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Determination of Variances for Maximum and Minimum Transmissivities of Anisotropic Aquifers from Multiple Well Pumping Test Data
Author(s) -
Kern John W.,
Dobson Carl W.
Publication year - 1998
Publication title -
groundwater
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.84
H-Index - 94
eISSN - 1745-6584
pISSN - 0017-467X
DOI - 10.1111/j.1745-6584.1998.tb02817.x
Subject(s) - anisotropy , confidence interval , statistics , mathematics , inverse , orientation (vector space) , geometry , physics , optics
An extension of the least squares method given by Neuman et al. (1984) for estimating aquifer parameters is presented, and statistical tests for anisotropy are derived. Methods are also given to construct variance formulas for the principal axes of trans‐missivity and confidence intervals for the angles of orientation. The techniques developed here treat each monitoring well as the experimental unit, in contrast to inverse modeling methods which treat each time step for each well as the experimental unit. We argue that the latter is a form of pseudo‐replication in that the number of time steps may be arbitrarily selected. The example aquifer test data used by Neuman et al. (1984) are analyzed. The maximum transmissiviy was found to have a magnitude of 8.60 ± 5.30 m 2 /day oriented N29.6°W ± 11.3° at the 95% confidence level with a ratio of anisotropy of 1.91 ± 0.39. Both statistical tests indicated anisotropy. Results from a multiple well pumping test from the Powder River Basin, Wyoming, are also analyzed. The maximum transmissivity was found to have a magnitude of 230 m 2 /day ± 84.4 m 2 /day oriented N51.7°W ± 5.3° at the 95% confidence level with a ratio of anisotropy of 2.12 ± 0.48. Both statistical tests indicated anisotropy. The methods given in this paper can be performed with standard statistical software packages and spreadsheets. A program that uses Matlab® software is available from the authors to perform the necessary calculations at ftp2.wyoming.com/pub/users/FTP/west‐inc/groundwater/adapl.zip.