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

Manel Gasulla, Josep Jordana and Ramón Pallás-Areny

Divisió d'Instrumentació i Bioenginyeria, Departament d'Enginyeria Electrònica Universitat Politècnica de Catalunya

Jordi Girona 1-3, Edifici C-4 08034 Barcelona, SPAIN

Phone 34-93-401-7483 Fax 34-93-401-6756

e-mail: mgasulla@eel.upc.es

Abstract - 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.

Keywords: Subsurface resistivity imaging, Least-squares algorithm, Electrical resitance tomography, Spherical and cylindrical targets.