nutations of the Earth for evaluating the admissible range of the mass and moment of inertia for the liquid core.
The initial model for this study is taken in the form of the model distribution of density and mechanical Q
parameters of the mantle suggested in (Molodenskii, 2010; 2011a; 2011b). This model was constructed by the
steepest descent method in the space of 64 parameters, which determine the distribution of density and param-
eters of mechanical Q in the mantle, liquid outer core, and solid inner core of the Earth. We assumed the Q
parameter of the mantle and inner solid core to be constant and sought for the density variations for the simplest
two-parameter model of the piecewise-linear functions with the jumps on the boundary between the liquid core
and the mantle and at the olivine-spinel phase transition at a depth of 670 km in the mantle. After this, the com-
putations were repeated for the other distributions of Q (which were also assumed to be unchanged) that corre-
spond to their limiting admissible values. Using this approach, we managed to find the most probable values of
the mass and moment of inertia of the liquid core and determine the admissible range of their values. According
to our estimates, the ratios of the mass and moments of inertia of the liquid core to the mass and moment of
inertia of the whole Earth fall in the intervals 0.317996
0.00065 and 0.110319 0.00022, respectively. These values are lower than the corresponding values for the PREM model (0.322757 and 0.112297) by (1.48
0.30)% and (1.76
0.35)%, respectively. The interpretation of these results requires the revision and thorough analysis of the data on the admissible temperature range of the liquid core and (or) its chemical composition.