Earth and Atmospheric Sciences, Department of


Date of this Version



Published in Water Resources Research (May 1997) 33(5): 927-934. Copyright 1997, the American Geophysical Union. Used by permission.


A mathematical model of average nonuniform flow in heterogeneous stratified media is developed. The averaged Darcy's law is obtained by deriving the analytical expression of the effective conductivity tensor for media with small heterogeneities. The fundamental solution of the average flow equation (mean Green function) corresponding to the flow toward a single point source of deterministic discharge is derived. The mean head distribution is calculated for a fully penetrating well, for a finite length well in an infinite domain, and for a dipole well. The concept of equivalent conductivity is defined for use in identifying the formation conductivity properties. The procedure for identifying the mean conductivity log, conductivity variance, and vertical integral scale is suggested for the case of dipole flow.