scholarly journals Solved and unsolved questions in the non-rigid Earth nutation study

2007 ◽  
Vol 3 (S248) ◽  
pp. 374-378
Author(s):  
C. L. Huang
Keyword(s):  
Inner Core ◽  
Outer Core ◽  
Earth Model ◽  
Future Studies ◽  
Atmospheric Loading ◽  
The Earth ◽  
Core Boundary ◽  
Oceanic Tides ◽  
Rigid Earth ◽  
Electro Magnetic

AbstractAt the IAU 26th GA held in Prague in 2006, a new precession model (P03) was recommended and adopted to replace the old one, IAU1976 precession model. This new P03 model is to match the IAU2000 nutation model that is for anelastic Earth model and was adopted in 2003 to replace the previous IAU1980 model. However, this IAU2000 nutation model is also not a perfect one for our complex Earth, as stated in the resolution of IAU nutation working group. The Earth models in the current nutation theories are idealized and too simple, far from the real one. They suffer from several geophysical factors: the an-elasticity of the mantle, the atmospheric loading and wind, the oceanic loading and current, the atmospheric and oceanic tides, the (lateral) heterogeneity of the mantle, the differential rotation between the inner core and the mantle, and various couplings between the fluid outer core and its neighboring solids (mantle and inner core). In this paper, first we give a very brief review of the current theoretical studies of non-rigid Earth nutation, and then focus on the couplings near the core-mantle boundary and the inner core-outer core boundary, including the electro-magnetic, viscous, topographic, and gravitational couplings. Finally, we outline some interesting future studies.

scholarly journals Precession of the non-rigid Earth: Effect of the mass redistribution

2019 ◽  
Vol 626 ◽  
pp. A58 ◽  
Author(s):  
T. Baenas ◽  
A. Escapa ◽  
J. M. Ferrándiz
Keyword(s):  
Dynamical Problem ◽  
Earth Model ◽  
Linear Effect ◽  
The Earth ◽  
Mass Redistribution ◽  
Love Numbers ◽  
Oceanic Tides ◽  
Analytical Formulae ◽  
Rigid Earth ◽  
Relative Change

This research is focused on determining the contribution to the precession of the Earth’s equator due to the mass redistribution stemming from the gravitational action of the Moon and the Sun on a rotating solid Earth. In the IAU2006 precession theory, this effect is taken into account through a contribution of −0.960 mas cy−1 for the precession in longitude (with the unspecific name of non-linear effect). In this work, the revised value of that second-order contribution reaches −37.847 mas cy−1 when using the Love numbers values given in IERS Conventions, and −43.945 mas cy−1 if those values are supplemented with the contributions of the oceanic tides. Such variations impose a change of the first-order precession value that induces relative changes of the Earth’s dynamical ellipticity of about 7.3 and 8.5 ppm, respectively. The corresponding values for the obliquity rate are 0.0751 and 0.9341 mas cy−1, respectively, in contrast to 0.340 mas cy−1 considered in IAU2006. The fundamentals of the modeling have been revisited by giving a clear construction of the redistribution potential of the Earth through the corresponding changes in the Earth tensor of inertia. The dynamical problem is tackled within the Hamiltonian framework of a two-layer Earth model, introduced and developed by Getino and Ferrándiz. This approach allows for the achievement of closed-analytical formulae for the precession in longitude and obliquity. It makes it possible to obtain numerical values for different Earth models once a set of associated Love numbers is selected. The research is completed with a discussion on the permanent tide and the related estimation of the variation of the second degree zonal Stokes parameter, J2, and also the indirect effects on nutations arising from the relative change of the Earth’s dynamical ellipticity.

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.

Density and sound velocity of liquid Fe-S alloys at Earth's outer core P-T conditions

2020 ◽  
Vol 105 (9) ◽  
pp. 1349-1354
Author(s):  
Jie Fu ◽  
Lingzhi Cao ◽  
Xiangmei Duan ◽  
Anatoly B. Belonoshko
Keyword(s):  
Sound Velocity ◽  
Inner Core ◽  
Light Element ◽  
Outer Core ◽  
Earth Model ◽  
Thermal Equation ◽  
Fundamental Parameters ◽  
Core Boundary ◽  
Core Conditions ◽  
Dynamics Simulations

Abstract Pressure-temperature-volume (P-T-V) data on liquid iron-sulfur (Fe-S) alloys at the Earth's outer core conditions (~136 to 330 GPa, ~4000 to 7000 K) have been obtained by first-principles molecular dynamics simulations. We developed a thermal equation of state (EoS) composed of Murnaghan and Mie-Grüneisen-Debye expressions for liquid Fe-S alloys. The density and sound velocity are calculated and compared with Preliminary Reference Earth Model (PREM) to constrain the S concentration in the outer core. Since the temperature at the inner core boundary (TICB) has not been measured precisely (4850~7100 K), we deduce that the S concentration ranges from 10~14 wt% assuming S is the only light element. Our results also show that Fe-S alloys cannot satisfy the seismological density and sound velocity simultaneously and thus S element is not the only light element. Considering the geophysical and geochemical constraints, we propose that the outer core contains no more than 3.5 wt% S, 2.5 wt% O, or 3.8 wt% Si. In addition, the developed thermal EoS can be utilized to calculate the thermal properties of liquid Fe-S alloys, which may serve as the fundamental parameters to model the Earth's outer core.

scholarly journals Gravitational, Inertial and Toroidal Oscillations of the Outer Core and Their Related Free Wobbles

1980 ◽  
Vol 78 ◽  
pp. 185-186
Author(s):  
Po-Yu Shen
Keyword(s):  
Inner Core ◽  
Numerical Solutions ◽  
Outer Core ◽  
Angular Frequency ◽  
Inertial Oscillations ◽  
The Earth ◽  
Core Boundary ◽  
Restoring Forces ◽  
Rotation Of The Earth ◽  
Core Modes

According to the respective restoring forces of self-gravitation, Coriolis force, and inertial coupling at the boundaries, the free oscillations of a contained fluid can be classified into gravitational, inertial, and toroidal oscillations. For the outer core of the Earth, however, due to the interplay of rotation, elasticity, and self-gravitation, the gravitational undertones and inertial oscillations are not distinguishable. Both have eigenfunctions consisting of spheroidal and toroidal parts of about equal amplitude, and exist in alternating allowed and forbidden zones depending on the gravitational stability of the outer core. The forbidden zones for a stable core correspond to the allowed zones for an unstable core, while for a neutrally stratified core there appear to be no forbidden zones. The eigenfunction of a toroidal mode consists essentially of a primary toroidal field and a secondary spheroidal component of the order of ellipticity, coupled at the outer core-mantle or outer core-inner core boundary. Therefore, in general, toroidal core modes appear in doublets Sn+1m Tnm and Sn−1m Tn−1m with degenerate frequency equal to 2m/n(n+1) times the angular frequency of rotation of the Earth. The ellipticities of the outer core boundaries are responsible for the removal of the degeneracy. It is shown that the primary toroidal and secondary spheroidal fields constitute the “generalized Poincare motion” which, for the fundamental mode S21T11, reduces to the “simple motion” defined by Poincare in 1910. Numerical solutions have been obtained for all three types of free core modes. While those for gravitational undertones and inertial oscillations are obtained by arbitrarily truncating the hydrodynamic equations, it is shown that the eigensolutions for toroidal modes are correct to first order in ellipticity due to the particular geometry of the outer core of the Earth.

Revised velocities in the Earth's core

1973 ◽  
Vol 63 (3) ◽  
pp. 1073-1105 ◽  
Author(s):  
Anthony Qamar
Keyword(s):  
Transition Zone ◽  
Inner Core ◽  
Velocity Model ◽  
Outer Core ◽  
Travel Times ◽  
Zone Boundary ◽  
Underground Nuclear Explosions ◽  
Nuclear Explosions ◽  
Core Boundary ◽  
Velocity Jump

abstract Travel times and amplitudes of PKP and PKKP from three earthquakes and four underground nuclear explosions are presented. Observations of reflected core waves at nearly normal angles of incidence provide new constraints on the average velocities in the inner and outer core. Interpretation of these data suggests that several small but significant changes to Bolt's (1962) core velocity model (T2) are necessary. A revised velocity model KOR5 is given together with the derived travel times that are consistent with the 1968 tables for P. Model KOR5 possesses a velocity in the transition zone which is 112 per cent lower than that in model T2. In addition, KOR5 has a velocity jump at the transition zone boundary (r = 1782 km) of 0.013 km/sec and a jump at the inner core boundary (r = 1213 km) of 0.6 km/sec. These values are, respectively, 1/20 and 2/3 of the corresponding model T2 values.

scholarly journals Rigid-Earth Nutation Models

2000 ◽  
Vol 180 ◽  
pp. 190-195
Author(s):  
J. Souchay
Keyword(s):  
Transfer Function ◽  
Rigid Body ◽  
Earth Model ◽  
High Quality ◽  
Frequency Dependent ◽  
Relative Improvement ◽  
The Earth ◽  
Rigid Earth

AbstractDespite the fact that the main causes of the differences between the observed Earth nutation and that derived from analytical calculations come from geophysical effects associated with nonrigidity (core flattening, core-mantle interactions, oceans, etc…), efforts have been made recently to compute the nutation of the Earth when it is considered to be a rigid body, giving birth to several “rigid Earth nutation models.” The reason for these efforts is that any coefficient of nutation for a realistic Earth (including effects due to nonrigidity) is calculated starting from a coefficient for a rigid-Earth model, using a frequency-dependent transfer function. Therefore it is important to achieve high quality in the determination of rigid-Earth nutation coefficients, in order to isolate the nonrigid effects still not well-modeled.After reviewing various rigid-Earth nutation models which have been established recently and their relative improvement with respect to older ones, we discuss their specifics and their degree of agreement.

3. Minerals and the interior of the Earth

2014 ◽  
Author(s):  
David Vaughan
Keyword(s):  
Upper Mantle ◽  
Lower Mantle ◽  
Plate Tectonics ◽  
Inner Core ◽  
Indirect Evidence ◽  
Outer Core ◽  
The Earth ◽  
Granite Formation ◽  
Temperature And Pressure

‘Minerals and the interior of the Earth’ looks at the role of minerals in plate tectonics during the processes of crystallization and melting. The size and range of minerals formed are dependent on the temperature and pressure of the magma during its movement through the crust. The evolution of the continental crust also involves granite formation and processes of metamorphism. Our understanding of the interior of the Earth is based on indirect evidence, mainly the study of earthquake waves. The Earth consists of concentric shells: a solid inner core; liquid outer core; a solid mantle divided into a lower mantle, a transition zone, and an upper mantle; and then the outer rigid lithosphere.

scholarly journals New measurements of long-period radial modes using large earthquakes

2020 ◽  
Vol 224 (2) ◽  
pp. 1211-1224
Author(s):  
S Talavera-Soza ◽  
A Deuss
Keyword(s):  
Inner Core ◽  
Cross Coupling ◽  
Earth Model ◽  
Cylindrical Anisotropy ◽  
Long Period ◽  
Centre Frequency ◽  
The Earth ◽  
Radial Anisotropy ◽  
Crucial Information ◽  
Quality Factor Q

SUMMARY Radial modes, nS0, are long-period oscillations that describe the radial expansion and contraction of the whole Earth. They are characterized only by their centre frequency and quality factor Q, and provide crucial information about the 1-D structure of the Earth. Radial modes were last measured more than a decade ago using only one or two earthquakes. Here, we measure radial modes using 16 of the strongest and deepest earthquakes of the last two decades. By introducing more earthquake data into our measurements, we improve our knowledge of 1-D attenuation, as we remove potential earthquake bias from our results. For mode 0S0, which is dominated by compressional energy, we measure a Q value of 5982, much higher than previously measured, and requiring less bulk attenuation in the Earth than previously thought. We also show that radial modes cross-couple (resonate) strongly to their nearest spheroidal mode due to ellipticity and inner core cylindrical anisotropy. Cross-coupling improves the fit between data and synthetics, and gives better estimates of the centre frequency and attenuation value of the radial modes. Including cross-coupling in our measurements results in a systematic shift of the centre frequencies of radial modes towards the Preliminary Reference Earth Model. This shift in centre frequencies, has implications for the strength of the radial anisotropy present in the uppermost inner core, with our cross-coupling results agreeing with lower values of anisotropy than the ones inferred from just measuring the modes in self-coupling (isolation). Furthermore, cross-coupling between radial modes and angular-order two modes provides constraints on cylindrical inner core anisotropy, that will help us improve our knowledge of the 3-D structure of the inner core.

scholarly journals The ZMOA-1990 Nutation Series

1991 ◽  
Vol 127 ◽  
pp. 157-166 ◽  
Author(s):  
T.A. Herring
Keyword(s):  
Outer Core ◽  
Geophysical Model ◽  
Long Baseline ◽  
The Earth ◽  
Vlbi Data ◽  
Rigid Earth ◽  
Nutation Series ◽  
Two Parameters ◽  
Annual Period ◽  
Better Than

AbstractWe present a new nutation series for the Earth (ZMOA-1990) based on (1) the rigid Earth nutation series developed by Zhu and Groten [1989], (2) the normalized response for an elastic, elliptical Earth with fluid-outer and solid-inner cores developed by Mathews et al. [1990], and (3) corrections for the effects of ocean tides and anelasticity, computed to be consistent with the Mathews et al. [1990] normalized response function. In deriving this series, only two parameters of the geophysical model for the Earth have been modified from their values computed with PREM: the dynamic ellipticities of the whole Earth, e, and of the fluid outer core, ef. The adopted values for these parameters, determined from the analysts of very long baseline interferometry (VLSI) data, are e=0.00328915 which is about 1% higher than the value obtained from PREM and 6×10−5 times larger than the IAU adopted value, and ef=0.002665 which is 4.6% higher than the PREM value. The above values were obtained from an adjustment of −0.3 ʺ/cent to the IAU-1976 luni-solar precession constant for e, and from the amplitude of the retrograde annual nutation for ef. The ZMOA-1990 nutation series agrees with estimates of the in-phase and the out-of-phase nutation amplitudes obtained from VLBI data to within 0.5 mas for the terms with 18.6 year period, and to better than 0.1 mas for terms at all other periods except for the out-of-phase terms with annual period (differences 0.39 mas, retrograde, and 0.13 mas, prograde), and for the in-phase term with prograde 13.66 day period (difference −0.25 mas).

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