Non Linear Elasticity in the Free Oscillations of the Earth as Revealed by Spectral and Bispectral Analysis

摘要

In the present report the stationary waves following the Chilean earthquake of May 22, 1960, as recorded by the pair of horizontal pendulums situated in the Earth Tides Station of the Grotta Gigante near Trieste, are examined. Three distinct results have been achieved in the analysis of these records: (1) determination of the periods of the spheroidal and torsional modes by means of spectral analysis, and their comparison with the corresponding theoretical periods for the linear elastic models Gutenberg-Bullen A and Gutenberg-Bullen B; (2) determination by comparison of the spectral energies of successive sections of the spectrum of the Q parameter of the dissipation of energy due to departures from the elastic behavior in the terrestrial body; (3) determination by means of bispectral analysis of the interaction modes which are generated by the normal modes on account of the departures from the linear elastic behavior of the earth's body. With the scope of examining the origin and the nature of the interaction modes, Part I deals with the theory of the finite elastic deformations both in a system of n degrees of freedom and in a continuous system. Part II presents the results of the three analyses cited above. Taking advantage of the theoretical results obtained in Part I, one can estimate intervals allowable for the three new elastic parameters which, along with the Lame parameters of the classical theory, rule the anelastic behavior of the terrestrial body. (Author)