Models of large-scale viscous flow in the Earth's mantle with constraints from mineral physics and surface observations

Abstract

S U M M A R YModelling the geoid has been a widely used and successful approach in constraining flow and viscosity in the Earth's mantle. However, details of the viscosity structure cannot be tightly constrained with this approach. Here, radial viscosity variations in four to five mantle layers (lithosphere, upper mantle, one to two transition zone layers, lower mantle) are computed with the aid of independent mineral physics results. A density model is obtained by converting s-wave anomalies from seismic tomography to density anomalies. Assuming both are of thermal origin, conversion factors are computed based on mineral physics results. From the density and viscosity model, a model of mantle flow, and the resulting geoid and radial heat flux profile are computed. Absolute viscosity values in the mantle layers are treated as free parameters and determined by minimizing a misfit function, which considers fit to geoid, 'Haskell average' determined from post-glacial rebound and the radial heat flux profile and penalizes if at some depth computed heat flux exceeds the estimated mantle heat flux 33 TW. Typically, optimized models do not exceed this value by more than about 20 per cent and fit the Haskell average well. Viscosity profiles obtained show a characteristic hump in the lower mantle, with maximum viscosities of about 10 23 Pa s just above the D layer-several hundred to about 1000 times the lowest viscosities in the upper mantle. This viscosity contrast is several times higher than what is inferred when a constant lower mantle viscosity is assumed. The geoid variance reduction obtained is up to about 80 per cent-similar to previous results. However, because of the use of mineral physics constraints, a rather small number of free model parameters is required, and at the same time, a reasonable heat flux profile is obtained. Results are best when the lowest viscosities occur in the transition zone. When viscosity is lowest in the asthenosphere, variance reduction is about 70-75 per cent. Best results were obtained with a viscous lithosphere with a few times 10 22 Pa s. The optimized models yield a core-mantle boundary excess ellipticity several times higher than observed, possibly indicating that radial stresses are partly compensated due to non-thermal lateral variations within the lowermost mantle.

Influence of the Ringwoodite-Perovskite transition on mantle convection in spherical geometry as a function of Clapeyron slope and Rayleigh number

“…The mean absolute density, in contrast, is fairly well constrained from global radial seismological models at just over 4.15 Kg m −3 (Dziewonski and Anderson, 1981). The coefficient of thermal expansion at around 660 km depth is probably slightly less than 2 × 10 −5 K −1 for base of upper mantle and slightly more than 2 × 10 −5 K −1 for uppermost lower mantle (Steinberger and Calderwood, 2006). Considering the factors outlined above, we can reasonably expect this layering process to affect Earth's mantle dynamics.…”

“…Accepting this, to advance the discussion we estimate that present day mantle Ra might be ≈ 10 7 , assuming, e.g. mean viscosity η ≈ 5 × 10 21 Pa s, κ ≈10 −6 m 2 s −1 , α ≈2 × 10 −5 K −1 , super-adiabatic temperature drop of ≈2550 K (Steinberger and Calderwood, 2006). Earlier in Earth history, a hotter mantle is to be expected due to the dissipation of gravitational energy from the formation era and higher radioactivity.…”

Effects of upper mantle heterogeneities on lithospheric stress field and dynamic topography

“…For instance, the modeled dynamic geoid typically gives a good correlation with observations, due to a large contribution of the lower mantle (Čadek and Fleitout, 2003;5 Hager et al, 1985;Richards and Hager, 1984), but is sensitive to the choice of the mantle viscosity (Thoraval and Richards, 1997). However, the correlation between the modeled dynamic and residual topography is typically found to be weak (Heine et al, 2008;Flament et al, 2012;Steinberger and Calderwood, 2006;Steinberger, 2016;Hoggard et al, 2016). The residual topography is here defined as the observed topography corrected for the variations in the crustal and lithosphere thickness and density variations and for subsidence of the sea floor with age.…”

“…Lithosphere dynamics are defined by a combination of plastic, elastic and viscous flow properties of the lithospheric material (Burov, 2011;Tesauro et al, 2012), while the evolution of the sub-lithospheric mantle is predominantly driven by viscous flow (Davies, 1977;Forte and Mitrovica, 2001;Steinberger and Calderwood, 2006). This is evident from surface expressions of 5 different deformation processes around the globe, such as for example the ongoing crustal deformation processes that formed the Tibetan Plateau due to the continental collision of the Indian and Eurasian Plates (van Hinsbergen et al, 2011) or the rifting of the African Plate induced by its interaction with the Afar plume head (Ebinger and Sleep, 1998).…”

Deep mantle structure as a reference frame for movements in and on the Earth

“…However, this may be partly compensated for by a larger amount of slabs in the lower mantle as a result of lower sinking speeds. The exact shape of geoid kernels depends on viscosity structure and phase boundary parameters (Clapeyron slope, density jump, thermal expansivity); however, a degree-2 kernel that is positive in the upper part of the mantle and negative in its lower part is a robust feature of mantle models that successfully reproduce large-scale features of the geoid (24)(25)(26). Hence, we expect that the intermediate-to high-latitude subduction would preferentially induce true polar wander so that subduction zones shift toward the equator, possibly with some time delay (Fig.…”