An iterative stochastic inverse method: Conditional effective transmissivity and hydraulic head fields

Tian-Chyi J Yeh, Minghui Jin, Samuel Hanna

Research output: Contribution to journalArticle

145 Citations (Scopus)

Abstract

An iterative stochastic approach is developed to estimate transmissivity and head distributions in heterogeneous aquifers. This approach is similar to the classical cokriging technique; it uses a linear estimator that depends on the covariances of transmissivity and hydraulic head and their cross covariance. The linear estimator is, however, improved successively by solving the governing flow equation and by updating the covariances and cross-covariance function of transmissivity and hydraulic head fields in an iterative manner. As a result the nonlinear relationship between transmissivity and head is incorporated in the estimation, and the estimated fields are approximate conditional means. The ability of the iterative approach is tested with some deterministic and stochastic inverse problems. The results show that the estimated transmissivity and hydraulic head fields have smaller mean square errors than those obtained by classical cokriging even in the aquifer with variance of transmissivity up to 3.

Original languageEnglish (US)
Pages (from-to)85-92
Number of pages8
JournalWater Resources Research
Volume32
Issue number1
DOIs
StatePublished - Jan 1996

Fingerprint

hydraulic head
transmissivity
fluid mechanics
Hydraulics
Aquifers
aquifers
Inverse problems
Mean square error
methodology
aquifer
inverse problem
method

ASJC Scopus subject areas

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

Cite this

An iterative stochastic inverse method : Conditional effective transmissivity and hydraulic head fields. / Yeh, Tian-Chyi J; Jin, Minghui; Hanna, Samuel.

In: Water Resources Research, Vol. 32, No. 1, 01.1996, p. 85-92.

Research output: Contribution to journalArticle

@article{bbc91b369db04ed7ab0e7d7bccf16a32,
title = "An iterative stochastic inverse method: Conditional effective transmissivity and hydraulic head fields",
abstract = "An iterative stochastic approach is developed to estimate transmissivity and head distributions in heterogeneous aquifers. This approach is similar to the classical cokriging technique; it uses a linear estimator that depends on the covariances of transmissivity and hydraulic head and their cross covariance. The linear estimator is, however, improved successively by solving the governing flow equation and by updating the covariances and cross-covariance function of transmissivity and hydraulic head fields in an iterative manner. As a result the nonlinear relationship between transmissivity and head is incorporated in the estimation, and the estimated fields are approximate conditional means. The ability of the iterative approach is tested with some deterministic and stochastic inverse problems. The results show that the estimated transmissivity and hydraulic head fields have smaller mean square errors than those obtained by classical cokriging even in the aquifer with variance of transmissivity up to 3.",
author = "Yeh, {Tian-Chyi J} and Minghui Jin and Samuel Hanna",
year = "1996",
month = "1",
doi = "10.1029/95WR02869",
language = "English (US)",
volume = "32",
pages = "85--92",
journal = "Water Resources Research",
issn = "0043-1397",
publisher = "American Geophysical Union",
number = "1",

}

TY - JOUR

T1 - An iterative stochastic inverse method

T2 - Conditional effective transmissivity and hydraulic head fields

AU - Yeh, Tian-Chyi J

AU - Jin, Minghui

AU - Hanna, Samuel

PY - 1996/1

Y1 - 1996/1

N2 - An iterative stochastic approach is developed to estimate transmissivity and head distributions in heterogeneous aquifers. This approach is similar to the classical cokriging technique; it uses a linear estimator that depends on the covariances of transmissivity and hydraulic head and their cross covariance. The linear estimator is, however, improved successively by solving the governing flow equation and by updating the covariances and cross-covariance function of transmissivity and hydraulic head fields in an iterative manner. As a result the nonlinear relationship between transmissivity and head is incorporated in the estimation, and the estimated fields are approximate conditional means. The ability of the iterative approach is tested with some deterministic and stochastic inverse problems. The results show that the estimated transmissivity and hydraulic head fields have smaller mean square errors than those obtained by classical cokriging even in the aquifer with variance of transmissivity up to 3.

AB - An iterative stochastic approach is developed to estimate transmissivity and head distributions in heterogeneous aquifers. This approach is similar to the classical cokriging technique; it uses a linear estimator that depends on the covariances of transmissivity and hydraulic head and their cross covariance. The linear estimator is, however, improved successively by solving the governing flow equation and by updating the covariances and cross-covariance function of transmissivity and hydraulic head fields in an iterative manner. As a result the nonlinear relationship between transmissivity and head is incorporated in the estimation, and the estimated fields are approximate conditional means. The ability of the iterative approach is tested with some deterministic and stochastic inverse problems. The results show that the estimated transmissivity and hydraulic head fields have smaller mean square errors than those obtained by classical cokriging even in the aquifer with variance of transmissivity up to 3.

UR - http://www.scopus.com/inward/record.url?scp=0029777250&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029777250&partnerID=8YFLogxK

U2 - 10.1029/95WR02869

DO - 10.1029/95WR02869

M3 - Article

AN - SCOPUS:0029777250

VL - 32

SP - 85

EP - 92

JO - Water Resources Research

JF - Water Resources Research

SN - 0043-1397

IS - 1

ER -