Characterization of Uncertainties of Parameters with F-Statistic for Flows through Porous Media

by Guo-Qiang Yang.

Abstract: The F-test (lack-of-fit) is applied to characterize the uncertainties in the estimation of parameters for flows through porous media. In the forward simulation, mixed finite element and second-order donor cell methods are used for the pressure-velocity equation and concentration equation respectively. The treatment of the wells are described. We show that $F$-test is flexible when handling the (ill-posed) inverse problem and gives the (exact) confidence regions for the unknown permeability field. Although the high dimensional confidence regions usually cannot be visualized, the simple evaluation of the $F$-statistic for each realization is desirable, as opposed to the usual Monte Carlo methods, which can only lead to approximate confidence levels with sufficient many samplings.

Key Words: Uncertainty, Forward and Inverse Problems, Mixed Finite Element, Donor Cell, $F$-Test and Lack-of-Fit, Confidence Regions and Confidence Intervals, Singular Value Decomposition

Author:
Guo-Qiang Yang, yanggq@math.duke.edu

Editor: Alexander Kolesnik,kolesnik@math.md

READING THE ARTICLE: You can read the article in portable document (.pdf) format (443960 bytes.)

NOTE: The content of this article is the intellectual property of the authors, who retains all rights to future publication.

This page has been accessed 2110 times since July 24, 2006.


Return to the InterStat Home Page.