Stochastic analysis of boundaries effects on head spatial variability in heterogeneous aquifers: 2. Impervious boundary

The spatial variability of the head H in a two‐dimensional flow in the vicinity of an impervious boundary is investigated. This study is a continuation of a previous one (Rubin and Dagan, 1988) which dealt with the influence of a given head boundary. By representing H and the log transmissivity Y as space random function and by solving the flow equation, first‐order, closed form, analytical expressions for the head variogram and the head‐log transmissivity Y covariance are developed. These expressions offer the means to evaluate the influence of the boundary on the joint Y, H random field. The assumption of unbounded domain is examined, and it is found to be a good approximation at distances larger than three log transmissivity integral scales from the boundary. By using conditional probabilities, a simple method to estimate the statistical 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 analytical solution, showing favorable results.