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

Abstract

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.

Preferential Pathways for Fluid and Solutes in Heterogeneous Groundwater Systems: Self-Organization, Entropy, Work

“…3.3). The concepts of information and Shannon entropy have been widely used to characterize irreversible mixing and reaction processes and their predictability (Chiogna and Rolle, 2017), the emergence of order in distributed time series (Mälicke et al, 2020), information in multiscale permeability data (Dell'Oca et al, 2020), and the role of spatial variability of rainfall and topography in distributed hydrological modeling (Loritz et al, 2018(Loritz et al, , 2021. Woodbury and Ulrych (1993) and Kitanidis (1994) used the Shannon entropy to describe the spatial-time development and dilution of tracer plumes in groundwater systems.…”

Response to Reviewer 2

“…Our revised text now reads (Section 5): "Considering an operational context, including, e.g., groundwater resource management or (conventional/unconventional) oil recovery, we observe that it is common to have at our disposal permeability data associated with diverse support scales. These can be inferred from, e.g., large scale pumping tests, downhole impeller flowmeter measurements, core flood experiments at the laboratory scale, geophysical investigations, or particle-size curves (see e.g., Paillet, 1989;Day-Lewis et al, 2000;Zhang and Winter, 2000;Pavelic et al, 2006;Neuman et al, 2008;Riva et al, 2099;Barahona-Palomo et al, 2011;Quinn et al, 2012;Shapiro et al, 2015;Galvão et al, 2016;Menafoglio et al, 2016;Medici et al, 2017;Dausse et al, 2019, and reference therein). Assessing (i) the information C3 content and (ii) the amount of information shared between permeability data associated with differing support scales (and/or diverse measuring devices/techniques) along the lines illustrated in the present study can be beneficial to obtain a quantitative appraisal of possible feedbacks among diverse approaches employed for aquifer/reservoir characterization.…”