Implications of second order nutation terms in IAU2000 framework

<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>

Performance of Retaining Walls with Compressible Inclusions under Seismic Loading

This paper investigates the possible application of recycled tyre shreds as compressible inclusion behind retaining walls under dynamic loading. It is a novel method to reduce the magnitude of earthquake-induced dynamic forces against rigid earth retaining wall structures. A numerical model to analyze the behavior of retaining walls with compressible cushion was developed in PLAXIS 2D, a two-dimensional finite element analysis based software, and the results were validated by comparison with experimental findings from physical models. The study evaluates the effects of thickness of compressible cushion and the friction angle of the backfill on the seismic performance of retaining walls. To assess the effect of frequency on wall performance with and without cushion, the wall was subjected to 15 cycles of sinusoidal excitation with acceleration amplitudes of 0.1g to 0.3g at a frequency of 7 Hz. The results from the numerical analysis indicate that the permanent displacements of the wall were reduced in the range of 38% to 52% and the horizontal earth pressures were reduced by about 55% to 76% due to the presence of tyre shreds as a compressible cushion between the wall and backfill. Results showed that the dynamic load against the retaining wall can be considerably reduced through the proposed technique. Doi: 10.28991/cej-2020-03091631 Full Text: PDF

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

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.

Baltic-Iranian super lineament — long-lived Trans-Eurasian belt of dislocations and planetary megafractures

Information on fault tectonics and the deep structure of the global trans-Eurasian belt of dislocations and planetary megafractures (Baltic-Iranian Super Lineament) is generalized based on the analysis of literary, geological and geophysical, cartographic, cosmographic materials, including the results of tectonic lineaments interpretation of cosmo-images of the Earth’s surface. The features of its distribution and segmentation are clarified. This Super Lineament is the trans-Eurasian structure of a planetary rank — an integral part of the regularly spatially oriented ancient reghmatic fault net of Eurasia, formed at the early stages of the formation of the rigid earth crust under the influence of global stresses associated with the factor of rotation of the Earth. The long-lived nature of the belt (the Upper Proterozoic — Cenozoic) and its quasi-stationary position throughout its formation history, as well as the absence of large-scale, hundreds of kilometers, of shear displacements along it and at intersections with transverse tectolineament belts of a similar rank indicate the low probability of the plate-tectonic convergence model of Afro-Arabia and Eurasia. The destruction model of the once united Afro-Eurasian continent in a potentially shear field of relatively low amplitude (on a planetary scale) dislocations is preferable. The geodynamic mode of formation and development of the belt as a whole cannot be described by any one type — riftogenic, or collisional ones. Regional and supra-regional zones of extension (riftogenic zones) and compression (collision) alternate in it periodically. It shows the global nature of the belt, the union of different geodynamic regimes in it, as well as the wave character and hierarchy of the tectonic process.

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

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.

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

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.