On the Admissible Range for the Mass and Inertia Moments
of the Liquid Core: I. Solving the Inverse Problem of Nutations
and Free Oscillations of the Earth by Decomposition of
Mechanical Parameters in an Orthogonalized Basis

S. M. Molodenskii and M. S. Molodenskii

Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, ul. Bol’shaya Gruzinskaya 10, Moscow, 123995
Russia

Received October 11, 2012; in final form, December 7, 2012

Abstract—The results of solving the inverse problem of forced nutations and free oscillations of the Earth by
decomposing the Q-factor and small depth variations in density in a system of orthogonal functions are consid-
ered. These functions are determined by orthogonalization of the functional derivatives of the observed param-
eters with respect to the depth distributions of the sought parameters (assuming there are no distributions of the
velocities of body seismic waves V_p and V_S with depth and unchanged total mass M and inertia moments I of
the Earth). The examples are presented to illustrate the numerical solution of the inverse problem on finding the
density distributions in the mantle and core of the Earth using orthogonalization of the integral constraints for
the probable depth distributions of density describing the conditions of unchanged M and I, as well as the con-
straints posed by the data on the periods of the free low-order oscillations of the Earth.

DOI: 10.1134/S1069351313030099

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