Temporal variations of the polar moment of inertia and the second-degree geopotential

In order to study the geodynamic behaviour of the Earth over short (elastic Earth) and long (almost perfectly liquid Earth) geological periodic variations, the changes of the moment of inertia are decomposed into two parts: the first, described by a volume integral, explains the effect of the density variations, while the second gives the impact of the surface variations using a surface integral. It is shown that both components have physical significance, but their contribution is different in case of short (lunisolar) and long (connected to secular despinning) periods.