An Automatic Solution for the Inverse Problem

The automatic computing of the estimated hydraulic parameters of an aquifer when the data consist of the piezometric head and the flow rates of the wells (the ‘inverse problem’) is a very good example of an improperly posed problem, if we try to solve only its mathematical part. Yet if we use the available physical information about the structure of the desired solution, the problem becomes properly posed mathematically. The main idea is that the desired solution is the regional distribution of the hydraulic parameters and is consequently the softest mathematical solution. Nevertheless, as the mathematical problem improves, we need a practical way to obtain the best estimate of the hydraulic parameters from actual measures, which always include errors. The new method gives a solution to these two problems. Because of the complexity of the theoretical aspects of the method, the present paper is only an abstract.