Performance Bounds for an Inverse Resistivity Problem

A procedure has been proposed for recovering a radially varying electrical resistivity profile from a particular series of dc electrical measurements. Such a procedure has potential applications to the study of the invasion of porous materials by electrically conductive fluids. This paper concerns the sensitivity of such a procedure to inaccuracies in the measurements. It is shown that, for a layered conductivity profile, the sensitivity of the conductivity estimates to measurement inaccuracy grow exponentially with the number of layers. This result indicates that resolution will be severely limited by measurement inaccuracy in the reconstruction of a conductivity profile from this particular series of dc electrical measurements.