Frédéric Deschamps

Anomalies of temperature and iron in the uppermost mantle inferred from gravity data and tomographic models

We propose a method to interpret seismic tomography in terms of thermal and compositional anomalies. In addition to the tomographic model, we use gravity data, which provide information on the density expressed as a relative density-to-shear wave velocity scaling factor (ζ = ∂ ln ρ/∂ ln Vs). The inferred values of ζ are not consistent with the presence of thermal anomalies alone. However, simultaneous anomalies of temperature and composition explain the observations. Compositional anomalies can have several origins, but we find the most relevant parameter to be the global volumic fraction of iron ( xFe=Fe/(Fe +Mg)). We invert the tomographic model S16RLBM (Woodhouse and Trampert, 1995) and the density anomalies correlated to Vs-anomalies (δρ/ρ0 = ζδ Vs/V0) for anomalies of temperature (δT) and iron (δFe). The partial derivatives are provided by a numerical method that reconstructs density and seismic velocity for given temperatures and petrologic models (Vacher et al., 1998). Down to z = 300 km depth, the distribution of temperature and iron anomalies strongly depends on the surface tectonics. The continental mantle below old cratons and stable platforms is colder than average and depleted in iron, whereas the oceanic mantle is mostly homogeneous. Due to uncertainties on the reference state of the mantle, error bars on δT and δFe reach 10% of the inverted values. Finally, we apply these results to the stability of continental roots and test the hypothesis that the negative buoyancy induced by lower than average temperatures is balanced by the positive buoyancy induced by the depletion in iron. We find that continental roots are stable only if the viscosity of the mantle is strongly temperature-dependent. However, some uncertainties remain on the real effects and importance of rheology.

Thermal convection in the outer shell of large icy satellites

Evolution of large icy satellites is controlled by heat transfer across the outer ice I layer. After the core overturn a possible structure consists of a silicate core and a shell of molten ices. As the satellite cools down, the primordial ocean crystallizes. If the outer layer is thick enough, convection is very likely to occur in it. We have used the results of a recent two-dimensional numerical model of convection including variable viscosity to estimate the vigor and the efficiency of convection in this layer. Viscosity variations induce the apparition of a stagnant lid at the top of the fluid, which reduces the efficiency of heat transfer. In the present study, the Rayleigh number Ra and the heat flux Φ are computed as a function of the thickness of the layer, assuming that the ice flow is Newtonian. Calculations are first made for a generic satellite of radius R = 2500 km and mean density = 1.9 g/cm 3 . It is then shown that variations of ±500 km on the radius and ±0.5 g/cm 3 on the mean density do not induce significant differences in the values of Ra and Φ. On the other hand, variations of the reference viscosity μ 0 , and of the activation energy E induce major differences. The reference viscosity is equal to the viscosity close to the melting point, and its possible value yields around μ 0 = 5×10 13 Pa s. A possible value of E is 60 kJ/mol. For these values of the rheological parameters we find that the initial ocean may crystallize completely in ∼3.6 Gyr. Higher values of μ 0 and/or E reduce significantly the vigor and the efficiency of convection. The influence of the composition of the initial ocean is also investigated. The presence of ammonia reduces the convective strength and the heat flux. The upper structure of icy satellites is discussed as a function of the rheological and compositional parameters. The presence of a sub-surface ocean could be explained by either the presence of volatiles in the initial ocean or the presence of additional heat sources, such as tidal dissipation.

The relative density to shear velocity scaling in the uppermost mantle

We perform inversions of gravity data (geopotential model EGM96) and seismic tomography model (S16RLBM) for the scaling factor (ζ ), which relates relative density anomalies to relative S-wave velocity anomalies. The gravity data and tomographic model are anti-correlated below continents down to a depth of z = 200 km. This anti-correlation is not present below oceans. Except for smoothness, which is controlled by a damping factor, no a priori information is added to the inversion. Data are filtered between degrees � = 11 and � = 16 of the spherical harmonic expansion. This spectral window is well suited for the study of intermediate-size (2000–4000 km) anomalies in the uppermost mantle. Calculations are made separately for sub-continental and sub-oceanic mantle. The sub-continental and sub-oceanic scaling factors are significantly different at depths shallower than 260 km. In both cases, the magnitude of ζ is around 0.05. The sub-continental scaling factor has a positive root down to z = 220 km, whereas the sub-oceanic scaling factor yields positive values down to z = 140 km only. At depth shallower than 350 km, models of ζ do not depend on the damping factor or the viscosity model. At depths greater than 350 km, the resolution of ζ (z) decreases significantly and low degrees (� = 2–4) add information from large-scale anomalies and from the lower mantle. As a result, the shape and values of ζ for � = 2–16 and � = 11–16 are significantly different at depths greater than 350 km. A possible explanation of the discrepancies between the sub-continental and sub-oceanic scaling factor is that intermediate-scale anomalies are more important in the continental uppermost mantle than in the oceanic uppermost mantle.

THERMO-CHEMICAL STRUCTURE OF THE LOWER MANTLE: SEISMOLOGICAL EVIDENCE AND CONSEQUENCES FOR GEODYNAMICS

We combine recent progress in seismic tomography and numerical modeling of thermochemical convection to infer robust features on mantle structure and dynamics. First, we separate the observed density anomalies into their thermal and compositional contributions. The tomographic maps of thermo-chemical variations were computed using a new approach that combines a careful equation of state modeling of the lower mantle, independent constraints on density from probabilistic tomography, and a full statistical treatment for uncertainties analyses. We then test models of thermo-chemical convection against these density components. We compute synthetic anomalies of thermal and compositional density from models of thermo-chemical convection calculated with the anelastic approximation. These synthetic distributions are filtered to make meaningful comparisons with the observed density anomalies. Our comparisons suggest that a stable layer (i.e., that no domes or piles are generated from it) of dense material with buoyancy ratio B ≥ 0.3 is unlikely to be present at the bottom of the mantle. Models of piles entrained upwards from a dense, but unstable layer with buoyancy ratio B ∼ 0.2, explain the observation significantly better, but discrepancies remain at the top of the lower mantle. These discrepancies could be linked to the deflection of slabs around 1000 km, or to the phase transformation at 670 km, not included yet in the thermo-chemical calculations.

Anisotropic Rayleigh wave phase velocity maps of eastern China

We explore the variations of Rayleigh wave phase velocity beneath eastern China in a broad period range (20–200 s). Rayleigh wave dispersion curves are measured by the two-station technique for a total of 734 interstation paths using vertical component broadband waveforms at 39 seismic stations in eastern China from 466 global earthquakes. In addition, 599 waveform inversion interstation measurements were added to this data set. The interstation dispersion curves are then inverted for high-resolution isotropic and azimuthally anisotropic phase velocity maps at periods between 20 and 200 s. At shorter periods sampling the crustal depth range, phase velocities are higher in the southeastern part of the region, reflecting the thinner crust there. The Jiangnan Belt separates Cathaysia from the Yangtze Craton, the latter with thicker crust and a deep, high-velocity cratonic root. The eastern part of Yangtze Craton, however, east of 115–116°E, does not display a deep root and has a thin lithosphere. Azimuthal anisotropy at long periods (>120 s) shows fast propagation directions broadly similar to that of the absolute plate motion. Beneath Cathaysia and eastern Yangtze Craton, anisotropy in the asthenosphere is strong and suggests coast-perpendicular flow. Asthenospheric flow from beneath Chinas thick continental lithosphere toward the thinner lithosphere of the margin and the resulting decompression melting may be the fundamental causes of the intraplate basaltic volcanism along the eastern coast of China.

Stagnant lid convection in bottom‐heated thin 3‐D spherical shells: Influence of curvature and implications for dwarf planets and icy moons

Because the viscosity of ice is strongly temperature dependent, convection in the ice layers of icy moons and dwarf planets likely operates in the stagnant lid regime, in which a rigid lid forms at the top of the fluid and reduces the heat transfer. A detailed modeling of the thermal history and radial structure of icy moons and dwarf planets thus requires an accurate description of stagnant lid convection. We performed numerical experiments of stagnant lid convection in 3-D spherical geometries for various ice shell curvatures f (measured as the ratio between the inner and outer radii), effective Rayleigh number Ram, and viscosity contrast Δ�� . From our results, we derived scaling laws for the average temperature of the well-mixed interior, �� m, and the heat flux transported through the shell. The nondimensional temperature difference across the bottom thermal boundary layer is well described by (1 − �� m )= 1.23 �� f 1.5 ,

THE ROLE OF METHANOL IN THE CRYSTALLIZATION OF TITAN'S PRIMORDIAL OCEAN

A key parameter that controls the crystallization of primordial oceans in large icy moons is the presence of anti-freeze compounds, which may have maintained primordial oceans over the age of the solar system. Here we investigate the influence of methanol, a possible anti-freeze candidate, on the crystallization of Titans primordial ocean. Using a thermodynamic model of the solar nebula and assuming a plausible composition of its initial gas phase, we first calculate the condensation sequence of ices in Saturns feeding zone, and show that in Titans building blocks methanol can have a mass fraction of ~4 wt% relative to water, i.e., methanol can be up to four times more abundant than ammonia. We then combine available data on the phase diagram of the water-methanol system and scaling laws derived from thermal convection to estimate the influence of methanol on the dynamics of the outer ice I shell and on the heat transfer through this layer. For a fraction of methanol consistent with the building blocks composition we determined, the vigor of convection in the ice I shell is strongly reduced. The effect of 5 wt% methanol is equivalent to that of 3 wt% ammonia. Thus, if methanol is present in the primordial ocean of Titan, the crystallization may stop, and a sub-surface ocean may be maintained between the ice I and high-pressure ice layers. A preliminary estimate indicates that the presence of 4 wt% methanol and 1 wt% ammonia may result in an ocean of thickness at least 90 km.

Effects of low-viscosity post-perovskite on the stability and structure of primordial reservoirs in the lower mantle

We performed numerical experiments of thermochemical convection in 3-D spherical geometry to investigate the effects of a low viscosity of post-perovskite (pPv) on the stability and structure of primordial reservoirs of dense material in the lower mantle of the Earth. Our results show that weak pPv (1000 × viscosity reduction in regions containing pPv) strongly increases the core-mantle boundary (CMB) heat flux. The volume-averaged mantle temperature with weak pPv is slightly higher than that with regular pPv, except in the lowermost mantle. This is because weak pPv weakens the base of the cold downwellings, allowing cold slabs to spread more easily and broadly along the CMB. The stability and size of the dense reservoirs is not substantially altered by weak pPv. In the weak pPv case, slabs spreading along the CMB slightly decreases the stability of dense reservoirs, i.e., the amount of dense material entrained upward is slightly larger than in the regular pPv case (i.e., viscosity of pPv identical to that of perovskite). Furthermore, the topography and steepness of these reservoirs slightly increase. However, as in the regular pPv case, the dense reservoirs are maintained over periods of time comparable to the age of the Earth.

Rayleigh-wave dispersion reveals crust-mantle decoupling beneath eastern Tibet

The Tibetan Plateau results from the collision of the Indian and Eurasian Plates during the Cenozoic, which produced at least 2,000 km of convergence. Its tectonics is dominated by an eastward extrusion of crustal material that has been explained by models implying either a mechanical decoupling between the crust and the lithosphere, or lithospheric deformation. Discriminating between these end-member models requires constraints on crustal and lithospheric mantle deformations. Distribution of seismic anisotropy may be inferred from the mapping of azimuthal anisotropy of surface waves. Here, we use data from the CNSN to map Rayleigh-wave azimuthal anisotropy in the crust and lithospheric mantle beneath eastern Tibet. Beneath Tibet, the anisotropic patterns at periods sampling the crust support an eastward flow up to 100°E in longitude, and a southward bend between 100°E and 104°E. At longer periods, sampling the lithospheric mantle, the anisotropic structures are consistent with the absolute plate motion. By contrast, in the Sino-Korean and Yangtze cratons, the direction of fast propagation remains unchanged throughout the period range sampling the crust and lithospheric mantle. These observations suggest that the crust and lithospheric mantle are mechanically decoupled beneath eastern Tibet, and coupled beneath the Sino-Korean and Yangtze cratons.

High Rayleigh number thermal convection in volumetrically heated spherical shells

2ðÞ 3 ar 2 gHD 5 hkk , where f is the ratio between the inner and outer radii of the shell. Our experiments show that the scenario proposed by Parmentier and Sotin (2000) to describe convection in volumetrically heated 3D-Cartesian boxes fully applies in spherical geometry, regardless of the shell curvature. The dynamics of the thermal boundary layer are controlled by both newly generated instabilities and surviving cold plumes initiated by previous instabilities. The characteristic time for the growth of instabilities in the thermal boundary layer scales as RaVH 1/2 , regardless of the shell curvature. We derive parameterizations for the average temperature of the shell and for the temperature jump across the thermal boundary layer, and find that these quantities are again independent of the shell curvature and vary as RaVH 0.238 and RaVH 1/4 , respectively. These findings appear to be valid down to relatively low values of the Rayleigh-Roberts number, around 10 5 .