A distribution-based parametrization for improved tomographic imaging of solute plumes
Bibliographic record
Abstract
Difference geophysical tomography (e.g. radar, resistivity and seismic) is used increasingly for imaging fluid flow and mass transport associated with natural and engineered hydrologic phenomena, including tracer experiments, in situ remediation and aquifer storage and recovery. Tomographic data are collected over time, inverted and differenced against a background image to produce ‘snapshots’ revealing changes to the system; these snapshots readily provide qualitative information on the location and morphology of plumes of injected tracer, remedial amendment or stored water. In principle, geometric moments (i.e. total mass, centres of mass, spread, etc.) calculated from difference tomograms can provide further quantitative insight into the rates of advection, dispersion and mass transfer; however, recent work has shown that moments calculated from tomograms are commonly biased, as they are strongly affected by the subjective choice of regularization criteria. Conventional approaches to regularization (Tikhonov) and parametrization (image pixels) result in tomograms which are subject to artefacts such as smearing or pixel estimates taking on the sign opposite to that expected for the plume under study. Here, we demonstrate a novel parametrization for imaging plumes associated with hydrologic phenomena. Capitalizing on the mathematical analogy between moment-based descriptors of plumes and the moment-based parameters of probability distributions, we design an inverse problem that (1) is overdetermined and computationally efficient because the image is described by only a few parameters, (2) produces tomograms consistent with expected plume behaviour (e.g. changes of one sign relative to the background image), (3) yields parameter estimates that are readily interpreted for plume morphology and offer direct insight into hydrologic processes and (4) requires comparatively few data to achieve reasonable model estimates. We demonstrate the approach in a series of numerical examples based on straight-ray difference-attenuation radar monitoring of the transport of an ionic tracer, and show that the methodology outlined here is particularly effective when limited data are available.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| 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".