Invariant imbedding and the identification of aquifer parameters

Abstract

The technique of invariant imbedding is applied to the problem of identifying the parameters in an unconfined aquifer system. This new technique is shown to be a very effective way of converting field observations based upon pumping tests into the desired aquifer parameters. The procedure is straightforward as it requires neither curve plotting nor graphical matching. The parameters to be identified are the hydraulic conductivity and specific storage in an extensive unconfined aquifer system. Results and numerical experiments are presented. Identification is an inverse process whereby the parameters embedded in a differential equation are determined from observations of systems input and output along with appropriate initial and boundary conditions. These parameters are usually noy physically measurable. In general, the governing equation is nonlinear with no closed-form solution. In this paper, this inverse problem is solved by invariant imbedding and quasilinearization. A comparison is made between these methods. The problem of convergence and stability is discussed and demonstrated by numerical experimentation.