Numerical upscaling of frequency‐dependent P‐ and S‐wave moduli in fractured porous media
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Bibliographic record
Abstract
ABSTRACT Relating seismic attributes to the characteristics of mesoscopic fractures is inherently challenging, yet these heterogeneities tend to dominate the mechanical and hydraulic properties of the medium. Analytical approaches linking the effects of material properties on seismic attributes, such as attenuation and velocity dispersion, tend to be limited to simple geometries, low fracture densities, and/or non‐interacting fractures. Furthermore, the influence of fluid flow within interconnected fractures on P‐wave and S‐wave attenuation is difficult to accommodate in analytical models. One way to overcome these limitations is through numerical upscaling. In this paper, we apply a numerical upscaling approach based on the theory of quasi‐static poroelasticity to fluid‐saturated porous media containing randomly distributed horizontal and vertical fractures. The inferred frequency‐dependent elastic moduli represent the effective behaviour of the underlying fractured medium if the considered sub‐volume has at least the size of a representative elementary volume. We adapt a combined statistical and numerical approach originally proposed for elastic composites to explore wether the overall statistical properties of simple fracture networks can be captured by computationally feasible representative‐elementary‐volume sizes. Our results indicate that, for the considered scenarios, this is indeed possible and thus represent an important first step towards the estimation of frequency‐dependent effective moduli of realistic fracture networks.
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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 | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 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 it