THE MINIMUM STRUCTURE SOLUTION TO THE INVERSE PROBLEM

The inverse problem of estimating the conductivity function from head observations is generally ill posed: Many conductivity functions are c onsistent with the data. It is widely accepted now that a well-defined estimate can be obtained only if additional information about the fun ction structure is introduced into the problem formulation. This work presents a method to obtain a stable and reasonable estimate that util izes only the data and the flow or transport model with the minimum po ssible suppositions about the unknown function or its structure. The m otivation is to develop a solution that has only characteristics that are traced directly to the data and the flow or transport model, witho ut taking advantage of spatial continuity or other ''prior information .'' The solution is obtained by minimizing the upper bound to the erro r, or, in a stochastic conceptual framework, as the most likely soluti on given the data. This solution, although generally not the most accu rate since it neglects to utilize structural information that may be a vailable, is of fundamental importance and may be useful as a benchmar k. For example, by comparing this solution with other solutions, one c an become aware of how prior information or the model of spatial struc ture affects the solution to the inverse problem.