71 2. Surface geophysical methods Electrical methods Electrical methods, in DC current, are based on the measurement from the surface of the apparent resistivities of the ground. Resistivity of geological formations can vary: • from 1 to 10 ohm.m for clay and marl, • from 10 to 100 ohm.m for sands and sandstone, • from 100 to several thousands of ohm.m for limestone and the eruptive rocks, • in practice DC currents are sent in formation using current electrodes A or B (Figure 2.12a). The current sent by an electrode A(+) is collected by an electrode B(–), but according to the principle of superposition, the potential in a point M or N is the same one for a current I(+) independently sent by A or B. The measurement of the potential difference ΔV created by the passage of the current I between two electrodes M and N allows to estimate the resistivity ρ of the formation (Figure 2.12b). If the formation is isotropic and homogeneous the measured resistivity is the true resistivity of the formation. If the ground is heterogeneous, the measured resistivity is an apparent resistivity, which is a function of the nature of the ground and the dimension of the array used. The array is conventionally a 4 electrodes array AMNB (Figures 2.12b and 2.12c), the depth of investigation of which being function of its characteristic length L (Figure 2.12c). AMNB array, with constant distances between electrodes and a given characteristic length L, moved along profiles, is currently used to establish profiles or maps of resistivity, associated with a depth of about constant depth investigation. To investigate several depths, several profiles must be recorded with several characteristic lengths L (Figure 2.12d). Figure 2.12e shows an example of a resistivity map obtained with a characteristic length of 100 m. A Schlumberger array with a constant distance between electrodes M and N and a variable increasing distance between electrodes A and B is used to obtain a distribution of resistivity versus depth. One of the limitations of the electrical soundings comes to the fact that they do not consider the horizontal variations of the resistivity of the ground. Methods of electrical imagery 2D and 3D have been developed to obtain a model of the ground where the distribution of resistivities varies vertically and horizontally along the profile. 2D or 3D acquisitions generally use a great number of electrodes connected to multicore cables and placed along profiles. An acquisition device automatically selects the electrodes used for the injection of the current and for the measurement of the potential difference ΔV. It also computes the distribution of apparent resistivities versus depth Z and distances X and Y, considering the different geometries of acquisition. In a next step, 2D or 3D iterative electrical tomographic inversion algorithms are used to obtain resistivity distribution in the 2D, or 3D space. The methodology, called electrical resistivity tomography ERT, requires an a priori distribution of resistivity used to initiate the inversion process. The process
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