Attenuation of free spheroidal oscillations of the Earth after the M = 9 earthquake in Sumatra and super-deep earthquake in the Sea of Okhotsk: II. interpretation of the observed Q-factor

Abstract

In the first part of the paper, the range of the admissible values of the Q-factor for the fundamental spheroidal modes and overtones was calculated from the records of the free oscillations of the Earth after the earthquake with M = 9 in Sumatra and the super-deep earthquake in the Sea of Okhotsk. Below, the interpretation of the data obtained in the first part of the paper is presented. By orthogonalization of the functional derivatives of the eigenfrequencies with respect to the density and Q-factor of the mantle, the model distributions of these parameters which best fit the whole set of the data about the attenuation of the free oscillations and the phases of forced nutations of the Earth are reconstructed. The use of the attenuation data for the free oscillations recorded after the super-deep earthquake in the Sea of Okhotsk on May 24, 2013 significantly improves the accuracy of the Q-factor reconstruction at different depths in the mantle. The implications of the free oscillations’ attenuation data for the solution of the inverse problem of reconstructing the profiles of density and creep function of the mantle in the interval of periods from 1 s to one day are studied. Without the allowance for the attenuation data, the reconstruction errors for the density profiles were about 0.1 g/cm3, and for the shear moduli at the oscillation period of 200 s, about 4 × 109 dyn/cm2. The use of the free oscillation attenuation data largely removes this uncertainty. Although the relative measurement accuracy of the Q-factor is by about two orders of magnitude lower than the measurement accuracy of all eigenfrequencies, the weights of relative residuals of Q in the minimand functional of the weighted mean square deviations should be of the same order of magnitude as the weights for the relative changes in the free oscillation frequencies. With the allowance for the new attenuation data obtained in the first part of the paper, the reconstruction errors for these parameters have become about 1.5 times lower.