TY - JOUR

T1 - Stochastic identification of transmissivity and effective recharge in steady groundwater flow

T2 - 1. Theory

AU - Rubin, Yoram

AU - Dagan, Gedeon

PY - 1987/7

Y1 - 1987/7

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0023524376&partnerID=8YFLogxK

U2 - 10.1029/WR023i007p01185

DO - 10.1029/WR023i007p01185

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AN - SCOPUS:0023524376

SN - 0043-1397

VL - 23

SP - 1185

EP - 1192

JO - Water Resources Research

JF - Water Resources Research

IS - 7

ER -