Aquifer Parameter Identification

This paper presents an analysis of the inverse problem of parameter (or parameters) identification in unsteady ground-water flow. The response of the system is governed by a typical nonlinear second-order partial differential equation for which there exists no closed-form solution. Identification is an inverse process whereby the parameters embedded in a differential equation are determined from observations of the system's input and output along with appropriate initial and boundary conditions. These parameters are usually not physically measurable. In this paper, a simple but illustrative inverse problem is analyzed by quasilinearization, maximum principle, gradient method, the influence coefficient method, and linear programming. A comparison is made between these methods. The problem of convergence and stability is examined and demonstrated by numerical experimentation.