Quasi-Linear Geostatistical Theory for Inversing
Article first published online: 9 JUL 2010
Copyright 1995 by the American Geophysical Union.
Water Resources Research
Volume 31, Issue 10, pages 2411–2419, October 1995
How to Cite
1995), Quasi-Linear Geostatistical Theory for Inversing, Water Resour. Res., 31(10), 2411–2419, doi:10.1029/95WR01945.(
- Issue published online: 9 JUL 2010
- Article first published online: 9 JUL 2010
- Manuscript Accepted: 22 JUN 1995
- Manuscript Received: 3 JAN 1995
A quasi-linear theory is presented for the geostatistical solution to the inverse problem. The archetypal problem is to estimate the log transmissivity function from observations of head and log transmissivity at selected locations. The unknown is parameterized as a realization of a random field, and the estimation problem is solved in two phases: structural analysis, where the random field is characterized, followed by estimation of the log transmissivity conditional on all observations. The proposed method generalizes the linear approach of Kitanidis and Vomvoris (1983). The generalized method is superior to the linear method in cases of large contrast in formation properties but informative measurements, i.e., there are enough observations that the variance of estimation error of the log transmissivity is small. The methodology deals rigorously with unknown drift coefficients and yields estimates of covariance parameters that are unbiased and grid independent. The applicability of the methodology is demonstrated through an example that includes structural analysis, determination of best estimates, and conditional simulations.