Subsurface resistivity imaging using two single-step algorithms

This paper compares two single-step algorithms to obtain 2D subsurface resistivity images based in the sensitivity theorem The first algorithm is based in the Marquardt-Levenburg method whereas the second algorithm uses a weighted backprojection technique. An approximate' analytical solution yields the data (surface potential) for a spherical anomaly immersed in a homogeneous medium when using dipole-dipole and Schlumberger-based electrode arrays A fidelity measure quantifies the reconstruction error of each algorithm, which is defined as squared inner product of the normalized difference between the true resistivity profile and the estimate. The Marquardt-Levenburg method yields smaller errors but requires a damping factor that must be obtained experimentally. The reconstruction algorithms have been validated experimentally by placing a spherical object in a plastic water tank. Data for the dipole-dipole array are less accurate at higher depths because of the small voltages detected. Errors in the reconstructed image because of the uncertainty in electrode positioning and the finite dimensions of the phantom are partially canceled by taking a reference measurement.