Parameter identification for the linear equation of groundwater flow

Abstract

A mathematical model is presented for identification of the parameter (S/T) in a two-dimensional, linear equation describing groundwater flow through a heterogeneous, isotropic aquifer. This model does not require an iterative solution of the aquifer equation, which is an essential characteristic of many, current identification schemes. The shape of the surface representing the piezometric head is approximated from measured samples with a second-degree polynomial. Then first and second derivatives are calculated by differentiating this polynomial, which has been fitted to the experimental data with a least squares technique. Since derivatives of the piezometric surface are calculated directly from experimental data in relatively small regions, the identification problem reduces: to the simultaneous solution of linear, algebraic equations of small dimension. No initial or boundary conditions are necessary. The method has been verified by assuming a value for S and comparing the resulting distribution of T with values that have been found in previous investigations of the region. A sensitivity analysis has been done to find the sensitivity of the method to the error in measured piezometric head.