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Inversion of the Borden Tracer Experiment data: Investigation of stochastic moment models
Author(s) -
Woodbury Allan D.,
Sudicky E. A.
Publication year - 1992
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/92wr01005
Subject(s) - mathematics , moment (physics) , monte carlo method , inversion (geology) , probability density function , statistical physics , statistics , geology , physics , geomorphology , classical mechanics , structural basin
Inversion of Dagan's two‐ and three‐dimensional stochastic models using Freyberg's (1986), Rajaram and Gelhar's (1988, 1991), and Barry and Sposito's (1990) moment data from the Borden experiment is carried out to examine (1) the validity of the two‐dimensional (Dagan, 1982) and three‐dimensional (Dagan, 1988) models and (2) the reduction in uncertainty of the spatial moments over nonconditioned estimates. A direct application of Bayesian statistical inference, in conjunction with Monte Carlo integration, is used to produce posterior probability density functions for the parameters. The parameter ranges from all methods show horizontal integral scales λ between 1.85 and 4.04 m, vertical integral scales λ z between 0.144 and 0.459 m, and log hydraulic conductivities In ( K ) between 0.120 and 0.197. These results compare well to the earlier estimates of Woodbury and Sudicky (1991) and Robin et al. (1991). We show that moment prediction uncertainty is substantially reduced when both tracer moment data and prior estimates of the In ( K ) geostatistical parameters are incorporated into theoretical formulae based on stochastic dispersion theory.