The density and Q-factor models based on the new data on the nutations and overtones of the free oscillations of the earth: 2. The results of the numerical modeling of the solution of the inverse problem

In the first part of the paper, we obtained the refined estimates for the periods and Q-factors of the fundamental modes and overtones of spherical and toroidal oscillations with periods longer than 3 min from the data on the free oscillations of the Earth, which were excited by the earthquakes with magnitude 9 that occurred in Sumatra, Japan, and the Sea of Okhotsk. In (Molodenskii et al., 2013), we analyzed the limits of the admissible density distributions in the mantle and liquid core of the Earth, using the data on the amplitudes and phases of the forced nutations, as well as the periods and attenuation factors of the fundamental modes of the free spheroidal and toroidal oscillations of the Earth. These studies were conducted with the fixed values of the total mass and total moment of inertia of the Earth and the fixed distributions of the body seismic waves in the mantle and in the core. The solution was obtained by orthogonalizing the kernels of the integral equations that link the residuals of the observed frequencies and attenuation factors of the free oscillations, as well as the amplitudes and phases of the forced nutations, with the sought densities and Q-factors of the mantle and liquid core. Below, we present the solution of the same problem with allowance for the results obtained in the first part of this paper, namely, the new data on the periods and attenuation factors of the fundamental modes of free oscillations of the Earth and on the periods of the first four overtones of the free spheroidal and toroidal oscillations. Despite the involvement of the new data on the overtones, which have not been considered in our calculations, the weighted root mean square deviations of the theoretical predictions from the observed periods and attenuation factors of the free oscillations, as well as the amplitudes and phases of the forced nutations, have significantly decreased. This is due to (1) the noticeable reduction of the real errors in estimating the parameters of the free oscillations described in the first part of the paper and (2) the inclusion of the quantities determining the depth- and frequency dependences of the Q-factor in the mantle in the set of the independently varied parameters.