Variations in the electric and magnetic fields are calculated for a non-homogeneous, two dimensional structure representing a sediment-filled graben surrounded by crystalline rocks. The apparent resistivities calculated along the cross-section profile for the electric field parallel (ρE) and perpendicular (ρH) to the strike are anisotropic. The two apparent resistivities, ρE and ρH, at a given point outside the graben, parallel each other over a broad range of periods. They do not show a convergence at long periods. Thus, it is not necessarily an indication of non-homogeneity at depth, when ρE and ρH are different at long periods. In this case, the apparent resistivity anisotropy is caused by a near-surface distortion of telluric currents. Although the ρE data are less disturbed by the non-homogeneity, it does not seem justified to interpret the ρE data in terms of Cagniard models.