Mode conversion to the fast magnetosonic wave by anisotropic ionospheric currents from a localized incident shear Alfv¿n wave is studied in detail, based on a simple layered model inclusive of an anisotropic conducting sheet (the ionospheric E layer) and an upper ionospheric ducting layer under vertical, uniform ambient magnetic field lines. A horizontal profile of electromagnetic field intensity at the E layer shows a wider spread than that of the incident wave due to trapping of the fast magnetosonic wave in the ducting layer. Since electrostatic electric field intensity of the incident Alfv¿n wave is dominant in the central region, the eddy Hall current associated with the Alfv¿n wave generates the ground magnetic field variations. On the other hand, since electromagnetic electric field intensity of the trapped fast magnetosonic wave exceeds to that of the incident Alfv¿n wave in the region surrounding the central region, both the magnetic field of the fast magnetosonic wave and the secondary field due to the eddy Pedersen current contribute to the ground magnetic field variations. ¿ American Geophysical Union 1988