Depth and size determination of concentric cylindrical anomalies applied to leak detection in buried pipes

This paper describes a novel approach to depth and size determination of electrical resistive concentric cylinders using the gradient array. The anomaly is assumed to be immersed in a uniform electrical field. The expression for the apparent resistivity of deep anomalies is relatively simple regardless of the number of cylindrical shells, and is based on the normalized dipole moment. The maximal absolute value of the normalized apparent resistivity profile and its zero crossings yield the depth of the buried anomaly. The radius of the external shell can be determined if the normalized dipole moment of the anomaly is known. The particularization of the analysis to two concentric cylinders can be applied to leak detection in buried pipes. The validity of the method has been tested by numerical simulations and by immersing several cylindrical objects in a phantom.