This study shows that the distributed model of permeabilities in geostatistics is proposed and uniquely solved in the numerical test. A hypothetical aquifer divided into twenty piecewise zones is designed. Twenty constant-permeabilities are individually identified and some of them result in inaccurate solution. The difficulties of an inverse problem with ill-posedness prevent us from getting the stable, unique and accurate solutions of identified permeabilities. A distribution model of permeabilities mapped through geostatistics is herein proposed. A sensitivity of observation updating to the parameters to be identified is then enhanced over the whole area. The mathematical foundation for the advances of the sensitivity is also investigated and discussed. It can be proven that the proposed approach is greatly helpful in identifying a spatial distribution of piecewise permeabilities.