The disturbances of the velocity and magnetic fields close to the Earth's core-mantle boundary, caused by sudden irregular changes in the Earth's rotation, are investigated. The problem leads to the investigation of the structure of the Ekman-Hartman hydromagnetic boundary layer, the magnetic diffusive region and the currentless region. Precise Laplacean inversions of the images of all disturbances in the Earth's core-mantle system are obtained for the limiting case of a zero magnetic Prandtl number, δ=0. The disturbance of the velocity in the direction of the axis of rotation (Ekman suction) in the currentless region has the nature of inertial oscillations with a frequency of 2Ω. Additional disturbances (with respect to the case of δ=0) of the velocity in the azimuthal and radial directions, particularly for the EHL and MDR region, are determined for the case when 0<δ « 1. The disturbance in the velocity again has the character of inertial oscillations with the frequency 2Ω, being exponentially damped in EHL asexp (−2α2Ωt) and in MDR asexp (−α2Ωt).