Study on the distortion of apparent resistivity curves caused by the ‘infinite’ electrode space of a Pole–Pole array and its correction

Abstract

The Pole–Pole (PP) array is widely used for measurements that incorporate two-dimensional (2-D) and three-dimensional (3-D) multi-electrode electrical resistivity surveys, although an effective equilibrium has not yet been achieved between two factors, the location of ‘infinite’ electrodes and the data utilisation of the effective resistivity, which affects the detection accuracy; thus, the data collected under the conditions of ‘infinite’ electrodes that are as finite as possible are maximally effective. Studies have shown that the optimum ‘infinite’ electrode distance must be greater than 20 times the current-potential electrode distance AM; this value is much greater than the currently used value of 5 to 10 times AM. However, limitations imposed by landforms and topographic conditions, such as mountainous areas and coal mine roadways, often prevent the ‘infinite’ condition from being satisfied. In this study, a field test was designed and performed by adopting a particular PP array to collect sounding data under different ‘infinite’ electrode distances, and the differences were analysed in the apparent resistivity curves calculated with different geometric coefficients. The results reveal that when the ‘infinite’ electrode space is finite relative to AM, significant distortion may occur, and a minimum inflection point may appear in the sounding curve of apparent resistivity that is calculated with the geometric coefficient Kpp. Although the data past the minimum inflection point of ρs-mpp curve lose their value for the sounding application, a portion of the first segment of the distorted curve can be used, therefore, a correction formula under the condition of non-infinite electrode (Bing and Greenhalgh, 1998) space in a PP array is derived based on traditional electric field theories and formulas of apparent resistivity under different electrode arrays. The error analysis after correction indicates that the data utilisation ratio in the corrected effective apparent resistivity is significantly improved, and all the data that appear before the minimum inflection point can be effectively corrected. Additionally, the error between the corrected apparent resistivity and the value under an ideal state (when BM is at least 20 times AM) is less than 5%. Engineering application cases are conducted to validate the effectiveness of this correction formula, and the results indicate that this formula can be applied to process the resistivity sounding data affected by the ‘infinite’ electrodes.