Roberto Sabadini

Long-term rotation and mantle dynamics of the Earth, Mars, and Venus

In response to internal and surface tectonic processes the terrestrial planets have the ability to displace the axis of rotation with respect to the mantle. This behavior is quantified by means of a nondimensional number, defined here as the rotational number Ro, that allows classification of the planets into two categories, the first containing Mars and the Earth, where true polar wander is a feasible mechanism, and the second, to which Venus belongs, where rotation equilibrium is attained by means of mega-wobbles driven by internal mass anomalies. The number Ro is related to the timescale characterizing the readjustment of the equatorial bulge during long-term polar motion and to the length of the sidereal day. If these two timescales are well separated, the planet experiences true polar wander. Nonlinear Liouville equations for stratified viscoelastic bodies with linear Maxwell rheology are solved in order to assess the relevance of surface and mantle processes in driving long-term rotation instabilities in the terrestrial planets. The amount of true polar wander estimated for the Earth and Mars is reproduced correctly by our modeling with mantle viscosities and lithospheric thickness consistent with other studies. The major difference between the Earth and Mars is the driving mechanism, subduction for the Earth and lithospheric loading for Mars. When mantle viscosities similar to those of the Earth are considered for Venus, the most updated estimate for the offset of about 0.5° between the rotation axis and the axis of maximum inertia is well reproduced during the mega-wobbles induced by internal mass redistribution. We show that the degree 2 topography of these three planets can be affected by their rotation, which is responsible for the dominance of the sectorial component on the Earth and Mars and for the zonal component on Venus.

The dynamical equations of polar wander and the global characteristics of the lithosphere as extracted from rotational data

Abstract The initial value problem describing the linear responses of the spin axis of a layered viscoelastic planet from surface loading is studied by means of Laplace transform techniques. A complete solution of polar motion requires the usage of two classes of eigenspectra: one arising from viscoelastic relaxation of the mantle due to surface forcing, the other involving the gradual readjustment of the spin axis as a consequence of mantle viscoelasticity. Our analytical 4-layer model comprising an elastic lithosphere, a two-layer, adiabatically stratified, viscoelastic mantle and an inviscid core has been incorporated into this formalism in which rotational deformation and isostatic relaxation are taken into account for all times. From employing both sets of rotational data, polar variations from the 70 years of data from the International Latitude Service (I.L.S.) and the non-tidal deceleration of the length of the day (l.o.d.) an estimate of the globally averaged lithosphere of between 130 and 200 km is obtained from the long wavelength flexural mode due to the degree-two harmonic. This range of values may have strong implications on the mode of continental evolution.

Postglacial rebound with a non-Newtonian upper mantle and a Newtonian lower mantle rheology

We have employed a composite rheology consisting of both linear and nonlinear creep mechanisms which are connected by a ‘transition’ stress. Background stress due to geodynamical processes is included. For models with a non-Newtonian upper-mantle overlying a Newtonian lower-mantle the temporal responses of the displacements can reproduce those of Newtonian models. The average effective viscosity profile under the ice-load at the end of deglaciation turns out to be the crucial factor governing mantle relaxation. This can explain why simple Newtonian rheology has been successful in fitting the uplift data over formerly glaciated regions.

DEEP CONTINENTAL ROOTS: THE EFFECTS OF LATERAL VARIATIONS OF VISCOSITY ON POST-GLACIAL REBOUND

The existence of lateral viscosity variations in the earth mantle could be inferred by recent tomographic results. This can potentially cause substantial changes in the interpretation of the results from usual postglacial uplift modelling which assumes a uniform mantle. In this work we study the impact of a high viscosity craton located below the lithosphere in Fennoscandia. The solution is obtained using a finite element code which treats the surface rebound of an axisymmetrical viscoelastic half-space. The effects on the vertical displacements and velocity fields could be of the order of 30% in the centre of deglaciated areas and become larger for horizontal displacements, strain-fields and vertical velocities at the peripheral region. Viscosity increases beneath continental regions with respect to oceanic regions may be able to explain the systematically lower viscosity values inferred from sea-level data from Pacific Island sites. Our findings are potentially very important in the interpretation of GPS data.

Finite element modeling of lateral viscosity heterogeneities and post-glacial rebound

Abstract The existence of lateral viscosity heterogeneities of a few orders of magnitude in the Earth mantle has recently been proposed by several authors, although classical post-glacial rebound models are consistent with a rather uniform structure. Tomographic results reveal the presence of lateral heterogeneities in seismic velocities within the mantle which can be correlated with temperature and viscosity variations. Our aim is to analyze the uplift in deglaciated areas, using a realistic horizontal viscosity profile of the mantle, in order to determine the influence of such models on global mantle viscosity evaluation. Since analytical models cannot handle lateral heterogeneities, we used a finite-element numerical approach. The code is a version of TECTON program (Melosh and Raefsky, 1983), suitable for treating the axisymmetric case and modified to take isostatic compensation of the surface load into account. We found that the average mantle viscosity values deviate from the “canonical” value of 1021 Pa · s when lateral variations are taken into consideration. The displacement in the center is controlled by the average viscosity underlying the load. For long wavelengths (heterogeneities of two orders of magnitude), the estimated average viscosity may differ by a factor 7 from the results obtained using radial models. For stronger variation (of four orders of magnitude) the deviation is a factor of 30, although such strong viscosity seems to be inconsistent with the data. Difficulties in data fitting are also encountered for smaller variations when short wavelengths are considered. When the interplay of vertical and lateral stratification is considered, we find that average viscosities in the upper and lower mantle depend on the magnitude and pattern of the heterogeneities in each layer. In particular, strong lateral viscosity contrasts in the upper mantle can overlie a uniform lower mantle.

Interaction of cryospheric forcings with rotational dynamics has consequences for ice ages

Recent geological evidence1,2 suggests that several degrees of true polar wandering have occurred since the mid-Pliocene. This rotational instability is supported by dynamical calculations3 of the spin axis of a layered viscoelastic Earth, which has been subjected to the periodic forcings characteristic of the late Cenozoic ice age. We propose here that polar wandering, induced by the intrinsic response of the viscoelastic planet to such cryospheric forcings, may be the underlying cause for the termination of the present ice age epoch.

Dynamic effects from mantle phase transitions on true polar wander during ice ages

The relaxation spectrum of a stratified viscoelastic mantle with phase transitions contains a class of extremely long decaying modes with relaxation times 0 (106 yr), exceeding the characteristic time scale of an individual glacial cycle. Consequently, the net motion of the rotation pole produced by the cyclic loading and unloading of ice sheets would display a nonequilibrium behaviour in the initial stages of an ice age epoch. We present here calculations of the net polar speed as a function of time for the late Cenozoic ice ages. These results show an initial transient net velocity of 0 (1° Myr−1) which, after a few million years, decays to a steady value of 0(0.1° Myr−1). We propose that the length of a typical ice age period around 0(107 yr), is controlled by the time scale required for the steady-state polar wander to drift sufficiently far such that the necessary conditions for the Milankovitch mechanism to operate can no longer be maintained.

The role of subduction on the horizontal motions in the Tyrrhenian Basin : a numerical model

The horizontal motions in the Tyrrhenian basin and surrounding chains, induced by subduction along the Calabrian Arc and Northern Apennines, are analyzed by means of numerical models based on finite element techniques. The driving mechanism, in 2-dimensional vertical cross-sections perpendicular to the trench, is the slab-pull due to the negative buoyancy of a stratified viscoelastic plate that models the Ionic oceanic lithosphere or Adriatic plate sinking in the upper mantle. For the modern tectonic setting of the area, we test the sensitivity of extension in the back-arc and of roll-back of the overriding plate to variations in the viscosity structure and in the geometry of subduction. Our results are compared with extensional velocities inferred from geology and SLR-VLBI data.

Sea-level fluctuations due to subduction: The role of mantle rheology

By means of a stratified viscoelastic Earth model we study the effect of sinking slabs on the dynamic topography, the non-hydrostatic geoid and the long-term sea level variations. Sea level fluctuations due to subduction are found to be sensitive to the nature of the 670 km seismic discontinuity and to the rheological layering of the mantle. The response of our model to both a single subduction and a realistic distribution of slabs is studied by a numerical simulation based on a simplified approach. Consistent with previous results, we find that an upper bound to relative sea level time variations associated with the initiation of a new subduction in the upper mantle is ∼ 0.1 mm/yr. Relative sea level changes driven by the dynamic readjustment of internal mass heterogeneities may thus be comparable with those attributed to other changes in the tectonic regime on a large scale. This confirms the relevance of subduction as an important contributor to long-term sea level fluctuations.

True polar wander affects the Earth dynamic topography and favours a highly viscous lower mantle

True Polar Wander (TPW), the global motion of the Earths mantle relative to the axis of rotation, is considered for its impact on the degree 2 surface dynamic topography induced by mass anomalies in a viscously stratified mantle. These sources, responsible for a geoid and topographic signal at the Earths surface, mimic the effects of subductions and other thermal instabilities on long-term Earths rotation. A rotating, viscous planet has the ability to displace the axis of rotation with respect to internal mass anomalies in order to maintain, on the average, the excess of non-hydrostatic geoid along the equator, affecting at the same time the degree 2 pattern of the dynamic topography which supports the geoid. By means of a time series of synthetic mass anomalies, randomly distributed in order to avoid any bias due to the clustering of the sources on time scales of 107 yr, we show that TPW introduces a selection rule which favours in the dynamic topography the order m=0 for an isoviscous mantle and the order m=2 for lower mantle viscosities at least a factor 30 higher than in the upper mantle. The dominance of the order m=2 in the dynamic topography of the real Earth, induced by the mass anomalies inferred from seismic tomography, agrees with the requirements of a rotating planet deformed by internal sources, characterized by a substantial viscosity increase in the lower mantle. This agreement seems to indicate that the intimate physical reason of the high order 2 content in the topography stands on the interplay between the dynamic response of the mantle to internal sources and Earth rotation.