In this paper, a method was proposed which focused on the question, namely on how to invert data on arrival times at various (and numerous) points in the porous medium to map the permeability field. The method, elements of which were briefly described in (9), is based on a direct inversion of the data, as will be described below , rather than on the optimization of initial random (or partly constrained) guesses of the permeability field, to match the available data, as typically done in the analogous problem of pressure transients. The direct inversion is based on two conditions, that Darcy's law for single-phase flow in porous media is valid, and that dispersion of the concentration of the injected tracer is negligible. While the former is a well-accepted premise, the latter depends on injection and field conditions, and may not necessarily apply in all cases. Based on these conditions, we formulate a nonlinear boundary value problem, the coefficients of which depend on the experimental arrival time data.