AN INVERSE PROBLEM FOR THE HYDRAULIC-PROPERTIES OF POROUS-MEDIA

An inverse problem is formulated to determine the two coefficients in the pressure head formulation of the porous flow equation from a simpl e hydraulic experiment. Integral identities are derived which relate c hanges in the coefficients to changes in measured outputs. These ident ities are used to precisely define the sense in which the experimental data are able to distinguish between different porous media. It is al so shown that the mapping associating input coefficient values to outp ut data values is explicitly invertible and that there is a related ou tput least squares problem whose solution is the solution of the inver se problem.