Resolution of four collinear arrays to a 3D prism in multi-electrode resistivity surveys

The Earth Resistivity Tomography (ERT) is a geophysical technique widely used in many areas such as hydrogeology, mining, geothermal, and archeology applications. This method usually employs standard electrode arrays. Here, we examine the performance of four of these arrays (Wenner (WN), dipole-dipole (DD), pole-pole (PP), and pole-dipole (PD)) by analyzing their resolutions of the parameters of a simple three-dimensional (3D) prism embedded in a homogeneous host. The five model parameters are depth, length, width, thickness, and resistivity. We consider different versions of a base model by varying their five parameters. Sensitivities associated with the derivatives of the apparent resistivity response with respect to the parameters are weighted by the data errors. These errors are estimated considering a power law function for the error in the measured voltages. Parameter uncertainties are estimated performing a singular value decomposition of the sensitivity matrices. The best resolved parameters are the depth to top and length of the body, while the least resolved are the resistivity, width and thickness. The results show that the number of data is the most critical factor influencing the resolution of the prismatic body. The pole-dipole array is the best of the four arrays because it had more data, better than the Wenner array, despite having higher sensitivities. Another option with a larger number of data is the Schlumberger array with arbitrary separation between potential electrodes.