Oscillations Of Earth Research Articles

AZIMUTH VARIATION FROM OBSERVATIONS OF CLOSE CIRCUMPOLAR STARS

The phenomenon of the variation of azimuth due to the earth's oscillation about its instantaneous axis of rotation is of considerable importance in both astronomy and geophysics. In this paper an attempt has therefore been made to design an accurate method of determining the variation of azimuth from astronomical observations, making use of only precise horizontal circle readings on an astronomical theodolite at recorded instants of intersections of close circumpolar stars within short distances of their meridian transits on each side.The special feature of the method is that its observational procedure is exactly similar to that of time-determination by the usual method of meridian transists of stars making use of a much lesser number of stars in actual practice, and is thus much simpler and less time-consuming than any of the existing methods. Moreover the variation of azimuth obtained therefrom is free from the usual errors of clocks, declinations and right ascensions of stars, as well as adopted latitudes of stations of observations, so vital in the delicete researches on the motion of the pole.

Eigenvibrations of the Earth after the Alaskan earthquake

Spectrums of the free oscillations of the earth were computed from long-period pendulum seismograph recordings obtained at the Berkeley and Oroville seismographic stations after the Alaskan earthquake of March 28, 1964. Resolution was obtained for modal orders between l = 2 and l = 29. Longitudinal and transverse components of the ground motion at Oroville were synthesized by appropriate vector addition of the horizontal-component seismograms. Harmonic analysis of the separated components yielded spectrums of the torsional and spheroidal oscillations. A striking result was the appearance of the 0S12 mode in the spectrum of the longitudinal motion and its absence in the spectrum of the vertical motion. The Oroville station was therefore near a nodal line for the vertical component of the 0S12 mode. The variations of the spherical amplitudes at both the Berkeley and Oroville stations indicated an azimuthal order number m = 0. The average vertical ground amplitudes of several modes were estimated. Between 15 and 20 peaks on each spectrum were significant at the 95% confidence level. The measured eigenfrequencies are in close agreement with similar measurements from other earthquakes. Comparison with computed periods for four earth models showed that the Gutenberg-Bullen A model gives the most satisfactory agreement with the observations.

地球振動の微分方程式を<i>r</i>=0から積分するための一工夫

地球振動の微分方程式を<i>r</i>=0から積分するための一工夫

ねじれ振動と地球核の剛性率

ねじれ振動と地球核の剛性率

地球の振動により発生する熱 (1)

地球の振動により発生する熱 (1)

Statical deformations and free oscillations of a model Earth

The Gutenberg model of the earth mantle and a homogeneous core have been used in a study of statical deformations of the earth by tidal attractions and under surface loads of spherical harmonic n types. Displacement and potential distributions within the earth are shown for eleven n values less than 16, and the values of Love's numbers k, h, and l and the similar k′ and h′ in the load problem are calculated for these n values. Free oscillations of the earth model have also been studied. Displacement and potential distributions for the above n values are drawn. The effect of self-gravitation on the oscillation periods is about 1 per cent for n = 6, and it would be smaller for larger n. The upper limit of the rigidity of the core which is compatible with the observations of the free oscillations is shown to be 1010 dynes/cm2. The radial displacement distributions within the mantle and the core are shown for various rigidity values of the core.

重力計に記録された地球振動

重力計に記録された地球振動

Torsional Oscillations of the Earth

Torsional Oscillations of the Earth

A Bacteriophage Containing RNA

A Bacteriophage Containing RNA

A study of the free oscillations of the Earth

Published observations on the toroidal oscillations of the earth are critically reviewed. A supplementary analysis of the record obtained by the Lamont strain seismometer is presented. Eleven toroidal modes are identified, and it is concluded that the periods are known to within 1 per cent. A perturbation scheme involving the ratio of the angular velocity of the earth to the resonant frequency is used in calculating the effects due to the rotation of the earth on the resonant frequency. The free oscillations are viewed as a superposition of traveling waves. In a nonrotating system two traveling waves combine to produce a stationary standing wave. In a rotating system, the rotation distinguishes between waves that travel in the direction of rotation and those that travel in the opposite direction. Rotation removes a degeneracy and results in a splitting of a spectral peak of order l into 2 times l plus 1 peaks. The fractional displacement in frequency for the lowest-order toroidal oscillations is 1/206 and of the same order as the Q of the peak, so that splitting will probably not be observed in the toroidal oscillations. Viewed locally, rotation causes a particle to precess about a direction parallel to the axis of rotation. This precession will cause a variation of amplitude with time if the motion is recorded by an instrument with an anisotropic response function. Care is therefore needed in studying the time decay of a given spectral peak. Rotation also couples the normal coordinates so that a motion that is initially purely horizontal will develop a vertical component. It is expected that vertical seismometers should record particle motion with the toroidal frequencies. The perturbations of the toroidal oscillations due to core-mantle interaction are treated in detail. An exact expression is obtained for the rate of energy dissipated by a finitely conducting plate oscillating across a magnetic field. The energy dissipated at the core-mantle boundary due to viscous and hydromagnetic coupling is shown to be insignificant as compared with the energy dissipated within the mantle. The toroidal magnetic field leaking into the lower mantle combines with the dipole field, resulting in a stress on the mantle, tending to stiffen the lower boundary. The stress is of sufficient magnitude to produce a displacement toward higher frequency in the lower-order toroidal oscillations. Observations on the (sub 0) T (sub 2) oscillations lead to an estimate of the toroidal magnetic field in the lower mantle. A calculation of elastic energy in the low-order oscillations suggests a value of 10 (sup 18) ergs per cycles per hour for the energy density at low frequencies in the Chilean earthquake. Each mode of oscillation has a characteristic radial distribution of elastic energy associated with it. This distribution determines which parts of the earth contribute most heavily in determining a particular resonant frequency. The distribution of energy for the lower 17 modes for a homogeneous and a Gutenberg model earth is calculated. The resonant frequencies for models of the earth based on the Gutenberg and Lehmann distribution of elastic properties are presented. It is shown that the Gutenberg model earth fits the observations more closely than the Lehmann model and that a slight alteration of the Gutenberg model gives a significantly better fit to the observations. The alteration involves a lower shear-wave velocity in the lower mantle while the Gutenberg velocity distribution is maintained in the upper mantle. Various studies of the earth's oscillations coupled with surface-wave investigations substantiate Gutenberg's hypothesis of a layer of low velocity in the upper mantle. The physical conditions required for the formation of a region of low velocity are examined in detail. The results confirm Birch's earlier statement that a temperature gradient in excess of 6 degrees to 7 degrees per kilometer is needed to produce a decrease in velocity. The low-velocity layer does not require that the temperature approach or exceed the melting temperature. If tile upper mantle is homogeneous, the region of lower velocity should commence at the base of the crust and extend to 150 kilometers under the oceans and about 100 kilometers under continental regions. The distribution of thermal conductivity and radioactivity consistent with the low-velocity layer is also considered.

The oscillations of the Earth

The oscillations of the Earth

大氣の振動について

大氣の振動について

Die Pendulations-Theorie

FIRED by a new view of the shifting of the polar axis of the earth the speculative mind of a distinguished zoologist, Simroth, conceived the idea of a relation between earth oscillation and organic development. Die Pendulations-Theorie. Von Prof. Dr. H. Simroth. Zweite Auflage. Pp. xvi + 598. (Berlin: Konrad Grathlein, 1914.) 13.50 marks.

The Earthquake in Turkey on August 9

THE recent earthquake, reported as felt in Constantinople, and as very destructive near the Sea of Marmora, has left its mark on the photographic traces of our unifilar and bifilar magnetographs, but not on the vertical force balance; and, contrary to expectation, the disturbance is more pronounced on the unifilar than on the bifilar curve. The Milne seismograph failed to record the time of the maximum disturbance otherwise than that it occurred either between 1.44 and 1.45 or between 1.47 and 1.50 a.m. on August 9, during which intervals the oscillations of the boom overstepped the recording limits. The time as registered on the magnetograms is 1.45 a.m., and this, as the true time of greatest earth oscillation, would lead us to expect an origin nearer to us than the Sea of Marmora.