrained cooperative inversion is a promising tool for geophysical imaging provided that proper settings are chosen while it also identifies some objectives for future research to improve the approach.
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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 | 0.002 | 0.006 |
| 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 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".