Tomographic approach to identify transmissivity with differential system method

If two independent sets of data are available-the piezometric heads and the related source terms for two stationary flow situations, such that the hydraulic gradients are not parallel to each other-the aquifer transmissivity can be identified with the differential system method (DSM), provided that an initial value of transmissivity is given at least at one point. In field applications, it is difficult to collect two data sets that are independent throughout the aquifer, and the results depend on the location of the point where the initial value is assigned. These difficulties are reduced if several data sets are available and the differential system is obtained either by applying a least square technique to the whole ensemble of data sets, or by choosing the "best" couple of data at each point. Numerical tests on a synthetic aquifer show that both techniques yield good results and make the DSM more robust to noise on the piezometric heads than the standard DSM applied with two data sets only.