Information entropy to measure temporal and spatial complexity of unsaturated flow in heterogeneous media

Geologic heterogeneity, coupled with the nonlinear interplay of gravity, capillarity, and applied pressure gradients, results in a rich variety of flow behaviors in unsaturated fractured rocks and porous media. In this paper, we evaluate the complexity of these behaviors using information entropy. We create an empirical probability distribution function directly from a data set, then apply Shannon's definition of information entropy to quantify the complexity of the data. As an example, we use information entropy to evaluate the temporal and spatial complexity of simulated flow processes invoked by infiltration into heterogeneous porous media. Our analysis shows that the complexity of this unsaturated flow process depends on both geologic heterogeneity and uncertainty arising from the flow dynamics. Finally, we investigate the marginal value of additional data collection using randomly selected “virtual wells.” These calculations demonstrate that computed information entropy increases with additional virtual wells, but the rate of increase declines.