ON GEOSTATISTICAL FORMULATIONS OF THE GROUNDWATER-FLOW INVERSE PROBLEM

The problem of estimating log-transmissivity when it is assumed to be a random field can be faced using indirect iterative methods or using the so-called geostatistical approach. A close examination of the two formulations suggests that basic assumptions are similar. In fact, if the iterative method is stopped after one iteration of a Gauss-Newton method, starting from the mean log-T, we show that both estimates and estimation covariance matrices obtained with the two approaches are identical. We then argue that the main difference between the two formulations arises from the way linearization is performed, which is global in non-iterative methods and only local in iterative methods. As a result, the latter are less constrained by linearity than the former and lead to better estimates and to more consistent estimation covariance matrices. This is illustrated with two synthetic examples for several degrees of spatial variability.