Identification of aquifer transmissivities: The comparison model method

Abstract
A method for solving the inverse problem in hydrogeology is presented. This method is suitable for computing the interblock transmissivities (harmonic mean or others) referred to the sides of the network blocks of a nonhomogeneous, anisotropic aquifer in steady state flow. The interblock transmissivities computing procedure is based on the comparison between real gradients and the ones generated by a ‘comparison model’ whose initial transmissivity value is arbitrarily chosen and constant through out the surveyed area. Alternative solutions of interblock transmissivities, one for each constant initial transmissivity value utilized in the comparison model, are obtained. Generally, these solutions differ from each other, but all of them present the characteristics of being able to reproduce, with the precision of an arbitrarily small ϵ, the real piezometrie heads, respecting the geometry and the boundary conditions of the real aquifer. The selection of the value, or set of values, of the initial transmissivity to put into the comparison model in order to obtain one solution of computed interblock transmissivities close to the real ones, both as trends and as absolute values, is rather critical. The minimum head anomaly criterion and the bottleneck criterion enable one to select a value or a set of values of initial transmissivity. These criteria exploit only the data needed for the solution of the inverse problem (real piezometric heads, geometry, and boundary conditions), and they lead to a suitable initial transmissivity that, put into the comparison model, allow one to obtain a good and meaningful solution of computed interblock transmissivities. The comparison model method and the two aforementioned criteria have been applied to a numerical case study bearing good results. The method has been tested, in order to evaluate its effectiveness, even in the case of noisy piezometric heads (piezometric heads with random errors). Even in this case the method bore satisfactory and useful results. Finally, a promising approach to the inverse problem solution, when one has at his disposal at least four sets of data coming from as many hydraulic situations, has been briefly described.