Damping of free nutation and relaxation time of the earth

Abstract

The dissipation of energy in the mantle of the Earth is held to be the main cause of the damping of the free nutation. The mantle is treated as a “Maxwell body.” Under these assumptions the period and the time constant of the damping are calculated in analogy to a former calculation of Jeffreys, who restricted himself to the case of an ideal elastic body. Comparison with the observed period and damping gives Love parameter z ≈ 0.3 and relaxation time τ ≈ 10 8 sec. It turns out, however, that a layer with τ values of 10 5 sec below a large zone with τ ≈ 10 8 sec would give about the same dissipation: therefore one can't find such a layer from the damping data. Nevertheless, a sufficiently large zone in the mantle with τ ⪆ 10 8 sec seems to be necessary in order to excite free nutation. On the other hand, zones of many hundred kilometers in size with relaxation times of τ ≈ 10 6 sec may hardly exist in the mantle, otherwise the damping should be more effective.