Which geoelectric array sees the deepest in a noisy environment? Depth of detectability values of multielectrode systems for various two-dimensional models

In an urban environment, the two dominating difficulties of any geophysical measurement are as follows: (1) the area available for measurements is restricted, therefore, the length of the geoelectric layout is also limited; (2) the noise level is high, and noise diminishes the maximum depth at which any subsurface target can be detected. For this article, the depth of detectability values (i.e. the maximum depth values at which useful information can still be obtained about a given inhomogeneity at a given noise level) were determined from results of two-dimensional numerical model computations assuming multielectrode (electrical resistivity tomography) measurements. Depth of detectability studies were carried out for six different geoelectric arrays, assuming various noise levels. It was found that the depth of detectability is both array and model dependent. Therefore, in a field study it is advisable to select the array which has the greatest possible depth of detectability values for the given model at the given noise level. When there is no a priori assumption about the subsurface model, either the pole-dipole (P-DP) array or the dipole axial (DP-ax) array is recommended as a default selection, because for most of the studied models they provide the largest depth of detectability values. A twofold increase in the noise level may lead to a decrease of approximately one half in the depth of detectability itself.