Excitation of free oscillations of the earth by the Kurile Islands earthquake of 13 October 1963

1964 ◽  
Vol 54 (5A) ◽  
pp. 1341-1347
Author(s):  
L. E. Alsop
Keyword(s):  
Upper Mantle ◽  
Free Oscillation ◽  
Free Oscillations ◽  
Long Period ◽  
Kurile Islands ◽  
The Earth ◽  
Spectral Peaks ◽  
Good Agreement ◽  
Chilean Earthquake

Abstract Peaks corresponding to free oscillation of the earth have been observed in the spectrum of a seismogram written following the Kurile Islands earthquake of 13 October 1963 by a special long-period vertical seismograph, with a 60-second pendulum. The periods obtained for the free oscillations, which are all of the spheroidal type, and which lie in a range of 200 to 1000 seconds, are in good agreement with values previously obtained from the great Chilean earthquake of 22 May 1960. No spectral peaks are observed at periods shorter than 200 seconds. This same phenomenon was observed in the spectra of the Chilean earthquake, and it is probably associated with the properties of the vibrating medium, i.e., the upper mantle, rather than with the source.

Torsional oscillation of a homogeneous elastic spheroid

1962 ◽  
Vol 52 (3) ◽  
pp. 469-484 ◽  
Author(s):  
Tatsuo Usami ◽  
Yasuo Satô
Keyword(s):  
Fundamental Mode ◽  
Free Oscillation ◽  
Torsional Oscillation ◽  
Numerical Calculations ◽  
Higher Harmonics ◽  
Oblate Spheroidal ◽  
The Earth ◽  
Spectral Peaks ◽  
The Difference ◽  
Spheroidal Coordinates

abstract There are several causes for the observations of splitting of the spectral peaks determined from the free oscillation of the earth. In this paper, the splitting due to the ellipticity is studied assuming a homogeneous earth described by oblate spheroidal coordinates. Ellipticity causes the iTn mode to split into (n + 1) modes, while the earth's rotation causes it to split into (2n + 1) modes. 1/297.0 is adopted as the ellipticity of the earth. Numerical calculations are carried out for the fundamental mode (n = 2, 3, 4) and for the first higher harmonics (n = 1). The difference between the extreme frequencies for each value of n is 0.7% (n = 2), 0.5% (n = 3), and 0.4% (n = 4).

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.

Relationship of the Long-Period Free Oscillations of the Earth with Atmospheric Processes

2018 ◽  
Vol 481 (1) ◽  
pp. 958-962 ◽  
Author(s):  
G. M. Shved ◽  
G. S. Golitsyn ◽  
S. I. Ermolenko ◽  
A. E. Kukushkina
Keyword(s):  
Free Oscillations ◽  
Atmospheric Processes ◽  
Long Period ◽  
The Earth ◽  
Relationship Of

The response of the horizontal pendulum seismometer to Rayleigh and Love waves, tilt, and free oscillations of the earth

1968 ◽  
Vol 58 (5) ◽  
pp. 1385-1406
Author(s):  
P. W. Rodgers
Keyword(s):  
Correction Factor ◽  
Rayleigh Waves ◽  
Complete Response ◽  
Love Waves ◽  
Free Oscillations ◽  
Long Period ◽  
The Earth ◽  
Circular Particle ◽  
Rayleigh And Love Waves ◽  
Horizontal Pendulum

Abstract The horizontal pendulum seismometer is sensitive not only to acceleration along its sensitive axis but also to tilt, variations in the angle of inclination, and along-the-boom acceleration. The complete steady-state response of this type of seismometer to Rayleigh and Love waves, tilt, and free oscillations of the Earth is treated. An equation of motion is developed which includes the effects of tilt, variation in the angle of inclination, and along-the-boom acceleration. An approximate solution to this equation is obtained which separates out the response due to each effect. The response, including these effects, is developed for Rayleigh and Love waves and the conditions under which along-the-boom acceleration and variations in the angle of inclination are important are stated. The question “How much of the seismogram is due to tilt?” is answered in detail for long period Rayleigh waves and free oscillations. It is shown that the seismograms resulting from such waves can require sizable corrections depending on the wave parameters. A correction factor for Rayleigh waves is developed which is universal in the sense that it is independent of the parameters of the particular seismometer and thus applies to all pendulous horizontal seismographs. For Rayleigh waves it is a function only of ellipticity, phase velocity, and period. Correction factor curves for long-period retrograde Rayleigh waves are presented. For circular particle motions a ten per cent correction is required for a three hundred second Rayleigh wave. The problem of obtaining the horizontal ground motion is treated. The response of the horizontal seismometer as a tilt meter is examined; a conversion factor between displacement and tilt magnification is developed. The complete response to simultaneous spheroidal and torsional free oscillations of the Earth is developed. It is shown that the principal response to the low-order spheroidal modes is as a tilt meter. The relationship between the horizontal and vertical seismogram is developed.

Universal dispersion tables

1969 ◽  
Vol 59 (4) ◽  
pp. 1667-1693
Author(s):  
Don L. Anderson ◽  
Robert L. Kovach
Keyword(s):  
Upper Mantle ◽  
Free Oscillation ◽  
Velocity Structure ◽  
Shear Velocity ◽  
Average Density ◽  
Earth Model ◽  
The Core ◽  
The Earth ◽  
Small Change ◽  
Dominant Parameter

Abstract The effect of a small change in any parameter of a realistic Earth model on the periods of free oscillation is computed for both spheroidal and torsional modes. The normalized partial derivatives, or variational parameters, are given as a function of order number and depth in the Earth. For a given mode it can immediately be seen which parameters and which regions of the Earth are controlling the period of free oscillation. Except for oSo and its overtones the low-order free oscillations are relatively insensitive to properties of the core. The shear velocity of the mantle is the dominant parameter controlling the periods of free oscillation and density can be determined from free oscillation data only if the shear velocity is known very accurately. Once the velocity structure is well known free oscillation data can be used to modify the average density of the upper mantle. The mass and moment of inertia are then the main constraints on how the mass must be redistributed in the lower mantle and core.

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