Length of day variations due to mantle dynamics at geological timescale

Abstract

S U M M A R YThe geological evolution of length of day (LOD) variations is mainly controlled by the frictional tidal torque responsible for the secular slowdown of the Earth's rotation and for the receding of the Moon. Superimposed on this variation, which has existed since the early history of the planet, there are, at shorter timescales (less than 1 Myr), LOD perturbations induced by the glaciation-deglaciation cycles. In this paper, we investigate the influence of mantle dynamics on LOD at the geological timescale. We use the complete non-linear equations to compute the influence of mantle density heterogeneities on the angular velocity of the rotation, that is to say on the LOD. We discuss the degree zero coefficient of the spherical harmonic expansion of the mantle mass anomaly, which is strongly dependent on the conservation of mass of the Earth.We first compute the effects induced by upwelling domes and subducted plates sinking into the mantle, which are known to induce geological variations in the orientation of the rotation axis with respect to a fixed terrestrial frame (the so-called True Polar Wander). We find that the time-variable mantle density heterogeneities associated with the large-scale pattern of plate tectonic motions since 120 Ma and with the upwelling domes can perturb LOD by about 0.4 µs per year, that is, with an order of magnitude smaller than the effects induced by the last deglaciation. Superimposed on this linear trend, we show that there are fluctuations around 0.1-0.2 s Myr −1 on a timescale of a few tens of millions of years.We then combine a spherical model of mantle circulation with solutions for the equations governing the rotation of a viscous planet, to improve the constraint of mantle mass conservation.Finally, we compare our results with other effects.

Sensitivity experiments on True Polar Wander

“…By MacCullagh's theorem [e.g., Munk and MacDonald , ], we may relate the components of the inertia tensor perturbation induced by the mantle mass anomalies ( I ij for ) to the degree 2 spherical harmonics coefficients of the geoid: where I o is the inertia tensor of a spherical nonrotating Earth with a mass M : ( ). We do not take into account the diagonal inertia tensor perturbation induced by the degree zero mantle mass anomalies, since such a perturbation will only cause variations in the length of day but no change in the TPW [ Greff‐Lefftz , ]. Consequently to compute the inertia perturbations induced by the mantle mass anomalies taking into account the viscous gravitational deformations, we use a “degree 2 geoid kernel”: this function is plotted (Figure b) for our reference Earth's model using a viscosity profile (Figure a) with V R = 4.…”

“…T R may be computed with the use of the tidal viscoelastic Love number [ Ricard et al ., ]. For our mantle model of viscosity, its value is about 20 kyr [ Greff‐Lefftz , ]. The time scale at which the rotation axis will adjust to the maximum principal inertia axis depends consequently on two terms: the relaxation of the rotational bulge ( ), and the amplitude and the temporal evolution of the inertia tensor perturbations induced by internal loads ( I kl ).…”

Possible relationship between the Earth's rotation variations and geomagnetic field reversals over the past 510 Myr

“…Because the latter reflects the glacial and interglacial periods, we hypothesize that it can be used as a possible indicator to explain LOD variations and consequently the reversal field frequency over the past 510 Myr. In this case, we FIGURE 1 | Geomagnetic reversal rates over the past 120 Ma period, which were calculated according to Pavlov and Gallet (2005) and compared with the LOD time derivative variations from Greff-Lefftz (2011). suggest that the superchrons can be the Earth's internal markers for LOD oscillations through the Phanerozoic.…”

Earth Rotation Variations – Long Period

“…Other mechanisms that may cause a linear trend in LOD over the last or next century include continental drift (Dickman, 1979), tectonic processes taking place under nonisostatic conditions (Sabadini and Vermeersen, 2004;Vermeersen and Vlaar, 1993;Vermeersen et al, 1994), plate subduction (Alfonsi and Spada, 1998;Greff-Lefftz, 2011;Ricard et al, 1993;Spada et al, 1992), mantle convection (Greff-Lefftz, 2011), upwelling mantle plumes (Greff-Lefftz, 2011), deformation of the mantle caused by pressure variations acting at the core-mantle boundary that are associated with the motion of the fluid core (Dumberry and Bloxham, 2004;Fang et al, 1996;Greff-Lefftz et al, 2004), earthquakes (Chao and Gross, 1987;Gross and Chao, 2006), and climate change (Abarca del Rio, 1999;de Viron et al, 2002;Huang et al, 2001;Landerer et al, 2007;Räisänen, 2003;Rosen and Gutowski Jr., 1992;Rosen and Salstein, 2000;Winkelnkemper et al, 2009). The fluctuation in LOD of 1500-year period found by Stephenson and Morrison (1995) and Morrison and Stephenson (2001) is currently of unknown origin.…”

“…The dotted black lines show the model of the decadal variations that they used when estimating the trend. Other mechanisms that may cause a linear trend in the path of the pole over the last or next century include continental drift (Dickman, 1979;Nakada, 2007Nakada, , 2008, tectonic processes taking place under nonisostatic conditions (Sabadini and Vermeersen, 2004;Vermeersen and Vlaar, 1993;Vermeersen et al, 1994), plate subduction (Alfonsi and Spada, 1998;Greff-Lefftz, 2011;Ricard and Sabadini, 1990;Ricard et al, 1992Ricard et al, , 1993Richards et al, 1997;Rouby et al, 2010;Spada et al, 1992;Steinberger and Torsvik, 2010), mantle convection (Cambiotti et al, 2011;Chan et al, 2011aChan et al, , 2011bGreff-Lefftz, 2011;Nakada, 2008Nakada, , 2009bRichards et al, 1999;Schaber et al, 2009;Steinberger and O'Connell, 1997), upwelling mantle plumes (Greff-Lefftz, 2004Rouby et al, 2010;Steinberger and O'Connell, 2002), earthquakes (Alfonsi and Spada, 1998;Chao and Gross, 1987;Chao et al, 1996b;Gross and Chao, 2006;Soldati and Spada, 1999;Spada, 1997;Zhou et al, 2013), and climate change (Landerer et al, 2009;. Adapted from Gross RS and Vondrák J (1999)…”