Inverse problem for tripotential measures in the study of buried cavities

Abstract

This paper presents a solution to the inverse electrical problem for the interpretation of apparent resistivity anomalies due to empty buried cavities of quasi-spherical shape when tripotential measures are carried out. The anomalies of the apparent resistivities ra,rb andrg,and the composed resistivitiesrmand rt were previously calculated for a sufficient class of spherical models of resistivity anomalies. Then, for the whole class of models, some functionals of spatial distribution of the apparent and composed resistivity were identified and analyzed. They represent the average characteristics of the anomalies and, depending in a simple way on the fundamental parameters of the sources of the anomalies (average diameter and depth), they allow reliable estimates to be determined. Among the studied functionals, those allowing the most stable and less biased estimates of the anomaly source parameters are identified by numerical simulations with random noise perturbed data. Finally the trend of standard deviation and bias of the estimates of the unknown parameters were analyzed by varying the source models and the set of functionals used for the inversion.