Free Oscillations of the Earth (E. R. Lapwood and T. Usami)

SIAM Review ◽  
1982 ◽  
Vol 24 (4) ◽  
pp. 496-497
Author(s):  
Susan Friedlander
Keyword(s):  
Free Oscillations ◽  
The Earth

Free oscillations of parameters of the Earth's motion in the Earth-Moon system

2001 ◽  
Vol 45 (11) ◽  
pp. 922-928 ◽  
Author(s):  
G. S. Kurbasova ◽  
L. V. Rykhlova
Keyword(s):  
Free Oscillations ◽  
Moon System ◽  
The Earth

use of apparent complex frequencies of free oscillations to estimate aspherical structure of the Earth

1991 ◽  
Vol 18 (5) ◽  
pp. 905-908 ◽  
Author(s):  
Naoki Shibata ◽  
Naoki Suda ◽  
Yoshio Fukao
Keyword(s):  
Free Oscillations ◽  
The Earth

Comparison of theoretical and observational expressions for elastic strains of the earth

1965 ◽  
Vol 55 (1) ◽  
pp. 153-163
Author(s):  
H. Takeuchi ◽  
L. E. Alsop
Keyword(s):  
Theoretical Studies ◽  
Free Oscillations ◽  
The Earth ◽  
Tidal Deformation ◽  
Elastic Strains

Abstract Transitional equations are provided between the quantities obtained in theoretical studies of tidal deformation, loading, and free oscillations of the earth and the empirical quantities obtained from observations of these phenomena. Tables of theoretical quantities are provided so that estimates may be made of the values to be expected observationally. Several examples are discussed.

Free oscillation observations through 1968

1969 ◽  
Vol 59 (5) ◽  
pp. 2079-2099
Author(s):  
John S. Derr
Keyword(s):  
Confidence Level ◽  
Free Oscillation ◽  
Statistical Tests ◽  
Standard Errors ◽  
Free Oscillations ◽  
The Earth ◽  
Earth Models ◽  
Earth Structures ◽  
Path Dependent ◽  
Consistent Basis

abstract All observations of the free oscillations of the Earth published through 1968 are weighted to produce a set of means and standard errors of the means. Fundamental orders 0 to 97 for spheroidal and 2 to 99 for torsional are treated, as well as many overtones up to order 49. Statistical tests indicate that some observations are path dependent at the 99 per cent confidence level. Comparison of these means and standard errors with published Earth models indicate that they form a consistent basis for inversion of free oscillation observations to infer Earth structures.

An application of normal mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra

1975 ◽  
Vol 278 (1280) ◽  
pp. 187-269 ◽  
Keyword(s):  
Moment Tensor ◽  
The Other ◽  
Free Oscillations ◽  
Stress Release ◽  
Modal Data ◽  
Mechanical Structure ◽  
The Earth ◽  
Principal Axes ◽  
Source Mechanisms ◽  
The Moment

A cyclic process of refining models of the mechanical structure of the Earth and models of the mechanism of one or more earthquakes is developed. The theory of the elastic-gravitational free oscillations of the Earth is used to derive procedures for resolving nearly degenerate multiplets of normal modes. We show that a global network of seismographs (W.W.S.S.N.) permits resolution for angular orders l ≤ 76 and for frequencies a) w ≤ 0.090 s -1 . The peak or centre frequency of each nearly degenerate multiplet is interpreted to be a gross Earth datum. Together, the data are used to refine models of the mechanical structure of the Earth. The theory of free oscillations is used further to derive procedures for retrieving the mechanism, or moment tensor, of an earthquake point source. We show that a globa network of seismographs permits retrieval for frequencies 0.0125 s-1 ≤ w ≤ 0.0825 s-1 . We show that refined models of structure and mechanism lead to improved resolution and retrieval, and that an array of sources further complements the resolution of multiplets. We present a ‘standardized dataset’ of 1064 distinct, observed eigenfrequencies ol the elastic-gravitational free oscillations of the Earth. These gross-Earth data are compiled from 1461 modes reported in five studies: 2 modes reported by Derr (1969), 159 modes observed by Brune & Gilbert (1974), 240 modes observed by Mendiguren ( 1973), 248 modes observed by Dziewonski & Gilbert (1972,1973) and 812 modes reported here. It is our opinion that the establishment of a standardized dataset should precede the establishment of a standardized model of the Earth. Two new Earth models are presented that are compatible with the modal data. One is derived from model 508 (Gilbert & Dziewonski 1973) and the other from model B1 (Jordan & Anderson 1974). In the outer core and in the lower mantle, below a depth of about 950 km, the differences between the two models are negligibly small. In the inner core there are minor differences and in the upper mantle there are major differences in detail. The two models and the modal data are compatible with traditional ray data, provided that appropriate baseline corrections are made to the latter. The source mechanisms, or moment tensors, of two deep earthquakes, Colombia (1970 July 31) and Peru-Bolivia (1963 August 15), have been retrieved from the seismic spectra. In both cases the moment tensor possesses a compressive (implosive) isotropic part. There is good evidence that isotropic stress release begins gradually, over 80s before the origin time derived from the onset of short-period P and S waves. During the process of stress release the principal axes of the moment rate tensor migrate. The axis of compression is relatively stable, the compressive stress rate is dominant, and the other two axes rotate about the axis of compression. We speculate that earthquakes, occurring deep within descending lithospheric plates, are not sudden shearing movements alone but do exhibit compressive changes in volume such as would be associated with a phase change. We further speculate that compressive changes in volume may occur without sudden shearing movements, that there may be ' silent earthquakes’.

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