Characteristic periods of fundamental and overtone oscillations of the earth following a deep-focus earthquake

1972 ◽  
Vol 62 (1) ◽  
pp. 247-274 ◽  
Author(s):  
A. A. Nowroozi

Abstract The deep-focus earthquake of July 31, 1970, (1.5°S, 72.6°W, h = 651 km, Mb = 7.1) excited a set of fundamental and overtone free oscillations. From analysis of seismograms recorded at Berkeley, California, at an ocean-bottom station in the Pacific, and at Ogdensburg, New Jersey, the fundamental spheroidal oscillations, l = 10-98, and a number of overtones with n = 1, 2, and 3, fundamental torsional oscillations, l = 3-70, and overtones with n = 1, 2, 3, and 4, are identified. The majority of resolved spectral peaks are above the 95 per cent confidence level. For some modes with periods less than 300 sec, the observed period at each station differs by up to 2 sec. This path-dependency of the period may thus suggest the existence of lateral heterogeneity in the upper mantle. The observed periods are compared to calculated periods for Haddon-Bullen's model HB1 and Derr's model DI-11; for fundamental modes the agreements are good, while differences up to 2 sec exist for some overtone modes. A relationship between order of oscillations, l, the frequency, nωl, and the ray parameter dt/dθ is derived, which is equivalent to the Jean's equation for phase velocity. The relationship implies that each mode with period nTl will travel with phase velocity dΔ/dt along its own ray with parameter dt/dθ. Other models will travel along the same ray if they have the same ray parameter.

1964 ◽  
Vol 54 (2) ◽  
pp. 755-776
Author(s):  
L. E. Alsop

ABSTRACT Spectral peaks corresponding to the spheroidal free periods of oscillation of the earth exist in the spectra of eight seismograms written at stations in different parts of the world shortly after the great Chilean earthquake of 22 May 1960. These data have been combined with those previously reported by various authors to obtain a very precise phase velocity vs period curve for Rayleigh waves in the period range of 200 to 3200 seconds. The observed spectral amplitudes lend some support to the assumption of a moving source, but they also indicate that the present theory is not adequate. The vertical motion is found to be symmetric with respect to reflections through the pole.


1966 ◽  
Vol 56 (6) ◽  
pp. 1269-1288
Author(s):  
Ali A. Nowroozi

Abstract Fourier analysis of the four-component strain recordings at Ogdensburg, New Jersey, after the Rat Island earthquake of February 4, 1965, has yielded spectra of the earth oscillations. Three horizontal components were used to calculate synthetic longitudinal, transverse, and shearing strain components. Analysis of the different components or their combinations yielded spectra of the torsional and spheroidal oscillations. The spectral peaks corresponding to l = 3 through l = 24 were resolved and were significantly above the 95 per cent confidence level. The novelty of this analysis is the appearance of 9 first overtones and 8 second overtones of the spheroidal oscillations from cross-correlation of two sections of the vertical component of the strain recording. The observed periods are compared to theoretical periods of four earth models: M1 of Landisman; R1 of Dorman; Jeffreys-Bullen B; and Gutenberg-Bullen A. The M1 and R1 models gave the most satisfactory agreement with the observations of the fundamental modes, whereas the Jeffreys-Bullen B model had a better agreement with the observations of the overtones than other models considered. Assuming the azimuthal order number, m, of the source as a combination of m = 0, m = 1, and m = 2, the variations of the spectral amplitudes at Ogdensburg indicated that the main contributing component of the azimuthal order number of the source was not only zero, but it was 1 for the modes corresponding to l = 2,4,7,9,12, and 2 for the modes corresponding to l = 3, 5,6,8,10, and 13.


Author(s):  
Svetlana Poygina ◽  
Nataliya Petrova ◽  
N. Boldyreva

The information on the Earth seismicity in 2013 at the level of strong earthquakes with M≥6 is provided according to the Seismological Bulletin of the Geophysical Survey of RAS (GS RAS). The initial Seismo-logical Bulletin for 2013 contains parameters of 4212 earthquakes in the world, versus 4845 in 2012. This article analyzes parameters of 160 strong earthquakes of the Earth in 2013 with M≥6, including 24 strongest earthquakes with M≥7 and the maximum earthquake of the Earth with Mw8.3 occurred in Okhotsk Sea, as well as four earthquakes with M6.0–6.8, which resulted in significant sacrifices and destructions. The location of earthquake epicenters and seismic stations, whose data were used to deter-mine the main parameters of earthquake foci, are shown, as well as a comparative analysis of the number of earthquakes and seismic energy released within the Earth's seismic regions is given. The information on focal mechanisms and consequences of 28 strongest earthquakes, including macroseismic effect, number of victims, landslides, tsunamis, etc. is given. The epicenters of most of them are confined to the boundaries of the largest tectonic plates of the Earth, and their focal mechanisms correspond to the basic laws of plate movement. The hypocenters of most of the strongest earthquakes are located within the Earth's crust, with the exception of earthquakes in Colombia, the Kuril Islands and south of the Fiji Is-lands, which had intermediate depths (h=98–171 km), and the strongest in 2013 Okhotsk earthquake, the source of which lay in the upper mantle at the depth of h=617 km. The movement in the source of the Okhotsk earthquake corresponds to the subduction process of the Pacific plate under the continent and indicates that the subducted plate is at the depth of 617 km.


1961 ◽  
Vol 51 (2) ◽  
pp. 223-225
Author(s):  
H. Takeuchi ◽  
N. Kobayashi

Abstract Free periods of the earth's spheroidal oscillations are calculated for the wave numbers n up to 16. The earth's sphericity, self-gravitation and a liquid core are taken into account. Period-wave number and period-phase velocity relations obtained are shown in Figs. 1 and 2, respectively.


1964 ◽  
Vol 54 (5A) ◽  
pp. 1341-1347
Author(s):  
L. E. Alsop

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.


1967 ◽  
Vol 57 (5) ◽  
pp. 1047-1061
Author(s):  
John S. Derr

Abstract It is well-known that Rayleigh and Love waves over continental and oceanic structures have different periods (T) for a given order (n). In the present study, this difference is explored over the spectrum for periods greater than 30 sec, and particularly the graver fundamental spheroidal and torsional oscillations. The oceanic model is the same as the continental model below 400 km depth, is adjusted between 400 km and 10 km to preserve the Earth's overall mass and moment of inertia, and has 5 km of crust and 5 km of ocean. For torsional oscillations, the difference in period for a given n is about 3 sec throughout the range of 2 ≦ n ≦ 120, or 0.15 per cent to 3.3 per cent. However, the two curves for the group velocity are not parallel in this range: continental group velocity increases monotonically with T, while oceanic group velocity has a broad minimum for 160 < T < 200 sec. For spheroidal oscillations, the difference in period for a given n is about 2 sec for 2 ≦ n ≦ 120, or 0.1 per cent to 2 per cent. For n = 0, the difference is only 0.1 sec or 0.008 per cent. The two group velocity curves are almost parallel with minima in the same range, 205 to 210 sec. Comparison with the precision of available measurements of the free periods shows that the presence of an oceanic crust and upper mantle is important for fitting models of the earth to any set of free oscillation observations.


2017 ◽  
Vol 23 (1) ◽  
Author(s):  
Willie Van Heerden

A central concern of ecological biblical hermeneutics is to overcome the anthropocentric bias we are likely to find both in interpretations of the biblical texts and in the biblical text itself. One of the consequences of anthropocentrism has been described as a sense of distance, separation, and otherness in the relationship between humans and other members of the Earth community. This article is an attempt to determine whether extant ecological interpretations of the Jonah narrative have successfully addressed this sense of estrangement. The article focuses on the work of Ernst M. Conradie (2005), Raymond F. Person (2008), Yael Shemesh (2010), Brent A. Strawn (2012), and Phyllis Trible (1994, 1996).


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