Long-term polar motion on a quasi-fluid planetary body with an elastic lithosphere: Semi-analytic solutions of the time-dependent equation

Harada, Yuji

doi:10.1016/j.icarus.2012.05.024

Cited by 8 publications

(14 citation statements)

References 65 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This has been often referred as the 'polar wander' and mainly ascribed to the Earth's viscoelastic relaxation after the Pleistocene deglaciation (e.g., Nakiboglu & Lambeck 1980), known as the 'glacial isostatic adjustment' or 'post glacial rebound'. Recently, it has been pointed by Mitrovica & Wahr (2011) and Harada (2012) that the polar wander associated with the glacial isostatic adjustment of thousand years time scale should be less than previous estimates not considering the Earth's fossil bulge.…”

Section: Introductionmentioning

confidence: 90%

Changes in the Earth’s Spin Rotation due to the Atmospheric Effects and Reduction in Glaciers

Na¹,

Cho²,

Kim³

et al. 2016

Journal of Astronomy and Space Sciences

View full text Add to dashboard Cite

The atmosphere strongly affects the Earth’s spin rotation in wide range of timescale from daily to annual. Its dominant role in the seasonal perturbations of both the pole position and spinning rate of the Earth is once again confirmed by a comparison of two recent data sets; i) the Earth orientation parameter and ii) the global atmospheric state. The atmospheric semi-diurnal tide has been known to be a source of the Earth’s spin acceleration, and its magnitude is re-estimated by using an enhanced formulation and an up-dated empirical atmospheric S2 tide model. During the last twenty years, an unusual eastward drift of the Earth’s pole has been observed. The change in the Earth’s inertia tensor due to glacier mass redistribution is directly assessed, and the recent eastward movement of the pole is ascribed to this change. Furthermore, the associated changes in the length of day and UT1 are estimated.

show abstract

Section: Introductionmentioning

confidence: 90%

Changes in the Earth’s Spin Rotation due to the Atmospheric Effects and Reduction in Glaciers

Na¹,

Cho²,

Kim³

et al. 2016

Journal of Astronomy and Space Sciences

View full text Add to dashboard Cite

show abstract

“…It can be seen that the difference in the fluid Love number between M5 and M4 is almost the same as the mode strength ofT 1 in M4: k M4 f −k M5 f ≈ (k 1 ∕s 1 ) M4 . The remnant bulge is dealt with in previous studies by either those dealing with an elastic lithosphere (Cambiotti et al, 2010;Chan et al, 2014;Harada, 2012;Mitrovica et al, 2005) or viscoelastic lithosphere (Cambiotti et al, 2010;Moore et al, 2017) by isolating this part of the Love number and formulating the influence of it separately. Figure 7.…”

Section: Effect Of a Remnant Bulge On Tpw And A Study Of Marsmentioning

confidence: 99%

A Full‐Maxwell Approach for Large‐Angle Polar Wander of Viscoelastic Bodies

Wal

Vermeersen

2017

JGR Planets

View full text Add to dashboard Cite

For large‐angle long‐term true polar wander (TPW) there are currently two types of nonlinear methods which give approximated solutions: those assuming that the rotational axis coincides with the axis of maximum moment of inertia (MoI), which simplifies the Liouville equation, and those based on the quasi‐fluid approximation, which approximates the Love number. Recent studies show that both can have a significant bias for certain models. Therefore, we still lack an (semi)analytical method which can give exact solutions for large‐angle TPW for a model based on Maxwell rheology. This paper provides a method which analytically solves the MoI equation and adopts an extended iterative procedure introduced in Hu et al. (2017) to obtain a time‐dependent solution. The new method can be used to simulate the effect of a remnant bulge or models in different hydrostatic states. We show the effect of the viscosity of the lithosphere on long‐term, large‐angle TPW. We also simulate models without hydrostatic equilibrium and show that the choice of the initial stress‐free shape for the elastic (or highly viscous) lithosphere of a given model is as important as its thickness for obtaining a correct TPW behavior. The initial shape of the lithosphere can be an alternative explanation to mantle convection for the difference between the observed and model predicted flattening. Finally, it is concluded that based on the quasi‐fluid approximation, TPW speed on Earth and Mars is underestimated, while the speed of the rotational axis approaching the end position on Venus is overestimated.

show abstract

“…With these equations for the inertia tensor in hand, the fundamental underlying assumption we make to solve for the time-varying rotation axis is that the time scale being considered is long enough that the rotation axis stays aligned with the principle axis of inertia (Ricard et al, 1993;Harada, 2012;Chan et al, 2014). In this case, our calculations of TPW are based on diagonalizing equation (12) (or equation 13) and computing the time-varying orientation of the principle axis of inertia.…”

Section: Mathematical Theorymentioning

confidence: 99%

“…Their theory was valid for small displacements of the pole, and they demonstrated that the range of validity was a strong function of the location of the loads relative to the rotation axis. To overcome this small-angle limitation, Harada (2012), Creveling et al (2012) and Chan et al (2014) extended the pioneering approach of Ricard et al (1993) to incorporate the effects of the remnant bulge on the predicted TPW history. In these studies, the lithosphere was treated as a purely elastic layer, with effectively infinite viscosity.…”

Section: Introductionmentioning

confidence: 99%

“…In reality, a lithosphere will have finite viscosity, and it will viscously relax in the case of a loading of sufficiently long time scale, and no rotational stability theory for terrestrial planets has yet considered this more realistic case. In this study, we extend the TPW theories of Ricard et al (1993), Harada (2012), Creveling et al (2012) and Chan et al (2014) to include stabilization by a viscoelastic lithosphere of high (but finite) viscosity. On such a planet, TPW driven by loading of short time scale (i.e., a time scale shorter than the viscous relaxation time of the lithosphere) will be strongly stabilized by a remnant bulge, while on long time scales the lithosphere will provide no such stabilization and the physics described by Gold (1955) and Goldreich and Toomre (1969) will prevail.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Time-dependent rotational stability of dynamic planets with viscoelastic lithospheres

Moore

Chan

Daradich

et al. 2017

Icarus

View full text Add to dashboard Cite

We extend previous work to derive a non-linear rotational stability theory governing true polar wander (TPW) of terrestrial planets with viscoelastic lithospheres. We demonstrate, analytically and using numerical examples, that our expressions are consistent with previous results in the limiting cases of low and infinite (i.e., purely elastic) viscosity lithospheres. To illustrate the stability theory, we compute TPW on Mars driven by a simple, prescribed mass loading. Our calculations demonstrate that on short time scales relative to the relaxation time of the viscoelastic lithosphere, the rotation axis follows a constrained path that reflects stabilization by remnant strength in the lithosphere, but that on long times scales this stabilization disappears and the load ultimately reaches the equator. Earlier work based on the assumption of a permanent remnant bulge in the case of a purely elastic lithosphere has suggested that Martian TPW would not persist for any significant time after a load is emplaced, and thus an equilibrium stability theory is sufficient to model long-term (order 1 Myr or longer) polar motion of the planet. Our results

show abstract

Long-term polar motion on a quasi-fluid planetary body with an elastic lithosphere: Semi-analytic solutions of the time-dependent equation

Cited by 8 publications

References 65 publications

Changes in the Earth’s Spin Rotation due to the Atmospheric Effects and Reduction in Glaciers

Changes in the Earth’s Spin Rotation due to the Atmospheric Effects and Reduction in Glaciers

A Full‐Maxwell Approach for Large‐Angle Polar Wander of Viscoelastic Bodies

Time-dependent rotational stability of dynamic planets with viscoelastic lithospheres

Contact Info

Product

Resources

About