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

2020 ◽  
Vol 643 ◽  
pp. A159
Author(s):  
T. Baenas ◽  
A. Escapa ◽  
J. M. Ferrándiz
Keyword(s):  
Layer Structure ◽  
Earth Model ◽  
Fluid Core ◽  
International Astronomical ◽  
Mass Redistribution ◽  
Love Numbers ◽  
The Standard Model ◽  
Precessional Motion ◽  
Analytical Formulae ◽  
Rigid Earth

In this research, we computed the nutation of the figure axis for a non-rigid Earth model due to the mass redistribution resulting from the lunisolar attraction on the deformable Earth, thus extending our previous work on the precessional motion. The basic Earth model is a two-layer structure composed of a fluid core and an anelastic mantle. We used the Hamiltonian approach, leading to closed-form analytical formulae that describe the nutations in longitude and obliquity of the figure axis as a sum of Poisson and Oppolzer terms. Those formulae were evaluated assuming different Earth rheologies by means of the Love number formalism. In particular, we first computed the effect using the standard model of the International Earth Rotation and Reference Systems Service Conventions (2010) solid tides, and then the Love numbers computed by Williams and Boggs, accounting for the complete oceanic tide contribution, which should provide more consistent and updated values for the nutations. The main amplitudes correspond to the 18.6 yr nutation component and reach 201 μas and −96 μas in the in-phase components in longitude and obliquity, respectively. The obtained values differ greatly from those considered in the current nutation model, IAU2000, of the International Astronomical Union (IAU) – and later similar studies – which includes this effect under the denomination of non-linear terms and derives its numerical contribution on the basis of the Sasao, Okubo, and Saito framework. The differences are significant and reach more than 30 μas for some nutation amplitudes. They can be likely attributed to several factors: an incomplete modelling of the redistribution potential; a different treatment of the permanent tide; and the use of different oceanic tide models.

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 On the Adoption of Empirical Corrections to Woolard's Nutation Theory

1980 ◽  
Vol 78 ◽  
pp. 117-124 ◽  
Author(s):  
D. D. McCarthy ◽  
P. K. Seidelmann ◽  
T. C. Van Flandern
Keyword(s):  
Solid Earth ◽  
Earth Tides ◽  
Earth Model ◽  
Working Standard ◽  
Astronomical Observations ◽  
International Astronomical ◽  
Solid Earth Tides ◽  
Rigid Earth ◽  
Empirical Corrections

Commission 4 of the International Astronomical Union has deferred the question of revisions to the constants and theory of nutation in anticipation that there might be recommendations from Symposium No. 78 in Kiev. The present rigid-Earth theory of nutation does not adequately represent current precise astronomical observations for the major nutation terms. Discrepancies between the presently adopted theory and observations can accumulate to 0″1 in right ascension and significantly affect the determination of UT1 and materially influence the derivation of the new fundamental catalog of star positions and proper motions, FK5 There appears to be no obvious choice for a non-rigid-Earth model at present. The analysis of solid-Earth tides shows nutation coefficients in substantial agreement with astronomical observations and these values have been used in the reduction of radio interferometric and laser ranging observations. In the absence of a non-rigid-Earth model which can satisfy all requirements it is suggested that the coefficients found from the investigation of solid-Earth tides be adopted as a working standard until such a model can be adopted as a basis for nutation.

scholarly journals The Theory of the Nutation for a Rigid Earth Model: Current State of the Situation

1998 ◽  
Vol 11 (1) ◽  
pp. 163-167
Author(s):  
J. Souchay ◽  
H. Kinoshita
Keyword(s):  
The Other ◽  
Earth Model ◽  
International Astronomical Union ◽  
Current State ◽  
Vlbi Observations ◽  
International Astronomical ◽  
Rigid Earth

Whereas no particular attention was paid to the theory of the nutation for a rigid Earth model, for more than a decade after the adoption by the International Astronomical Union (IAU) of coefficients as calculated and listed by Kinoshita (1977), an increasing number of studies have been done in the recent years aiming to improve this theory. The improvement became necessary mainly because of the big parallel improvement of the VLBI observations itself, which leads to present determinations of some coefficients of nutation at the level of a few 10μas. Therefore the amelioration of the theory of the nutation for a rigid Earth model can be divided in two aspects: one is to consider a smaller level of truncation of the coefficients of nutation; the other is to evaluate in the best way the coefficients already taken into account, particularly the leading coefficients which are typically those subject to the largest absolute differences.

scholarly journals Limitations of the IAU2000 nutation model accuracy due to the lack of Oppolzer terms of planetary origin

2018 ◽  
Vol 618 ◽  
pp. A69
Author(s):  
José M. Ferrándiz ◽  
Juan F. Navarro ◽  
M. C. Martínez-Belda ◽  
Alberto Escapa ◽  
Juan Getino
Keyword(s):  
International Association ◽  
Earth Model ◽  
International Astronomical Union ◽  
Medium Term ◽  
Model Accuracy ◽  
Short Term ◽  
Model Following ◽  
Hamiltonian Theory ◽  
International Astronomical ◽  
Rigid Earth

Context. The current IAU2000 nutation model performed different approximations, one of them being that the Oppolzer terms associated to the planetary perturbations of the nutations were assumed to be smaller than 5 μas and thus were neglected. At present, the uncertainties of the amplitudes of individual components of the observed nutations are better, and the conventional nutation model does not fit the accuracy requirements pursued by the International Astronomical Union (IAU) and the International Association of Geodesy (IAG). Aims. The objective of this work is to estimate the magnitude of the lacking Oppolzer terms of the planetary nutations and find out whether they are still negligible or not. Methods. The Oppolzer terms resulting from the direct and indirect planetary perturbations of the Earth’s rotation have been computed for a two-layer Earth model following the Hamiltonian theory of the non-rigid-Earth. Results. The planetary Oppolzer terms for the non-rigid Earth are not really negligible as believed, and some of them have amplitudes larger than 10 μas, therefore significantly above the current level of uncertainty of individual harmonic constituents. Conclusions. In the short term, the IAU2000 nutation model must be supplemented with suitable corrections accounting for those missing components; its planetary component must be thoroughly revised in the medium term.

scholarly journals Towards sub-microarsecond rigid Earth nutation series in the Hamiltonian theory

2000 ◽  
Vol 180 ◽  
pp. 196-200
Author(s):  
J. Souchay ◽  
M. Folgueira
Keyword(s):  
Transfer Function ◽  
Inner Core ◽  
Precise Determination ◽  
Lunar Laser Ranging ◽  
Long Baseline ◽  
Fluid Core ◽  
International Astronomical ◽  
Lunar Laser ◽  
Rigid Earth ◽  
Nutation Series

AbstractThe nonrigid Earth nutation series adopted by the IAU (International Astronomical Union) are based on the works of Kinoshita (1977) and Wahr (1979). In the first one, the rigid Earth nutation series were calculated by the application of the Hamiltonian canonical equations to the rotation of the rigid and elliptical Earth. In the second one, the transfer function for the nutations of an elliptical, elastic and oceanless Earth with fluid core and a solid inner core was obtained. The nonrigid Earth nutation coefficients were derived from the convolution between Wahr’s transfer function and Kinoshita’s rigid Earth nutation series.The improvement in the accuracy of the techniques as a Very Long Baseline (VLBI), Lunar Laser Ranging (LLR) and Global Positioning System (GPS) has led in this decade to the extension of Kinoshita’s theory and more precise determination of Wahr’s transfer function. In the present paper and starting from Kinoshita’s work (1977), we present the different steps carried out, during this last decade, to obtain the sub-microarcsecond rigid Earth nutation series REN 2000 from the Hamiltonian study of the rotation of a rigid Earth (Souchay et al., 1999).

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.

Improved estimation of elastic attributes from prestack seismic data for reservoir characterization

Geophysics ◽  
2020 ◽  
Vol 85 (1) ◽  
pp. R41-R53
Author(s):  
Yijie Zhou ◽  
Franklin Ruiz ◽  
Yequan Chen ◽  
Fan Xia
Keyword(s):  
Nonlinear Optimization ◽  
Seismic Data ◽  
Reservoir Characterization ◽  
Layer Structure ◽  
High Sensitivity ◽  
Optimization Techniques ◽  
Earth Model ◽  
L1 Norm ◽  
Linear Inversion ◽  
Elastic Impedance

Seismic derivable elastic attributes, e.g., elastic impedance, lambda-rho, mu-rho, and Poisson impedance (PI), are routinely being used for reservoir characterization practice. These attributes could be derived from inverted [Formula: see text], [Formula: see text], and density, and usually indicate high sensitivity to reservoir lithology and fluid. Due to the high sensitivity of such elastic attributes, errors or measurement noise associated with the acquisition, processing, and inversion of prestack seismic data will propagate through the inversion products, and will lead to even larger errors in the computed attributes. To solve this problem, we have developed a two-step cascade workflow that combines linear inversion and nonlinear optimization techniques for the improved estimation of elastic attributes and better prediction and delineation of reservoir lithology and fluids. The linear inversion in the first step is an inversion scheme with a sparseness assumption, based on L1-norm regularization. This step is used to select the major reflective layer locations, followed in the second step by a nonlinear optimization process with the predefined layer structure. The combination of these two procedures produces a reasonable blocky earth model with consistent elastic properties, including the ones that are sensitive to reservoir lithology and fluid change, and thus provides an accurate approach for seismic reservoir characterization. Using PI, as one of the target elastic attributes, as an example, this workflow has been successfully applied to synthetic and field data examples. The results indicate that our workflow improves the estimation of elastic attributes from the noisy prestack seismic data and may be used for the identification of the reservoir lithology and fluid.

scholarly journals Models and nomenclature in Earth rotation

2009 ◽  
Vol 5 (S261) ◽  
pp. 69-78
Author(s):  
Nicole Capitaine
Keyword(s):  
Earth Model ◽  
Earth’S Rotation ◽  
New Paradigm ◽  
Earth Orientation Parameters ◽  
Earth's Rotation ◽  
Fundamental Astronomy ◽  
Rigid Earth ◽  
Definition Of ◽  
Celestial Reference System ◽  
Orientation Parameters

AbstractThe celestial Earth's orientation is required for many applications in fundamental astronomy and geodesy; it is currently determined with sub-milliarcsecond accuracy by astro-geodetic observations. Models for that orientation rely on solutions for the rotation of a rigid Earth model and on the geophysical representation of non-rigid Earth effects. Important IAU 2000/2006 resolutions on reference systems have been passed (and endorsed by the IUGG) that recommend a new paradigm and high accuracy models to be used in the transformation from terrestrial to celestial systems. This paper reviews the consequences of these resolutions on the adopted Earth orientation parameters, IAU precession-nutation models and associated nomenclature. It summarizes the fundamental aspects of the current IAU precession-nutation models and reports on the consideration of General Relativity (GR) in the solutions. This shows that the current definitions and nomenclature for Earth's rotation are compliant with GR and that the IAU precession-nutation is compliant with the IAU 2000 definition of the geocentric celestial reference system in the GR framework; however, the underlying Earth's rotation models basically are Newtonian.

Implications of second order nutation terms in IAU2000 framework

2021 ◽  
Author(s):  
Alberto Escapa ◽  
Juan Getino ◽  
Jose Manuel Ferrándiz ◽  
Tomás Baenas
Keyword(s):  
Transfer Function ◽  
Second Order ◽  
Earth Structure ◽  
First Order ◽  
The Earth ◽  
Fluid Core ◽  
Rigid Earth

<p>IAU2000 (Mathews et al. 2002) incorporates some second order terms in the sense of perturbation theories in its formulation. In particular, the second order Poisson amplitudes independent of the Earth structure. They are borrowed from the rigid Earth theory REN2000 by Souchay et al. (1999). Their inclusion, however, is inconsistent (Escapa et al. 2020) since they are convolved with the MHB2000 transfer function, rendering them Earth dependent.</p><p>In that IAU2000 scheme, second order contributions depending on the Earth structure are totally ignored, as it is the case in the rigid Earth theory (Souchay et al. 1999). That structure dependent terms affect both a part of Poisson second order amplitudes and all the Oppolzer ones. Getino et al. (2021) have shown that the numerical contribution of the ignored Poisson terms is not negligible. In addition, the dependence of the respective amplitudes on the fluid core present quite different features from those of first order terms.</p><p>These facts pose some significant problems in the application of IAU2000 transfer function and the estimation of basic Earth parameters when second order terms are included, which are discussed in this communication.</p>

Venus internal structure and global deformation

2021 ◽  
Author(s):  
Christelle Saliby ◽  
Agnes Fienga ◽  
Giorgio Spada ◽  
Daniele Melini ◽  
Anthony Memin
Keyword(s):  
Gravity Field ◽  
Internal Structure ◽  
Terrestrial Planet ◽  
Love Number ◽  
Tidal Forces ◽  
The Earth ◽  
Mass Redistribution ◽  
Love Numbers ◽  
Fortran 90 ◽  
Global Deformation

<p>Tidal forces acting on a planet cause a deformation and mass redistribution in its interior, involving surface motions and variation in the gravity field, which may be observed in geodetic experiments. The change in the gravitational field of the planet, due to the influence of an external gravity field, described primarily by its tidal Love number k of degree 2 (denoted by k<sub>2</sub>) can be observed from analysis of a spacecraft radio tracking. The planet’s deformation is linked to its internal structure, most effectively to its density and rigidity. Hence the tidal Love number k<sub>2</sub> can be theoretically approximated for different planetary models, which means comparing the observed and theoretical calculation of k<sub>2</sub> of a planet is a window to its internal structure.</p> <p>The terrestrial planet Venus is reminiscent of the Earth twin planet in size and density, which leads to the assumption that the Earth and Venus have similar internal structures. In this work, with a Venus we investigate the structure and elastic parameters of the planet’s major layers to calculate its frequency dependent tidal Love number k<sub>2</sub>. The calculation of k<sub>2</sub> is done with ALMA, a Fortran 90 program by <em>Spada [2008]</em> for computing the tidal and load Love numbers using the Post-Widder Laplace inversion formula. We test the effect of different parameters in the Venus model (as a layer’s density, rigidity, viscosity and thickness) on the tidal Love numbers k<sub>2 </sub>and different linear and non-linear combinations of k<sub>2</sub> and<sub> </sub>h<sub>2</sub> (as the tidal Love number h<sub>2</sub> describes the radial displacement due to tidal effects).</p>

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