Stochastic identification of transmissivity and effective recharge in steady groundwater flow: 1. Theory

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Abstract
The study is a continuation and extension of a previous work (Dagan, 1985a) whose aim was to identify the values of the log‐transmissivity Y for steady flow. The common basic assumptions are that Y is a normal and stationary random space function, the aquifer is unbounded, and a first‐order approximation of the flow equation is adopted. The expected value of the water head H, as well as the Y unconditional autocovariance, are supposed to have analytical expressions which depend on a parameters vector θ. The proposed solution of the inverse problem consists of identifying θ with the aid of the model and of the measurements of Y and H and subsequently computing the statistical moments of Y conditioned on the same data, The additional features of the present study are (1) incorporation of a constant, but random, effective recharge and its identification and (2) accounting for the fact that θ estimation is associated with some uncertainty, whereas before θ was assumed to be identified with certainty. Analytical expressions are derived for the Y and H covariances for an exponential autocovariance of Y. Paper 2 (Rubin and Dagan, this issue) of the study illustrates the applications of the method to a real‐life case.