Stochastic Hydrology: Flow-through Porous Media

Random functions are ideally suited to model the problem of flow through porous media. The equations governing the flow of the fluid through this medium can be treated as partial differential equations with stochastic parameters. The objective of the modeling is to be able to determine the statistics of this uncertain parameter based on observations of the output variables. This report serves as an introduction to the modeling issues involved with this topic - namely the inverse problem and that of parameter estimation. The report also provides a brief introduction to two new methods based on stochastic finite elements and wavelet discretization that might be useful in the study of this problem. Department of Mechanical Engineering & Material Science, Rice University, Houston, Texas, 77005-1892. 1 Introduction Hydrological problems involving groundwater flow have been the subject of detailed study for a long period time - the first attempt at understanding the physics of these pro..