Impact of reciprocity principle on parameters identification through interference pumping tests

In groundwater science, flow problems have great importance: they allow technicians to understand, and predict, the global behavior of an aquifer which might be subjected to stresses (i.e. pumping) or variations in its configuration (i.e. variations in boundary conditions). Partial differential equations able to describe the process have been written: they include both state variables and parameters. For extremely simple cases, analytical solutions can be found, but when the geometry of the aquifer, or the spatial distribution of aquifer parameters, become complex, numerical solutions are needed. In present work, both these aspects will be faced in order to provide a global description of what is called direct problem: from a given data set, being able to describe state variables as an output. The question of how to choose the 'given' data set is another important aspect in flow modeling, and is named inverse problem when aquifer parameters are searched starting from state variables (head distributions subsequent to stresses, i.e. pumping tests). Inverse modeling is not peculiar of groundwater flow: it can be adapted to each situation where state variables and parameters are involved to describe a phenomena. The most common approach to solve an inverse problem is through the progressive minimization of a quantity that is function both of state variables and parameters and is named objective function. The aim of this work is to look for the influence, in the context of inverse modeling, of some measurements of the state variables (heads) that, according to what is called Reciprocity principle, might bring to the inverse problem the same amount of information of other measurements already taken into account. We will study the influence of these reciprocal information, both from a theoretical and a numerical point of view, on the minimization procedure, on the confidence interval of estimated parameters, on computational cost. Numerical simulations will be performed both on a simple square domain and on a more complex and realistic domain, an area in the Oristano plain, Sardinia.