Definition and interests of reciprocity and reciprocity gap principles for groundwater flow problems

We introduce the reciprocity and reciprocity gap principles for flow problems in hydrogeology and illustrate their interest in addressing identification problems. The reciprocity principle is derived from mechanics and establishes for flow problems a relationship between different sets of forcing terms, including sources, sinks and boundary conditions, and the resulting head fields. The reciprocity gap principle compares different head fields resulting from the same forcing terms applied to different structures. We give general 2D expressions of the reciprocity and reciprocity gap principles for transient flow problems and give two examples of applications for the identification of transmissivity values and interfaces between different transmissivities. Identification capacities of the reciprocity and reciprocity gap principles yielding direct inversion methods could be used as initial guesses for more advanced inverse problem methodologies.