Explicit algebraic influence coefficients: a one-dimensional transient aquifer model

This work makes explicit an algebraic expression giving the matrix of transient influence coefficients associated with a one-dimensional semi-confined aquifer model. The domain studied is divided into a series of connected and completely mixed compartments over which the governing equation is discretized. The discrete equations obtained are solved for the compartmental hydraulic head and used to derive the algebraic expression in question. The basic properties of the so-called algebraic influence coefficients are investigated. In particular, their consistency with the exact Green function is highlighted. Finally, the newly derived influence coefficients are applied to a simplified aquifer system in order to formulate and solve the problem of identifying illegal groundwater pumping.