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>

scholarly journals Reducing filter effects in GRACE-derived polar motion excitations

2020 ◽  
Author(s):  
Franziska Göttl ◽  
Michael Murböck ◽  
Michael Schmidt ◽  
Florian Seitz
Keyword(s):  
Gravity Field ◽  
Polar Motion ◽  
Grid Point ◽  
Ocean Model ◽  
Earth System ◽  
Satellite Mission ◽  
Geophysical Model ◽  
The Earth ◽  
Mass Redistribution ◽  
Filter Effects

<p><span>Polar motion is caused by mass redistribution and motion within the Earth system. The GRACE satellite mission observed variations of the Earth’s gravity field which are caused by mass redistribution. Therefore GRACE time variable gravity field models are a valuable source to estimate individual geophysical mass-related excitations of polar motion. Since GRACE observations contain erroneous meridional stripes, filtering is essential in order to retrieve meaningful information about mass redistribution within the Earth system. However filtering reduces not only the noise but also smooths the signal and induces leakage of neighboring subsystems into each other.</span></p><p><span><span>We present a novel approach to reduce these filter effects in GRACE-derived equivalent water heights and polar motion excitation functions which is based on once and twice filtered gravity field solutions. The advantages of this method are that it is independent from geophysical model information, works on global grid point scale and can therefore be used for mass variation estimations of several subsystems of the Earth (e.g. continental hydrosphere, oceans, Antarctica and Greenland). In order to validate this new method, we perform a closed-loop simulation based on a realistic orbit scenario and error assumptions for instruments and background models, apply it to real GRACE data (GFZ RL06) and show comparisons with ocean model results from ECCO and MPIOM.</span></span></p>

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.

Determining dislocation love number of vertical displacement using GPS observations: case study of 2011 Tohoku-Oki earthquake (Mw 9.0)

2020 ◽  
Vol 222 (2) ◽  
pp. 965-977
Author(s):  
Junyan Yang ◽  
Wenke Sun
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Vertical Displacement ◽  
Fault Slip ◽  
Earth Model ◽  
Love Number ◽  
The Earth ◽  
Love Numbers ◽  
Vertical Displacements

SUMMARY The concept of determining the dislocation Love numbers using GNSS (Global Navigation Satellite System) data and calculating the corresponding Green's functions is presented in this paper. As a case study, we derive the dislocation Love number h of vertical displacement by combining 1232 onshore GPS data and 7 GPS-Acoustic data with the 2011 Tohoku-Oki earthquake (Mw 9.0). Three fault-slip distributions are used to compare and verify the theory and results. As the GPS stations are only located in Japan Island and along the Japan trench, we use the theoretical vertical displacements of a spherically layered Earth structure to constrain the low-order signal. The L-curve and an a priori preliminary reference skill are applied in the inversion method. Then, the GPS-observed vertical displacement changes are used to invert for the vertical displacement dislocation Love numbers h based on three different fault-slip models. Our results indicate that the estimated dislocation Love numbers $h$ fluctuate significantly from the earth model (i.e. the preliminary reference earth model), especially for the $h_{n1}^{32}$ component, and these changes in $h_{n2}^{12}$ and $h_{n0}^{33} - h_{n0}^{22}$ are relatively small. The vertical displacements derived from the inversion results agree well with the GPS vertical observations. The inverted dislocation Love numbers are considered to profile the regional structure which differs from the mean 1-D heterogeneous structure of the Earth, and the corresponding Green's functions of four independent dislocation sources describe a more reasonable seismic deformation field.

scholarly journals Reducing filter effects in GRACE-derived polar motion excitations

2019 ◽  
Vol 71 (1) ◽  
Author(s):  
Franziska Göttl ◽  
Michael Murböck ◽  
Michael Schmidt ◽  
Florian Seitz
Keyword(s):  
Gravity Field ◽  
Polar Motion ◽  
Grid Point ◽  
Earth System ◽  
Satellite Mission ◽  
Geophysical Model ◽  
The Earth ◽  
Novel Approach ◽  
Mass Redistribution ◽  
Filter Effects

Abstract Polar motion is caused by mass redistribution and motion within the Earth system. The GRACE (Gravity Recovery and Climate Experiment) satellite mission observed variations of the Earth’s gravity field which are caused by mass redistribution. Therefore GRACE time variable gravity field models are a valuable source to estimate individual geophysical mass-related excitations of polar motion. Since GRACE observations contain erroneous meridional stripes, filtering is essential to retrieve meaningful information about mass redistribution within the Earth system. However filtering reduces not only the noise but also smoothes the signal and induces leakage of neighboring subsystems into each other. We present a novel approach to reduce these filter effects in GRACE-derived equivalent water heights and polar motion excitation functions which is based on once- and twice-filtered gravity field solutions. The advantages of this method are that it is independent from geophysical model information, works on global grid point scale and can therefore be used for mass variation estimations of several subsystems of the Earth. A closed-loop simulation reveals that due to application of the new filter effect reduction approach the uncertainties in GRACE-derived polar motion excitations can be decreased from 12–48% to 5–29%, especially for the oceanic excitations. Comparisons of real GRACE data with model-based oceanic excitations show that the agreement can be improved by up to 15 percentage points.

scholarly journals Tidal response of rocky and ice-rich exoplanets

2019 ◽  
Vol 630 ◽  
pp. A70 ◽  
Author(s):  
G. Tobie ◽  
O. Grasset ◽  
C. Dumoulin ◽  
A. Mocquet
Keyword(s):  
Dissipation Rate ◽  
Scaling Laws ◽  
Accurate Determination ◽  
Relative Size ◽  
Iron Core ◽  
Love Number ◽  
Tidal Forces ◽  
The Earth ◽  
Rocky Planets ◽  
Tidal Response

The amount of detected planets with sizes comparable to that of the Earth is increasing drastically. Most of the Earth-size planet candidates orbit at close distances from their central star, and therefore are subjected to large tidal forces. Accurate determination of the tidal parameters of exoplanets taking into account their interior structure and rheology is essential to better constrain their rotational and orbital history, and hence their impact on climate stability and planetary habitability. In the present study, we compute the tidal response of rocky and ice-rich solid exoplanets for masses ranging between 0.1 and 10 Earth masses using a multilayer approach and an Andrade rheology. We show that the amplitude of tidal response, characterized by the gravitational Love number, k2, is mostly controlled by self-gravitation and increases as a function of planet mass. For rocky planets, k2 depends mostly on the relative size of the iron core, and hence on the bulk iron fraction. For ice-rich planets, the presence of outer ice layers reduces the amplitude of tidal response compared to ice-free rocky planets of similar masses. For both types of planet (rocky and ice-rich), we propose relatively simple scaling laws to predict the potential Love number value as a function of radius, planet mass and composition. For the dissipation rate, characterized by the Q−1 factor, we did not find any direct control by the planet mass. The dissipation rate is mostly sensitive to the forcing frequency and to the internal viscosity, which depends on the thermal evolution of the planet, which is in turn controlled by the planet mass and composition. The methodology described in the present study can be applied to any kind of solid planet and can be easily implemented into any thermal and orbital evolution code.

scholarly journals Forming terrestrial planets and delivering water

2015 ◽  
Vol 11 (A29B) ◽  
pp. 427-430
Author(s):  
Kevin J. Walsh
Keyword(s):  
Planet Formation ◽  
Semimajor Axis ◽  
Giant Planet ◽  
Terrestrial Planet ◽  
Giant Planets ◽  
Asteroid Belt ◽  
Terrestrial Planets ◽  
The Earth ◽  
Building Models ◽  
Rich Material

AbstractBuilding models capable of successfully matching the Terrestrial Planet's basic orbital and physical properties has proven difficult. Meanwhile, improved estimates of the nature of water-rich material accreted by the Earth, along with the timing of its delivery, have added even more constraints for models to match. While the outer Asteroid Belt seemingly provides a source for water-rich planetesimals, models that delivered enough of them to the still-forming Terrestrial Planets typically failed on other basic constraints - such as the mass of Mars.Recent models of Terrestrial Planet Formation have explored how the gas-driven migration of the Giant Planets can solve long-standing issues with the Earth/Mars size ratio. This model is forced to reproduce the orbital and taxonomic distribution of bodies in the Asteroid Belt from a much wider range of semimajor axis than previously considered. In doing so, it also provides a mechanism to feed planetesimals from between and beyond the Giant Planet formation region to the still-forming Terrestrial Planets.

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