Typical 3-D electrical resistivity tomography sampling schemes, which require a grid of electrode lines to be deployed, are limited by physical conditions of the area under study. New array techniques are needed to characterize the subsoil beneath anthropogenic or natural structures to define hazardous zones. Use of multiple L-shaped arrays overcome the need for a grid of electrodes by surrounding an area in a square of electrode lines; however, in some instances, the physical environment does not allow closure of a square of electrodes. An alternative array introduced in this investigation is termed the horseshoe array. The horseshoe array combines the L-shaped arrays with equatorial and minimum coupling arrays to overcome array closure problems. Three synthetic examples were investigated to establish the limitations of the horseshoe array, and to describe the geological conditions of the subsoil, e.g., building foundations and fractures.
The first two examples represent two resistive cubes initially located in the southern and northern positions of the array, and then are moved to a diagonal of the array. In both examples, the cube located near the electrode lines was well defined, while the cube located near the line with no electrodes was not detected. On the other hand, a weak signal for the cube located along the diagonal was observed, but only when located near the electrode line. This alternative array revealed a low tri-dimensional resolution zone possessing an inverted triangular-shaped geometry towards the line with no electrodes.
A third example consisted of a low resistivity thin fracture embedded in a highly resistive infill. The solution computed demonstrated that the horseshoe array can resolve the infill close to the surface; however, the thin fracture is masked by the infill.
The above-mentioned methodology was applied on a residential complex named La Concordia. Several buildings within the residential area suffered strong structural damage caused by fractures and subsidence within the subsurface. The residential complex, consisting of six four-story buildings in an area 33 × 80 m2, is located towards the eastern region of Mexico City. The horseshoe geometry, combined with Wenner-Schlumberger, dipole-dipole, equatorial-dipole, and minimum-coupling arrays, was used to investigate the subsurface beneath the buildings.
A maximum depth of 8 m was investigated. A pattern of elongated resistivity anomalies (northwest-southeast direction) were associated with possible fracturing or differential compaction. Such features are caused by intense water extraction of the poorly consolidated clays that cover most of the central portion of the Mexican Basin.