Prediction of Log-Transmissivity

Abstract

The log-transmissivity may in many cases be predicted from the log-transformed specific capacity of wells by applying a linear statistical model. The coefficients of the linear equation can be estimated by the least-square method. It is shown that if the estimated slope of the line differs from unity then it may indicate that the specific capacity is correlated with the well efficiency. The above prediction method is applied to case studies of aquifers in three different formations: the prediction should not be used for a homogeneous fluvioglacial formation because the variance of the well efficiency dominates the variance of the transmissivity; the prediction is fair for a heterogeneous fluvioglacial formation; and the prediction is poor for a homogeneous limnic formation. In the study of the first formation a correlation between specific capacity and well efficiency can be identified directly from the slope of the regression line. If the predictor values are taken from the drillers log then the standard error of prediction in all the cases is 0.35. This seems to be unacceptable in most practical applications. However, if one needs to predict the mean of a domain and the domain contains a number of observations of the predictor, then the averaging will reduce the prediction error. The averaging procedure ought to take the covariance structure of the variables into consideration.