Cauchy data requirement of the inverse problem of the mean age equation

Abstract

AbstractA classical theoretical inverse problem in groundwater hydraulics is the calibration of a heterogeneous isotropic hydraulic conductivity field using known hydraulic head data at each point in the domain. It has been long known that a necessary condition for the uniqueness of the solution to this theoretical inverse problem is the Cauchy data, i.e., the hydraulic conductivity values (or, equivalently, flux) along a line crossing all streamtubes in the entire domain. This result has been cited in identifying the value of boundary flux data in practical inverse problems, although in general such data are generally not available. In this work, we show that groundwater mean age data replace this Cauchy data requirement.