## 3 Methods
### Static Shift Correction and Strategy for 2D Inversion Models  
Heterogeneity of small sized bodies and resistivity discontinuities across a geological boundary can generate a local distortion of electric field amplitudes and can produce a static shift of the apparent resistivity curve [30; 31]. Thus, measured resistivity curves are shifted up or down by an unknown real factor. On the other hand, the shape of the true level of the resistivity curve remains at least same as the shifted resistivities curves. This effect should be removed to correctly infer the geoelectrical properties of the area under investigation. For the last two decades, researchers tried to find which method is most appropriate to correct the static shift phenomenon [30; 31; 32; 33]. The Time Domain Electromagnetic Method (TDEM) is unaffected by static shift and this method is usually used to perform the correction when TDEM surveys can be performed coincidently with MT soundings [9; 34; 35]. In this study, the TDEM method is thus used in order to correct the static shift of each MT sounding where MT stations are close to the TDEM stations for the 2D profile perpendicular to the rift axis (Figure 1). A TDEM survey was carried out by ISOR with the collaboration of Djibouti government and the TDEM penetration overlapped with shallow MT penetration. Static shift correction was performed to find and determine the proportionality coefficient between resistivity derived from TDEM data and resistivity derived from MT data. Consequently, both resistivity of TE and TM modes are shifted to the level of TDEM resistivity which implies that the near surface is 1D. At the surface and in the shallow subsurface of geothermally active regions such as the Asal rift, resistive environments and dry volcanic rock are more common, and small-scale resistivity contrasts are likely to significantly distort the amplitudes of electric fields [31] and static shift should be corrected to avoid the distortion generated by the small-scale bodies near surface. In addition, in some areas with hilly landscape, topography effect can cause a misinterpretation of MT data because the induced current density can be concentrated in valleys and spread out on hills. In this study, the topography effect was not considered for the 2D inversion. The topography of the study area where electromagnetic soundings are available varies from 100 to 300 m above sea level (Figure 1) and this can be approximate by a slope angle of less than 9%. Moreover, 3D topography and bathymetry effect on MT data was studied by [36], who suggested that this effect is small for a short period range (corresponding to shallow depth approximately the depth of the crust) and can be neglected if the slope angle is less than 9\({}^{\circ}\). So, in the Asal rift, the topographic effect is assumed to be negligible and a 2D mesh where the top of the 2D inversion model did not vary with the altitude of MT stations along the 2D profile is used. 3D galvanic distortion was adequately corrected by the TDEM data, whereas the potential 3D inductive effect or 3D inductive regional conductivity was checked by analysing the value of phase sensitive skew. Thus, values of phase sensitive skew greater than 0.3 are correlated by the presence of 3D inductive effects [29]. In cases where 3D inductive effects are not dominant, 2D inversion can be a good reasonable solution.