Two and three-dimonsional ERT modelling for a buried tunnel

Nowadays, finding either natural or man-made hollows in the subsurface is a challenge for civil engineers. Thanks to advancements in science, geophysical methods can handle this problem. Two and three-dimensional distribution of subsurface electrical resistivity are known as electrical resistivity tomography. Nowadays, geoelectrical tomography is an inseparable part of engineering, exploration and the environmental studies. A growing number of electrical arrays have several advantages and disadvantages. Choosing appropriate array and considering the relation between array parameters and geometry of exploration target are the necessities of geophysical studies. Regarding the heterogeneous nature of the earth, it is clear that 2-D studies have obviously higher accuracy and reliability compared with 1-D. likewise, 3-D studies are more accurate and reliable compared with 2-D ones. The purpose of this study is to investigate geoelectrical response of tunnel space and its geometrical relationship with the data-acquisition parameters so as to boost the efficiency of electrical resistivity method in similar studies. For this purpose, the geological circumstances of the tunnel were two-dimensionally modeled with finite difference method, assuming 3% noise, for Wenner-Alpha, Wenner-Schlumberger and Dipole-Dipole arrays. Thus, resistivity of tunnel and surrounding medium are 100 and 10 ohm-meter, respectively. Then the values of resistivity were inverted and obtained norm L1 method. For all arrays, number of electrodes and electrode spacing were considered 36 and 1 meter, respectively. Data point density, sensitivity, horizontal and vertical resolution of arrays helped to select appropriate array and find the relation between the array's geometry and geometry of tunnel. It is found that Dipole-Dipole array has higher data coverage and sensitivity compared to Wenner-Alpha and Schlumberger. The vertical distance of data points is a function of the dipole length. Meanwhile, the horizontal distance between two adjacent data points depends on the array midpoint movement. In order to detect the tunnel, the horizontal length of tunnel must be at least twice as much as horizontal distance of two adjacent data points. What is more, vertical length should be at least twice the vertical distance of two adjacent data points. Therefore, the electrode spacing must be less and equal to half of horizontal length of tunnel and dipole length should be less and equal to 1.78 times of vertical length of tunnel. 3-D forward and inverse modelling were implemented. The results of 3-D inversion of 2-D data indicate reasonable ability of this method. Expanding horizontal resolution relations among profiles leads to obtaining a clear image of anomalies which in turn results in the distances among parallel profiles should be less or equal to half of the width of anomaly along the perpendicular to profiles. In spite of efficiency of this method for mapping tunnel space, the contrast between tunnel space and surrounding medium, earth heterogeneity, high level of noise in depth and dip of tunnel are some limitations which have adverse effects on results.