A Bayesian/Maximum Entropy Approach for Stochastic Analysis of Groundwater Flow

Marc Serre, University of North Carolina

Classical Geostatistics methods have been designed to use mainly statistical knowledge about natural variables and they lack the ability to incorporate important forms of knowledge like physical laws and scientific theories into the mapping process. On the other hand, the powerful and versatile Bayesian maximum entropy (BME) method of Modern Geostatistics can accomplish such a task, rigorously and efficiently. In this work, BME is used to incorporate the Darcy law of subsurface hydrology in the spatial mapping of a hydraulic head field. The hydraulic map thus obtained is physically meaningful as well as numerically more accurate than that obtained using classical methods (e.g., kriging). Moreover, taking advantage of the Darcy law the BME hydraulic head mapping can involve other related soil properties, like hydraulic conductivity. The approach leads to very accurate hydraulic head solutions, and may be also applied to study the inverse problem, in which one seeks to estimate hydraulic conductivity from hydraulic head measurements.

Abstract Author(s): Marc Serre