Mutual information analysis to approach nonlinearity in groundwater stochastic fields

Abstract

In heterogeneous porous media, transmissivity can be regarded as a spatial stochastic variable. Transmissivity fluctuations induce stochasticity in the groundwater velocity field and transport features. In order to model subsurface phenomena, it is important to understand the relationships that exist between the variables that characterize flow and transport. Linear relationships are easier to deal with. Nevertheless, it is well known that flow and transport variables exhibit interdependences that become more and more nonlinear as the heterogeneity increases. The aim of this work is to draw attention to the information contained in nonlinear linkages, and to show that it can be of great relevance with respect to the linear information content. Information theory tools are proposed to detect the presence of nonlinear components. By comparing the cross-covariance function and mutual information, the amount of linear linkage is compared with nonlinear linkage. In order to avoid analytical approximations, data from Monte Carlo simulations of heterogeneous transmissivity fields have been considered in the analysis. The obtained results show that the presence of nonlinear components can be relevant, even when the cross-covariance values are nil.