On the dynamical theory of the rotation of the earth

1948 ◽  
Vol 44 (3) ◽  
pp. 345-359 ◽  
Author(s):  
H. Bondi ◽  
R. A. Lyttleton
Keyword(s):  
Rigid Body ◽  
Inner Core ◽  
Deformable Body ◽  
A Priori ◽  
Dynamical Theory ◽  
Outer Shell ◽  
Angular Velocity Vector ◽  
The Core ◽  
The Earth ◽  
Rotation Of The Earth

In the dynamical theory of the motion of the Earth relative to its centre of mass, the planet is usually regarded as a rigid or at most only slightly deformable body, and moments of inertia are adopted that are taken to refer to the Earth as a whole, while the motion itself at any instant is assumed capable of representation by a single angular velocity vector. This procedure, however, appears to involve unwarranted assumptions the recognition and removal of which may lead to conclusions of considerable importance. For it is well known from the theory of earthquake waves that the material of the central core of the Earth behaves like a liquid in that it transmits only longitudinal wave vibrations, while there is also other evidence suggesting that the material of the core is a true liquid (1). There is accordingly no a priori reason for supposing that the core will behave like a rigid body firmly attached to the surrounding shell if more or less permanent shearing forces are applied to it. In particular, in respect of any couple known to act on the outer shell, it is not permissible to assume, without examination of the assumption, that its effect will be transferred immediately to the inner core in a way preserving rigid-body rotation of the whole. If the material of the core behaves like a liquid where wave-motion is concerned, this suggests that it will probably also behave like a liquid whatever shearing forces act on it, and the extent to which changes in the rotatory motion of the outer shell can be communicated to the core, and what effects direct gravitational forces acting on the core may have, must in the first instance be questions of hydrodynamics and not rigid dynamics.

On the dynamical theory of the rotation of the earth. II. The effect of precession on the motion of the liquid core

1953 ◽  
Vol 49 (3) ◽  
pp. 498-515 ◽  
Author(s):  
H. Bondi ◽  
R. A. Lyttleton
Keyword(s):  
Angular Velocity ◽  
Liquid Core ◽  
Rotation Period ◽  
Steady Motion ◽  
Dynamical Theory ◽  
Rate Of Change ◽  
Body Motion ◽  
Angular Velocity Vector ◽  
The Core ◽  
The Earth

In an earlier paper of the same general title (1) the possibility that the core of the Earth, in view of its supposed liquid nature, does not partake of the rigid-body motion of the outer shell was discussed with particular reference to the secular diminution of the angular velocity. In addition to this small rate of change of the magnitude of the angular velocity vector of the shell there occur changes in its direction consisting of the precession and nutation, but all the rates of change therein involved are small. The secular retardation takes place with extreme slowness, the nutations involve deviations of the axis with small angular amplitudes, while the precession, though of large angular amplitude, is of very long period compared with the rotation period of the Earth. Accordingly, it may be supposed that the effects of these various changes in the angular velocity can be considered separately in their relation to the motion within the core, and it is the object of this paper to give an account of our investigation into what may be termed for brevity the precession problem. It should perhaps be stated at the outset that the work does not constitute a solution of the problem, which our studies have led us to believe is one of the utmost mathematical difficulty presenting features of an exceptional character in hydro-dynamic theory. After first obtaining the equations of steady motion applicable to the interior, and those applicable to the boundary layer, the solution of the latter equations has been obtained; but in respect of the former equations we have been able to carry the question of the interior motion only as far as showing that no motion representable everywhere by analytic functions and consistent with the boundary conditions is possible. The investigation strongly suggests that no steady-state motion of a permanent character is possible for the interior, though the precise nature of the motion that actually occurs poses a problem of special interest from a hydrodynamic standpoint, but it is one to which we are not able to arrive at any definite answer at present. Without making any progress with the problem thus produced, the paper nevertheless makes clear the inherent difficulties of the problem and also serves to emphasize the inadequacy of any simplified mode of attack assuming classical fluid and resembling, for example, Poincaré's method for the nutation problem adopted by Lamb (3). Thus despite its incompleteness it seemed worth while to publish some account of such progress with these highly interesting questions as we have been able to make.

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.

Free spheroidal vibrations of the earth at very long periods, Part I— Calculation of periods for several earth models

1963 ◽  
Vol 53 (3) ◽  
pp. 483-501 ◽  
Author(s):  
Leonard E. Alsop
Keyword(s):  
Inner Core ◽  
Computer Programs ◽  
Free Vibrations ◽  
Stoneley Waves ◽  
The Core ◽  
The Earth ◽  
Earth Models ◽  
Shear Modes ◽  
Phase And Group Velocities ◽  
Group Velocities

Abstract Periods of free vibrations of the spheroidal type have been calculated numerically on an IBM 7090 for the fundamental and first two shear modes for periods greater than about two hundred seconds. Calculations were made for four different earth models. Phase and group velocities were also computed and are tabulated herein for the first two shear modes. The behavior of particle motions for different modes is discussed. In particular, particle motions for the two shear modes indicate that they behave in some period ranges like Stoneley waves tied to the core-mantle interface. Calculations have been made also for a model which presumes a solid inner core and will be discussed in Part II. The two computer programs which were made for these calculations are described briefly.

scholarly journals New Determination of the “Decade” Fluctuations in the Rotation of the Earth 1860–1978

1979 ◽  
Vol 82 ◽  
pp. 55-57
Author(s):  
L. V. Morrison
Keyword(s):  
Angular Momentum ◽  
Electromagnetic Coupling ◽  
Viscous Stress ◽  
Mantle Boundary ◽  
Core Mantle Boundary ◽  
Topographic Features ◽  
The Core ◽  
The Earth ◽  
Rotation Of The Earth

Observations of the Earth's rotation have shown irregular variations of rate which have characteristic times of decades. These have been attributed to transfer of angular momentum between core and mantle by some mechanism such as inertial coupling, viscous stress, electromagnetic coupling or stresses produced by topographic features on the core mantle boundary.

scholarly journals Teleseismic correlations of ambient seismic noise for deep global imaging of the Earth

2013 ◽  
Vol 194 (2) ◽  
pp. 844-848 ◽  
Author(s):  
P. Boué ◽  
P. Poli ◽  
M. Campillo ◽  
H. Pedersen ◽  
X. Briand ◽  
...  
Keyword(s):  
Seismic Noise ◽  
Ambient Noise ◽  
Inner Core ◽  
Global Analysis ◽  
Imaging Study ◽  
Ambient Seismic Noise ◽  
Core Mantle Boundary ◽  
The Core ◽  
The Earth ◽  
Earthquake Data

Abstract We present here a global analysis showing that wave paths probing the deepest part of the Earth can be obtained from ambient noise records. Correlations of seismic noise recorded at sensors located various distances apart provide new virtual seismograms for paths that are not present in earthquake data. The main arrivals already known for earthquake data are also present in teleseismic correlations sections, including waves that have propagated through the Earth's core. We present examples of applications of such teleseismic correlations to lithospheric imaging, study of the core mantle boundary or of the anisotropy of the inner core.

Viscous drag and the differential rotation of the Earth's core

1997 ◽  
Vol 57 (1) ◽  
pp. 231-233
Author(s):  
DAVID L. BOOK ◽  
J. A. VALDIVIA
Keyword(s):  
Simple Model ◽  
Differential Rotation ◽  
Dynamic Viscosity ◽  
Inner Core ◽  
Outer Core ◽  
Viscous Drag ◽  
Earth’S Rotation ◽  
The Core ◽  
The Earth ◽  
Earth’S Inner Core

It is proposed that the differential rotation of the Earth's inner core deduced by Song and Richards is due to a combination of the deceleration of the Earth's rotation and the viscous drag between the Earth's inner and outer cores. If this model is correct then the dynamic viscosity in the outer core of the Earth can be estimated to be μ≈104 poise. Besides providing a novel way of determining the viscosity of the core, this simple model suggests some new tests and shows how astronomical effects can influence geological phenomena.

scholarly journals Rotational Velocity of an Earth Model with a Liquid Core

1979 ◽  
Vol 82 ◽  
pp. 313-314
Author(s):  
S. Takagi
Keyword(s):  
Rotational Motion ◽  
Velocity Vector ◽  
Inner Core ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Liquid Core ◽  
Outer Core ◽  
Earth Model ◽  
The Earth ◽  
Rotation Of The Earth

There have been many papers discussing the rotation of the Earth (Jeffreys and Vicente, 1957; Molodenskij, 1961; Rochester, 1973; Smith, 1974; Shen and Mansinha, 1976). This report summarizes the application of the perturbation method of celestial mechanics to calculate the rotation of the Earth (Takagi, 1978). In this solution the Earth is assumed to consist of three components: a mantle, liquid outer core, and a solid inner core, each having a separate rotational velocity vector. Hamiltonian equations of motion were constructed to solve the rotational motion of the Earth.

scholarly journals Motion of the Core, and Its Influence on the Earth's Axis

1972 ◽  
Vol 48 ◽  
pp. 185-188
Author(s):  
Jose Mateo
Keyword(s):  
Gravitational Force ◽  
Slow Motion ◽  
The Core ◽  
Artificial Earth Satellites ◽  
The Earth ◽  
Accurate Knowledge ◽  
Secular Variations ◽  
Artificial Earth ◽  
Rotation Of The Earth ◽  
Centers Of Mass

After the advent of artificial Earth satellites, an accurate knowledge of the harmonic coefficients of the Earth's potential has enabled us to determine the size and shape of the Earth with extraordinary accuracy.The gravitational force between the core and the rest of the Earth, which makes both centers of mass tend to coincide, is so enormous that there is a strong possibility of a very slow motion of the core forcing its way into the mantle. It includes secular variations in both latitude and the time of rotation of the Earth.

scholarly journals Earth Rotation Velocity in Relation with Different Reference Frames

1995 ◽  
Vol 166 ◽  
pp. 293-293
Author(s):  
V. A. Brumberg
Keyword(s):  
Rigid Body ◽  
Reference System ◽  
Earth’S Rotation ◽  
Body Rotation ◽  
Dynamical Equations ◽  
Earth's Rotation ◽  
Rigid Body Rotation ◽  
Relativistic Corrections ◽  
The Earth ◽  
Rotation Of The Earth

The high precision of present observations makes it reasonable to clear up a question about GRT (general relativity theory) corrections in the problem of Earth's rotation. The answer is that one may almost forget about GRT corrections when dealing in an adequate reference system (RS). The problem of Earth's rotation may be related to the relativistic hierarchy of RS started in (Brumberg and Kopejkin, 1989) and completed in (Klioner, 1993). Let letters B, G and T be related to barycentric, geocentric and topocentric RS, respectively. Let DRS and KRS be dynamically nonrotating or kinematically nonrotating RS, respectively. From the dynamical equations of rotation it follows that the most adequate system for studying the Earth's rotation is DGRS. Apart from the geophysical factors the rotation of the Earth in this system is fairly well approximated by the rigid-body rotation with some angular velocity . The same rotation of the Earth as considered in BRS and DTRS may be also approximated by the rigid-body rotation but with some additive relativistic corrections and with other angular velocities ωi and , respectively. Substituting these three rotation relations into four-dimensional BRS-DGRS and DGRS-DTRS transformations one may express ωi and in terms of and determine the additive relativistic corrections in BRS and BTRS. These corrections are of importance for treating kinematics problems in various coordinate systems and for obtaining physically meaningful solutions of the dynamical equations of rotation in the barycentric reference system.The complete text will be published in Journal of Geodynamics.

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