  In a first approximation, the Earth's interior has an isotropic structure
with a spherical symmetry. Over the last decades the geophysical observations
have revealed, at different spatial scales, the existence of several
perturbations from this basic structure. In this paper we discuss the
hemispheric perturbations induced to this basic structure if the inner core is
displaced from the center of mass of the Earth. Using numerical simulations of
the observed hemispheric asymmetry of the seismic waves traveling through the
upper inner core, with faster arrival times and higher attenuation in the
Eastern Hemisphere, we estimate that the present position of the inner core is
shifted by tens of kilometers from the Earth's center eastward in the
equatorial plane. If the only forces acting on the inner core were the
gravitational forces, then its equilibrium position would be at the Earth's
center and the estimated displacement would not be possible. We conjecture
that, due to interactions with the flow and the magnetic field inside the outer
core, the inner core is in a permanent chaotic motion. To support this
hypothesis we analyze more than ten different geophysical phenomena consistent
with an inner core motion dominated by time scales from hundreds to thousands
of years.
