For aquifers having a zonation structure with the transmissivity varying smoothly and slowly over each zone, a common approach in determining transmissivity is to presume a known zonation structure and seek a constant approximation to the transmissivity over each zone. However, this procedure is not always acceptable as it may lead to instability in the estimation process.
In this paper, we discuss how one may simultaneously determine the zonation structure and a piecewise constant representation of the transmissivity by adapting the linear functional strategy proposed by Anderssen and Dietrich (1987). The implementation of this idea results in several adaptive and highly parallelizable procedures for the parameter identification problem. Some stability results and a generalization of the method using a Petrov-Galerkin interpretation are also described.