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Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers: 1. Constant head boundary


  • Yoram Rubin,

  • Gedeon Dagan


The spatial variability of log transmissivity Y and head H in aquifers assumes a major role in determining the solutions of the direct flow problem, as well as of the inverse problem. Investigation of the joint Y, H variability has been cast in the past in numerical and analytic frames. Analytic solutions for the Y, H statistical moments in two dimensions assumed the flow to occur in an unbounded domain. In this study, exact analytical expressions for the Y, H moments are derived, which account for the presence of a given head boundary in a half plane. This result is achieved by a first-order approximation and for an exponential Y covariance. The result offers the opportunity to examine the effects of boundaries on the semivariogram of H and on the Y, H cross covariance. The assumption of unbounded domain is examined and shown to be accurate at distances larger than two Y integral scales from the boundary. By using conditional probabilities, a general and simple method to estimate the moments close to the boundary is presented. It requires the knowledge of the moments of Y and H in the unbounded domain only. The method is compared with the exact analytic solution, showing excellent results.

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