Applied Stochastic Hydrogeology

Abstract

Stochastic Subsurface Hydrogeology is the study of subsurface, geological heterogeneity, and its effects on flow and transport process, using probabilistic and geostatistical concepts. This book presents a rational, systematic approach for analyzing and modeling subsurface heterogeneity, and for modeling flow and transport in the subsurface, and for prediction and decision-making under uncertainty. The book covers the fundamentals and practical aspects of geostatistics and stochastic hydrogeology, coupling theoretical and practical aspects, with examples, case studies and guidelines for applications, and provides a summary and review of the major developments in these areas.

Efficient stochastic finite element methods for flow in heterogeneous porous media. Part 2: Random lognormal permeability

“…Lognormal random fields are very popular among physical scientists and modelers for various reasons. First, there are several studies, the data of which are summarized in References 21 and 22, that show that parameters such as hydraulic conductivity or transmissivity are often lognormally distributed. Second, although the lognormal distribution possesses an infinite upper bound, it only admits the positive part of the physical spectrum.…”

Statistical Characterization of Environmental Hot Spots and Hot Moments and Applications in Groundwater Hydrology

“…where ( * ) ( | 0 , 0 ) is the probability distribution function (pdf) of the particle's trajectory at * (Dagan and Nguyen, 1989;Rubin, 2003). Other situations may be addressed by using the same framework.…”

“…Under the First-Order Approximation (FOA) (see e.g., Dagan, 1989;Gelhar 1993;Rubin, 2003), the pdf of the particle displacement is normal with mean < ( * ; , 0 ) > and auto-covariance tensor of the residual 425 displacements ′ ( * ) = ( * ) − 〈 ( * )〉 defined by ( * ; 0 , 0 ) = 〈 ′ ( * ; 0 , 0 ) ′ ( * ; 0 , 0 )〉, , = 1, 2, 3.…”

Non-Gaussian parameter inference for hydrogeological models using Stein Variational Gradient Descent

“…Parameter estimation for numerical models can synthesize different types of information into a physically plausible narrative. This is of particular relevance for the discipline of hydrogeology, where informed management demands detailed knowledge of the system, but direct measurements of the relevant subsurface properties are scarce and often of limited spatial representativeness (e.g., Rubin, 2003). The process of inferring subsurface properties from dependent information such as hydraulic head, chemical concentrations, or flow is known as inverse modelling (e.g., Carrera et al, 2005).…”