Yanick Ricard

A geodynamic model of mantle density heterogeneity

Using Cenozoic and Mesozoic plate motion reconstructions, we derive a model of present-day mantle density heterogeneity under the assumption that subducted slabs sink vertically into the mantle. The thermal buoyancy of these slabs is estimated from the observed thermal subsidence (cooling) of oceanic lithosphere. Slab velocities in the upper mantle are computed from the local convergence rate. We assume that slabs cross the upper/lower mantle interface and continue sinking into the lower mantle with a reduced velocity. For a velocity reduction factor between 2 and 5, our slab heterogeneity model is as correlated with current tomographic models as these models are correlated with each other. We have also computed a synthetic geoid from our density model. For a viscosity increase of about a factor of 40 from the upper to lower mantle, our model predicts the first 8 spherical harmonic degrees of the geoid with statistical confidence larger than 95% and explains 84% of the observed geoid assuming that the model C21 and S21 terms are absent due to a long relaxation time for Earths rotational bulge. Otherwise, 73% of the geoid variance is explained. The viscosity increase is consistent with our velocity reduction factor for slabs entering the lower mantle, since downwelling velocities are expected to scale roughly as the logarithm of viscosity (loge 40 = 3.7). These results show that the history of plate tectonics can explain the main features of the present-day structure of the mantle. The dynamic topography induced by this heterogeneity structure consists mainly of about 1-km amplitude lows concentrated along the active continental margins of the Pacific basin. Our model can also be used to predict the time variation of mantle heterogeneity and the gravity field. We find that the “age” of the geoid, defined as the time in the past before which the geoid becomes uncorrelated with the present geoid, is about 50 m.y. Our model for the history of the degree 2 geoid, which is equivalent to the history of the inertia tensor, should give us a tool to study the variations in Earths rotation pole indicated in paleomagiietic studies.

3SMAC: an a priori tomographic model of the upper mantle based on geophysical modeling

We present an a priori three-dimensional ‘tomographic’ model of the upper mantle. We construct this model (called 3SMAC — three-dimensional seismological model a priori constrained) in four steps: we compile information on the thickness of ‘chemical’ layers in the Earth (water, sediments, upper and lower crust, etc); we get a 3D temperature distribution from thermal plate models applied to the oceans and continents; we deduce the mineralogy in the mantle from pressure and temperature and we finally get a three-dimensional model of density, seismic velocities, and attenuation by introducing laboratory measurements of these quantities as a function of pressure and temperature. The model is thus consistent with various geophysical data, such as ocean bathymetry, and surface heat flux. We use this model to compute synthetic travel-times of body waves, and we compare them with observations. A similar exercise is performed for surface waves and normal modes in a companion paper (Ricard et al., 1996, J. Geophys. Res., in press). We find that our model predicts the bulk of the observed travel-time variations. Both the amplitude and general pattern are well recovered. The discrepancies suggest that tomography can provide useful regional information on the thermal state of the continents. In the oceans, the flattening of the sea-floor beond 70 Ma seems difficult to reconcile with the seismic observations. Overall, our 3SMAC model is both a realistic model, which can be used to test various tomographic methods, and a model of the minimum heterogeneities to be expected from geodynamical modeling. Therefore, it should be a useful a priori model to be used in tomographic inversions, in order to retrieve reliable images of heterogeneities in the transition zone, which should, in turn, greatly improve our understanding of geodynamical processes in the deep Earth. 3SMAC and accompanying software can be retrieved by anonymous ftp at geoscope.ipgp.jussieu.fr.

A two‐phase model for compaction and damage: 1. General Theory

A theoretical model for the dynamics of a simple two-phase mixture is presented. A classical averaging approach combined with symmetry arguments is used to derive the mass, momentum, and energy equations for the mixture. The theory accounts for surficial energy at the interface and employs a nonequilibrium equation to relate the rate of work done by surface tension to the rates of both pressure work and viscous deformational work. The resulting equations provide a basic model for compaction with and without surface tension. Moreover, use of the full nonequilibrium surface energy relation allows for isotropic damage, i.e., creation of surface energy through void generation and growth (e.g., microcracking), and thus a continuum description of weakening and shear localization. Applications to compaction, damage, and shear localization are investigated in two companion papers.

Differential Rotation Between Lithosphere and Mantle' A Consequence of Lateral Mantle Viscosity Variations

The description of plate motions in the so-called hotspot reference frame introduces a global rotation of the lithosphere with respect to the mantle. This rotation, called toroidal field of degree 1, is roughly westward. It reaches an amplitude of about 2 cm/yr and has been consistently found in the different generation of plate tectonic models. Various authors have tried to relate this observation to the deceleration of the Earths rotation, to polar wander, or to tidal drag. However, these different physical mechanisms cannot explain the requested amplitude. In this paper, we compare the values of this rotation vector using different relative plate motion models expressed in the hotspot reference frame. In a model Earth with lateral viscosity variations, a differential rotation is predicted. The observed net lithospheric rotation is consistent with the dynamics of a model Earth where the asthenospheric viscosity below the oceans is at least one order of magnitude lower than underneath the continents. This relative westward drift of the lithosphere may account for the significant structural differences between east or west dipping subduction zones.

Global warming of the mantle at the origin of flood basalts over supercontinents

Continents episodically cluster together into a supercontinent, eventually breaking up with intense magmatic activity supposedly caused by mantle plumes ([Morgan, 1983][1]; [Richards et al., 1989][2]; [Condie, 2004][3]). The breakup of Pangea, the last supercontinent, was accompanied by the emplacement of the largest known continental flood basalt, the Central Atlantic Magmatic Province, which caused massive extinctions at the Triassic-Jurassic boundary ([Marzoli et al., 1999][4]). However, there is little support for a plume origin for this catastrophic event ([McHone, 2000][5]). On the basis of convection modeling in an internally heated mantle, this paper shows that continental aggregation promotes large-scale melting without requiring the involvement of plumes. When only internal heat sources in the mantle are considered, the formation of a supercontinent causes the enlargement of flow wavelength and a subcontinental increase in temperature as large as 100 °C. This temperature increase may lead to large-scale melting without the involvement of plumes. Our results suggest the existence of two distinct types of continental flood basalts, caused by plume or by mantle global warming. [1]: #ref-21 [2]: #ref-26 [3]: #ref-5 [4]: #ref-17 [5]: #ref-19

Geochemical observations and one layer mantle convection

Rare gas systematics are at the heart of the discrepancy between geophysical and geochemical models. Since more and more robust evidence of whole mantle convection comes from seismic tomography and geoid modeling, the interpretation of high 3 He/ 4 He in some oceanic island basalts as being primitive has to be revisited. A time dependent model with five reservoirs (bulk mantle, continental crust, atmosphere, residual deep mantle and DQ) is studied for Rb/ Sr and U/Pb/He systems. The dynamics of this model correspond to whole mantle convection in which subducted oceanic crust, transformed into dense assemblages, partially segregates to form a DQ layer growing with time as in Christensen and Hofmann [J. Geophys. Res. 99 (1994) 19867^19884]. A complementary cold and depleted harzburgitic lithosphere remains above DQ. We assume that hotspots arise from the deep thermal boundary layer and tap, in variable proportions, material from both the residual deep mantle and DQ. The difference between HIMU and Hawaiian basalts is attributed to HIMU being mostly from strongly degassed oceanic crust, though enriched in incompatibles (DQ), while Hawaii is mostly from MORB source residuals that are variably degassed and depleted. We suggest that a significant part of the Earth’s radioactive elements (V1/3) is trapped in the DQ layer. fl 1999 Elsevier Science B.V. All rights reserved.

LONG-TERM FLUXES AND BUDGET OF FERRIC IRON : IMPLICATION FOR THE REDOX STATES OF THE EARTH'S MANTLE AND ATMOSPHERE

Net flux of ferric iron from the subducted oceanic crust to the mantle has been estimated to constrain the evolution of the redox state of the Earths mantle. The main mechanism responsible for the transfer of ferric iron towards the mantle is the production of magnetite during the hydrothermal alteration of the oceanic crust. Both modeling and compilation of chemical data lead to a flux of 21 × 103 kg s−1 of ferric iron transported by the subducted oceanic crust. The net flux of ferric iron towards the deep mantle is estimated to be 12 × 103 kg s−1 when corrected from the production rates of basic magmas at oceanic ridges, island arcs, and hot spots. We discuss several hypotheses. Ferric iron could react at depth with reduced species that buffer the redox state of the mantle to its present-day value. One possible mechanism could be the reaction of this ferric iron with the core that would have been reduced by only 500 m since 2 Ga. At the opposite, we may also consider that ferric iron accumulates in the deep mantle, being possibly accepted by the structure of spinel, garnet, and perovskite. The transfer of ferric iron from subducted slabs to the mantle contributes from 10 to 25% in the global budget of the ferric iron component of the mantle. The long-term loss of ferric iron from the Earths surface may be considered as a plausible mechanism to regulate the photosynthetic production of molecular oxygen.

Plate tectonics, damage and inheritance

The initiation of plate tectonics on Earth is a critical event in our planet’s history. The time lag between the first proto-subduction (about 4 billion years ago) and global tectonics (approximately 3 billion years ago) suggests that plates and plate boundaries became widespread over a period of 1 billion years. The reason for this time lag is unknown but fundamental to understanding the origin of plate tectonics. Here we suggest that when sufficient lithospheric damage (which promotes shear localization and long-lived weak zones) combines with transient mantle flow and migrating proto-subduction, it leads to the accumulation of weak plate boundaries and eventually to fully formed tectonic plates driven by subduction alone. We simulate this process using a grain evolution and damage mechanism with a composite rheology (which is compatible with field and laboratory observations of polycrystalline rocks), coupled to an idealized model of pressure-driven lithospheric flow in which a low-pressure zone is equivalent to the suction of convective downwellings. In the simplest case, for Earth-like conditions, a few successive rotations of the driving pressure field yield relic damaged weak zones that are inherited by the lithospheric flow to form a nearly perfect plate, with passive spreading and strike-slip margins that persist and localize further, even though flow is driven only by subduction. But for hotter surface conditions, such as those on Venus, accumulation and inheritance of damage is negligible; hence only subduction zones survive and plate tectonics does not spread, which corresponds to observations. After plates have developed, continued changes in driving forces, combined with inherited damage and weak zones, promote increased tectonic complexity, such as oblique subduction, strike-slip boundaries that are subparallel to plate motion, and spalling of minor plates.

Toroidal-poloidal partitioning of plate motions since 120 MA

Changes in plate motions and plate configurations during the Cenozoic and Mesozoic have been investigated extensively, but most geodynamical models have concentrated on present-day plate motions. We have investigated the recent evolution of plate tectonics by examining the history of toroidal-poloidal partitioning of plate motions. Taking into account estimated errors, our results suggest a significant increase in the ratio of toroidal to poloidal motions postdating the Hawaiian-Emperor (H-E) bend at 43 Ma, corresponding to an overall decrease in global plate motions. These changes may reflect greater mantle plume activity in the Mesozoic, but a causal mechanism is not obvious. In general, observed Cenozoic and Mesozoic plate motions do not appear to be random, which implies that they are correlated. We also find perhaps three significant changes in net rotation of the lithosphere with respect to hotspots since 120 Ma.

REGULAR VS. CHAOTIC MANTLE MIXING

Abstract Most quantitative models of mantle mixing have been based on simulations of tracer advection by 2-D flows. The present work shows that the mixing properties of 3-D time-independent flows cannot be understood or extrapolated from previous 2-D models. Steady convective flows appropriate to simulate a uniform fluid with large viscosity are restricted to poloidal components. They seem to have regular streamlines. However, the existence of plates on the Earths surface imposes the existence of a strong toroidal field. Flows where both poloidal and toroidal components are present can yield chaotic pathlines which are very efficient in mixing the mantle. Within areas of turbulent mixing where the stretching increases exponentially with time, regular islands of laminar stretching persist in which unmixed material can survive. Our findings indicate that the intrinsic three-dimensionality of convection coupled with plates as much as its time dependence must be included in numerical models to understand the mixing properties of the mantle. As the viscosity is significantly larger in the lower mantle than in the upper mantle, the toroidal component of the flow is confined to the upper mantle, where a more thorough mixing should take place.