Approximate three-dimensional resistivity modelling using Fourier analysis of layer resistivity in shallow soil studies

The approximate forward modelling method using Fourier analysis has been used in 2-D applications for several decades. It involves decomposition of the terrain parameters, either the resistivity or the layer thickness, into a Fourier series expansion to simplify the problem to that of a 1-D situation. In this study, the Fourier analysis is applied to 3-D forward modelling for the purposes of shallow DC resistivity imaging with pole-pole array. Our work is to assess advantages and drawbacks of the simplified approach by comparing to exact 3-D solutions, method of moments (MoM) and surface integrals and to the Born approximation applied to MoM. While the Fourier analysis method offers very short calculation times, it shows a significant, albeit systematic, reduction of the anomaly amplitudes; and its ability to delineate anomaly sources is lower than the other methods. Nevertheless, its rapidity makes it an interesting first approach in the modelling of DC resistivity results.