2D and 3D Subsurface Resistivity Imaging Using a Constrained Least-Squares Algorithm

− This work describes a single-step constrained least-squares algorithm able to image underground electrical resistivity distributions. Using an approximate analytical solution for a spherical object embedded in a homogeneous medium yields synthetic data. A 16-electrode array yields 104 independent measurements. Shifting the electrode array parallel to itself permits us to obtain 3D images. The image reconstruction algorithm needs to calculate a damping factor in order to obtain a useful image. The L-curve method calculates a suitable damping factor automatically. However, an experimental trial-and-error refinement improves the accuracy in target detection. Experimental measurements involving spherical and cylindrical objects immersed in a water tank validate the proposed algorithm. Images deteriorate for deeper targets, particularly for spherical objects. Cylindrical objects whose axis is perpendicular to the electrode array are described by a 2D cross section, which need a reduced number of voltage measurements. Taking a reference measurement before immersing the objects in the water tank reduces errors in the reconstructed image because of the uncertainty in electrode positioning and the finite dimensions of the tank. A field survey carried out on a farm field has permitted us to detect a 1 m plastic tube 16 cm in diameter, buried at 24 cm depth. The reconstruction algorithm is fast because it is non-iterative and takes only a few seconds to image the subsurface on a portable personal computer.