A note on the topographic distortion of magnetotelluric impedance

Magnetotelluric surveys are prone to interpretation errors in the presence of rough topography, which may need to be compensated for. In the present work we assume that the surface of the Earth is simulated by a single-valued, twice differentiable function f(x,y). By appropriately expanding the surface magnetic field, we obtain the distorted magnetotelluric impedance tensor in terms of an expansion depending on the external radii of curvature of f(x,y) at the observation point and on skin depth. Based on first principles, an analytic estimation of the topographic corrections of the magnetotelluric impedance tensor is obtained.