scholarly journals Mantle Rayleigh waves from the Kamchatka earthquake of November 4, 1952*

1954 ◽  
Vol 44 (3) ◽  
pp. 471-479
Author(s):  
Maurice Ewing ◽  
Frank Press
Keyword(s):  
Internal Friction ◽  
Rayleigh Waves ◽  
Shear Velocity ◽  
Velocity Curve ◽  
The Core ◽  
Long Period ◽  
A Value ◽  
The Earth ◽  
Dispersion Data ◽  
Kamchatka Earthquake

Abstract Mantle Rayleigh waves from the Kamchatka earthquake of November 4, 1952, are analyzed. The new Palisades long-period vertical seismograph recorded orders R6–R15, the corresponding paths involving up to seven complete passages around the earth. The dispersion data for periods below 400 sec. are in excellent agreement with earlier results and can be explained in terms of the known increase of shear velocity with depth in the mantle. Data for periods 400-480 sec. indicate a tendency for the group velocity curve to level off, suggesting that these long waves are influenced by a low or vanishing shear velocity in the core. Deduction of internal friction in the mantle from wave absorption gives a value 1/Q = 370 × 10−5 for periods 250-350 sec. This is a little over half the value reported earlier for periods 140-215 sec.

Attenuation, dispersion, and the wave guide of the G wave

1958 ◽  
Vol 48 (3) ◽  
pp. 231-251
Author(s):  
Yasuo Satô
Keyword(s):  
Group Velocity ◽  
Rayleigh Waves ◽  
New Guinea ◽  
Direct Consequence ◽  
Shear Velocity ◽  
Wave Channel ◽  
The Earth ◽  
Kamchatka Earthquake ◽  
The Fourier Transform ◽  
Constant Group

Abstract Using the strain seismograms of the New Guinea earthquake of 1938 and the Kamchatka earthquake of 1952, the decrement of the G wave in the mantle of the earth was determined from the comparison of the amplitude of Fourier components, which are obtained by analyzing the G phases at different epicentral distances. The value of 1/Q thus obtained is a little larger than that given by M. Ewing and F. Press using mantle Rayleigh waves, but is not much different. The phase velocity was also calculated using the argument of the Fourier transform. The dispersion curves obtained from (G1 and G3), (G2 and G4) of the New Guinea earthquake and (G1 and G3) of the Kamchatka earthquake agree quite well, giving a nearly constant group velocity 4.4 km/sec. as was anticipated. Theoretical consideration of the distribution of shear velocity that serves as the wave channel for the guidance of the G wave was given, and the shear velocity was calculated applying the method of T. Takahashi to the dispersion curve derived from the condition of constant group velocity, which is a direct consequence of the fact that the G wave shows almost no dispersion. The Vs(z)/V0 curve which was derived theoretically agrees well with the curve given by the distribution of shear velocity of Jeffreys-Bullen in the range between one and several hundred kilometers.

scholarly journals An investigation of mantle Rayleigh waves*

1954 ◽  
Vol 44 (2A) ◽  
pp. 127-147
Author(s):  
Maurice Ewing ◽  
Frank Press
Keyword(s):  
Internal Friction ◽  
Upper Mantle ◽  
Rayleigh Waves ◽  
Normal Pressure ◽  
Crystalline Rocks ◽  
Velocity Curve ◽  
Continental Margins ◽  
Long Period ◽  
Short Period ◽  
Small Scatter

abstract Dispersion of Rayleigh waves for a new range of periods ranging from 1 to 7 minutes is described. The group velocity curve shows a long-period and a short-period branch merging at a minimum value of 3.54 km/sec. with a corresponding period of about 225 sec. It is suggested that the known variation of velocity with depth in the mantle can account for the observed dispersion. The small scatter in the velocities and the absorption of these waves suggests that, unlike shorter-period surface waves, refraction and attenuation effects are negligible at the continental margins. From the absorption of mantle Rayleigh waves the internal friction in the upper mantle for periods of 140 and 215 sec. is found to be given by 1/Q = 670 × 10−5. This is of the same order as that reported from vibration measurements at audio frequencies on laboratory samples of crystalline rocks at normal pressure and temperature.

Free spheroidal vibrations of the earth at very long periods, Part II— effect of rigidity of the inner core

1963 ◽  
Vol 53 (3) ◽  
pp. 503-515
Author(s):  
Leonard E. Alsop
Keyword(s):  
Particle Motion ◽  
Inner Core ◽  
Shear Velocity ◽  
Free Vibrations ◽  
Numerical Calculations ◽  
Core Mode ◽  
Long Period ◽  
The Earth ◽  
Many Core ◽  
Core Modes

Abstract Numerical calculations have been made on an IBM 7090 of the periods and particle motion with depth of the lowest order free spheroidal vibrations of the fundamental and first two higher modes with inner core shear velocity as a parameter. All calculations were made for a model with velocities according to Jeffreys and with densities obeying Bullen's model B. These calculations show that the effect of the inner core shear velocity on these periods is slight, except for those velocities at which the modes have periods near to the periods of core modes. This means that observations of long period free vibrations will probably not give much information about rigidity of the inner core. A mode of vibration having many of the properties of the mode suggested by Slichter has been discovered. In addition, it appears that the presence of a solid inner core brings into existence many core type modes with periods both shorter and longer than the original core mode predicted by Alterman, Jarosch, and Pekeris.

Rayleigh wave dispersion in the Pacific Ocean for the period range 20 to 140 seconds

1962 ◽  
Vol 52 (2) ◽  
pp. 333-357 ◽  
Author(s):  
John Kuo ◽  
James Brune ◽  
Maurice Major
Keyword(s):  
Phase Velocity ◽  
Rayleigh Wave ◽  
Rayleigh Waves ◽  
Initial Phase ◽  
Velocity Curve ◽  
Period Range ◽  
Long Period ◽  
Phase Velocities ◽  
The Pacific ◽  
Group Velocities

ABSTRACT Rayleigh wave data obtained from Columbia long-period seismographs installed during the International Geophysical Year (I.G.Y.) at Honolulu, Hawaii; Suva, Fiji; and Mt. Tsukuba, Japan, are analyzed to determine group and phase velocities in the Pacific for the period range 20 to 140 seconds. Group velocities are determined by usual techniques (Ewing and Press, 1952, p. 377). Phase velocities are determined by assuming the initial phase to be independent of period and choosing the initial phase so that the phase velocity curve agrees in the long period range with the phase velocity curve of the mantle Rayleigh wave given by Brune (1961). Correlations of wave trains between the stations Honolulu and Mt. Tsukuba are used to obtain phase velocity values independent of initial phase. The group velocity rises from 3.5 km/sec at a period of about 20 see to a maximum of 4.0 km/sec at a period of about 40 sec and then decreases to 3.65 km/sec at a period of about 140 sec. Phase velocity is nearly constant in the period range 30–75 sec with a value slightly greater than 4.0 km/sec. Most of the phase velocity curves indicate a maximum and a minimum at periods of approximately 30 and 50 sec respectively. At longer periods the phase velocities increase to 4.18 km/sec at a period of 120 sec. Except across the Melanesian-New Zealand region, dispersion curves for paths of Rayleigh waves throughout the Pacific basin proper are rather uniform and agree fairly well with theoretical dispersion curves for models with a normal oceanic crust and a low velocity channel. Both phase and group velocities are comparatively lower for the paths of Rayleigh waves across the Melanesian-New Zealand region, suggesting a thicker crustal layer and/or lower crustal velocities in this region.

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.

scholarly journals A comment on the flattening of the group velocity curve of mantle Rayleigh waves with periods about 500 sec.

1959 ◽  
Vol 49 (4) ◽  
pp. 365-368
Author(s):  
H. Takeuchi
Keyword(s):  
Group Velocity ◽  
Rayleigh Waves ◽  
Velocity Curve ◽  
Earth’S Core ◽  
Earth's Core ◽  
The Earth ◽  
Scale Ratio ◽  
Surface Loads

Abstract A scale-ratio consideration and a calculation on statical deformations of the earth by surface loads suggest that the flattening of the group velocity curve of mantle Rayleigh waves with periods about 500 sec. is not due to the existence of the earth's core, as has been suggested.

Ups and Downs

2018 ◽  
Author(s):  
Roy Livermore
Keyword(s):  
Mantle Convection ◽  
Laboratory Experiments ◽  
Inner Core ◽  
Computer Modelling ◽  
Great Depth ◽  
New Horizons ◽  
The Core ◽  
The Earth ◽  
The World ◽  
The 1960S

Despite the dumbing-down of education in recent years, it would be unusual to find a ten-year-old who could not name the major continents on a map of the world. Yet how many adults have the faintest idea of the structures that exist within the Earth? Understandably, knowledge is limited by the fact that the Earth’s interior is less accessible than the surface of Pluto, mapped in 2016 by the NASA New Horizons spacecraft. Indeed, Pluto, 7.5 billion kilometres from Earth, was discovered six years earlier than the similar-sized inner core of our planet. Fortunately, modern seismic techniques enable us to image the mantle right down to the core, while laboratory experiments simulating the pressures and temperatures at great depth, combined with computer modelling of mantle convection, help identify its mineral and chemical composition. The results are providing the most rapid advances in our understanding of how this planet works since the great revolution of the 1960s.

Serial Homology as a Challenge to Evolutionary Theory

2017 ◽  
Author(s):  
Stéphane Schmitt
Keyword(s):  
Biological Sciences ◽  
Evolutionary Theory ◽  
Serial Homology ◽  
The Core ◽  
Long Period ◽  
Colonial Theory ◽  
Experimental Approaches ◽  
Evo Devo ◽  
The 19Th Century ◽  
Development And Evolution

The problem of the repeated parts of organisms was at the center of the biological sciences as early as the first decades of the 19th century. Some concepts and theories (e.g., serial homology, unity of plan, or colonial theory) introduced in order to explain the similarity as well as the differences between the repeated structures of an organism were reused throughout the 19th and the 20th century, in spite of the fundamental changes during this long period that saw the diffusion of the evolutionary theory, the rise of experimental approaches, and the emergence of new fields and disciplines. Interestingly, this conceptual heritage was at the core of any attempt to unify the problems of inheritance, development, and evolution, in particular in the last decades, with the rise of “evo-devo.” This chapter examines the conditions of this theoretical continuity and the challenges it brings out for the current evolutionary sciences.

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