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Hydrology and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/hess-2019-628
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-2019-628
© Author(s) 2019. This work is distributed under
the Creative Commons Attribution 4.0 License.

Submitted as: research article 29 Nov 2019

Submitted as: research article | 29 Nov 2019

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Hydrology and Earth System Sciences (HESS).

Interpretation of Multi-scale Permeability Data through an Information Theory Perspective

Aronne Dell'Oca, Alberto Guadagnini, and Monica Riva Aronne Dell'Oca et al.
  • Department of Civil and Environmental Engineering, Politecnicodi Milano, 20133, Milan, Italy

Abstract. We employ elements of Information Theory to quantify (i) the information content related to data collected at given measurement scales within the same porous medium domain, and (ii) the relationships among Information contents of datasets associated with differing scales. We focus on gas permeability data collected over a Berea Sandstone and a Topopah Spring Tuff blocks, considering four measurement scales. We quantify the way information is shared across these scales through (i) the Shannon entropy of the data associated with each support scale, (ii) mutual information shared between data taken at increasing support scales, and (iii) multivariate mutual information shared within triplets of datasets, each associated with a given scale. We also assess the level of uniqueness, redundancy and synergy (rendering, i.e., the information partitioning) of information content that the data associated with the intermediate and largest scales provide with respect to the information embedded in the data collected at the smallest support scale in a triplet.

Aronne Dell'Oca et al.
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Permeabilities A. Dell'Oca https://doi.org/10.17632/ygcgv32nw5.1

Aronne Dell'Oca et al.
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Short summary
Permeability of natural systems exhibits heterogeneous spatial variations linked with the size of the measurement support scale. As the latter becomes coarser, the system appearance is less heterogeneous. As such, sets of permeability data associated with differing support scales provide diverse amounts of information. In this contribution, we leverage on Information Theory to quantify the information content of gas permeability datasets collected with four diverse measurement support scales.
Permeability of natural systems exhibits heterogeneous spatial variations linked with the size...
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