Inverse stochastic moment analysis of steady state flow in randomly heterogeneous media

A. F. Hernandez, Shlomo P Neuman, A. Guadagnini, J. Carrera

Research output: Contribution to journalArticle

68 Citations (Scopus)

Abstract

Nonlocal stochastic moment equations have been used successfully to analyze steady state and transient flow in randomly heterogeneous media conditional on measured values of medium properties. We present a nonlinear geostatistical inverse algorithm for steady state flow that makes it possible to further condition such analyses on measured values of state variables. Our approach accounts for all scales of spatial variability resolvable by the computational grid. It is based on recursive finite element approximations of exact nonlocal first and second conditional moment equations. Hydraulic conductivity is parameterized geostatistically on the basis of measured values at discrete locations and unknown values at discrete "pilot points." Prior estimates of pilot point values are obtained (optionally) by generalized kriging. Posterior estimates at pilot points and (optionally) at measurement points are obtained by calibrating mean flow against measured values of head. The parameters are projected onto a computational grid via kriging. Maximum likelihood calibration allows estimating not only hydraulic but also (optionally) unknown variogram parameters with or without prior information about the former. The approach yields covariance matrices for parameter estimation as well as head and flux prediction errors, the latter being obtained a posteriori. We implement our inverse approach on highly and mildly heterogeneous media under superimposed mean uniform and convergent flows in a bounded two-dimensional domain. Our examples illustrate how conductivity and head data act separately and jointly to reduce parameter estimation errors and to model predictive uncertainty. We also evaluate the functional form of the log conductivity variogram and its parameters using likelihood-based model discrimination criteria.

Original languageEnglish (US)
Article numberW05425
JournalWater Resources Research
Volume42
Issue number5
DOIs
StatePublished - May 2006

Fingerprint

heterogeneous medium
Parameter estimation
kriging
variogram
Hydraulic conductivity
conductivity
Covariance matrix
Maximum likelihood
transient flow
Hydraulics
Calibration
Fluxes
hydraulic conductivity
fluid mechanics
calibration
uncertainty
hydraulics
matrix
prediction
parameter

ASJC Scopus subject areas

  • Environmental Science(all)
  • Environmental Chemistry
  • Aquatic Science
  • Water Science and Technology

Cite this

Inverse stochastic moment analysis of steady state flow in randomly heterogeneous media. / Hernandez, A. F.; Neuman, Shlomo P; Guadagnini, A.; Carrera, J.

In: Water Resources Research, Vol. 42, No. 5, W05425, 05.2006.

Research output: Contribution to journalArticle

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