Reliable linear transformation of pseudo-pole-pole electrical resistivity datasets

With a given fixed array of electrodes, a very large number of four-electrode measurements can be made. However, most of the possible measurements are not linearly independent, indicating that a smaller number of measurements can be made in order to save time, and the results of other measurements can be calculated later. In some cases, this calculation process can amplify measurement errors and so a robust quality control criterion is needed. In the past, it has been demonstrated that pole-pole, pole-dipole and pseudo-pole-dipole data can be used as a basis for calculating other measurements. In this study, we consider pseudo-pole-pole datasets as a basis. We define a pseudo-pole-pole array as one in which there is always a fixed current and potential reference electrode, but these reference electrodes are not necessarily far from the rest of the measurement array. We show that all four-electrode measurements can be easily calculated from pseudo-pole-pole data in ways that are similar to pole-pole data. We additionally show that good quality pseudosections and inversion results can be recovered from transformed data from pseudo-pole-pole data, especially for transformed data in configurations similar to the Wenner-α array. We also show that independent normal and reciprocal four-electrode measurements can be calculated for each four-electrode array and the comparison of these can be used as a quality control criterion. Our results show that a comprehensive dataset can be easily acquired from a pseudo-pole-pole survey which gives the geophysicist almost complete freedom of choice of array type to use in inversions.