Analysis of multi-scale permeability data via an Information Theory approach
Abstract
We employ elements of Information Theory to quantify (i) the Information content associated with a given observation/measurement scale at which data of porous media permeabilities are collected, and (ii) the relationships among Information contents associated with datasets characterized by diverse support scales. We focus on gas permeability data collected over a Berea Sandstone block at four measurement scales. We study the way information is shared across scales through (i) the Shannon Entropy of the data associated with each support/measurement scale, (ii) the Mutual Information shared between data taken at increasing support scales, and (iii) the multivariate Mutual Information shared within triplets of datasets. With reference to the latter, we also quantify the level of Information partitioning that sets of data associated with the intermediate and largest support scales provide with respect to the Information linked to the data collected at the smallest support scale in a triplet. Our results document that (a) simultaneous knowledge of data taken at the intermediate and coarser support scales in a triplet does not provide significant additional Information with respect to that already contained in the data taken at the fine scale, and (b) the Information shared by the intermediate and coarser support scales is mainly redundant with respect to what the intermediate scale shares with the finest scale.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2019
- Bibcode:
- 2019AGUFM.H31C..04G
- Keywords:
-
- 1829 Groundwater hydrology;
- HYDROLOGY;
- 1832 Groundwater transport;
- HYDROLOGY;
- 1847 Modeling;
- HYDROLOGY;
- 1869 Stochastic hydrology;
- HYDROLOGY