Temperature and heat flux scalings for isoviscous thermal convection in spherical geometry

Parametrized convection, which has long been used to reconstruct the thermal history of planetary mantles, is based on scaling relationships between observables (including heat flux) and controlling parameters (the most important being the Rayleigh number, Ra). To explore the influence of spherical geometry on heat transfer, we have conducted two series of numerical experiments of thermal convection (one with bottom heating and the other with mixed heating) in an isoviscous spherical shell with various curvatures. Using these calculations and a generalized non-linear inversion, we then derive scaling laws for the average temperature and for the surface heat flux. In the case of bottom heating, we found that the non-dimensional average temperature is given by θm=f2/(1 +f2), where f is the ratio between the core and total radii. The non-dimensional surface heat flux is fitted well by Nutop= 0.36f0.32 Ra(0.273+0.05f)θ0.6m. This scaling indicates that the available heating power decreases with increasing curvature (decreasing f). There exist strong trade-offs between the inverted parameters, that is, different sets of parameters explain our calculations well within error bars. For mixed heating, the non-dimensional average temperature and surface heat flux are well explained by θH=θm+ (1.68 − 0.8f)[(1 +f+f2)/3]0.79 h0.79/Ra0.234, where h is the non-dimensional rate of internal heating, and Nutop= 0.59f0.05 Ra(0.300−0.003f)θ1.23H. Due to a competition between the radiogenic and convective powers, and for given values of h and Ra, there is a curvature for which the Urey ratio reaches a minimum. Applied to the Earth's mantle, the mixed heating scaling predicts a Urey ratio between 0.4 and 0.6, depending on the Rayleigh number. Additional parameters, including the thermal viscosity ratio, phase transitions, the presence of dense material in the deep mantle, and variability of the flow pattern in time, may enter an appropriate modelling of the Earth's mantle thermal histor

Convective heat transfer as a function of wavelength: Implications for the cooling of the Earth

International audienceAttempting to reconstruct the thermal history of the Earth from a geophysical point of view has for a long time been in disagreement with geochemical data. The geophysical approach uses parameterized models of mantle cooling. The rate of cooling of the Earth at the beginning of its history obtained in these models is generally too rapid to allow a sufficient present-day secular cooling rate. Geochemical estimates of radioactive element concentrations in the mantle then appear too low to explain the observed present mantle heat loss. Cooling models use scaling laws for the mean heat flux out of the mantle as a function of its Rayleigh number of the form Q ~ Ra^b . Recent studies have introduced very low values of the exponent b, which can help reduce the cooling rate of the mantle. The present study instead focuses on the coefficient C in the relation Q = C Ra^b and, in particular, on its variation with the wavelength of convection. The heat transfer strongly depends on the wavelength of convection. The length scale of convection in Earth's mantle is that of plate tectonics, implying convective cells of wide aspect ratio. Taking into account the long wavelength of convection in Earth's mantle can significantly reduce the efficiency of heat transfer. The likely variations of this wavelength with the Wilson cycle thus imply important variations of the heat flow out of the Earth on a intermediate timescale of 100 Ma, which renders parameterized models of thermal evolution inaccurate for quantitative predictions

The stability and structure of primordial reservoirs in the lower mantle: insights from models of thermochemical convection in three-dimensional spherical geometry

Large-scale chemical lateral heterogeneities are inferred in the Earth's lowermost mantle by seismological studies. We explore the model space of thermochemical convection that can maintain reservoirs of dense material for a long period of time, by using similar analysis in 3-D spherical geometry. In this study, we focus on the parameters thought to be important in controlling the stability and structure of primordial dense reservoirs in the lower mantle, including the chemical density contrast between the primordial dense material and the regular mantle material (buoyancy ratio), thermal and chemical viscosity contrasts, volume fraction of primordial dense material and the Clapeyron slope of the phase transition at 660 km depth. We find that most of the findings from the 3-D Cartesian study still apply to 3-D spherical cases after slight modifications. Varying buoyancy ratio leads to different flow patterns, from rapid upwelling to stable layering; and large thermal viscosity contrasts are required to generate long wavelength chemical structures in the lower mantle. Chemical viscosity contrasts in a reasonable range have a second-order role in modifying the stability of the dense anomalies. The volume fraction of the initial primordial dense material does not effect the results with large thermal viscosity contrasts, but has significant effects on calculations with intermediate and small thermal viscosity contrasts. The volume fraction of dense material at which the flow pattern changes from unstable to stable depends on buoyancy ratio and thermal viscosity contrast. An endothermic phase transition at 660 km depth acts as a ‘filter' allowing cold slabs to penetrate while blocking most of the dense material from penetrating to the upper mantl

Buoyant melting instabilities beneath extending lithosphere: 1. Numerical models

Buoyant decompression melting instabilities in regions of partially molten upper mantle have been proposed to be an important process that might account for some characteristics of intraplate volcanism on Earth and other terrestrial planets. The instability is driven by variations in the melting rate within a partially molten layer whenever a relative decrease in density accompanies decompression melting of ascending mantle. Here, the development of buoyant decompression melting instabilities in a plane layer of passively upwelling and partially melting mantle beneath diffusely extending lithosphere is studied using numerical convection models covering a wide range of physical parameters. We find that the occurrence and nature of these instabilities in such a scenario is strongly affected by the rate of extension and melt percolation, as well as depth distribution of solid density variations arising from melt depletion. In some cases, instabilities do not occur during extension, but only develop after extension has slowed or stopped completely. This behavior creates two pulses of magma generation due to passive upwelling accompanying extension followed by the subsequent instability and is favored by a faster rate of extension, higher mantle viscosity, higher rate of melt percolation, and smaller amount of solid residuum depletion‐derived buoyancy. Larger degrees of solid density changes accompanying melt depletion can enhance the instability of partially molten mantle during extension but decrease the cumulative volume of generated melt. This kind of behavior modifies the conventional expectation of spatially and temporally correlated volcanism and extension and may lend insight into the observed increase in localized volcanic activity following Miocene Basin and Range extension in the western United States

Buoyant melting instabilities beneath extending lithosphere: 2. Linear analysis

In a companion paper, numerical models reveal that buoyant melting instabilities can occur beneath extending lithosphere for a sufficiently small mantle viscosity, extension rate, and rate of melt percolation. However, in some cases, instabilities do not develop during extension but only occur after extension slows or stops. These results are suggestive of a critical behavior in the onset of these kinds of instabilities and motivate a linear analysis to study the onset of instability in a partially melting, passively upwelling plane layer of mantle beneath extending lithosphere. The model we employ includes the effects of buoyancy arising from thermal expansion, the presence of a retained fraction of partial melt, and depletion of the solid by melt extraction. We find a critical behavior in the onset of instability controlled by melt retention buoyancy that is characterized by a “Rayleigh” number M, such that M must exceed some critical value M_(crit) which depends on the efficiency of Stokes rise of a partially molten body relative to the rate of background percolation. Comparison of this theory to the numerical results in the companion paper yields a close quantitative agreement. We also find that solid depletion buoyancy can either stabilize or destabilize a partially melting layer, depending upon both the distribution of preexisting depletion and the magnitude of density changes with depth. This theory is compared with previous studies of buoyant melting instabilities beneath mid‐ocean ridges where similar behavior was reported, and it suggests that the stability of passively upwelling, partially melting mantle underlying both narrow and wide rift settings is controlled by similar processes

Melting-induced crustal production helps plate tectonics on Earth-like planets

AbstractWithin our Solar System, Earth is the only planet to be in a mobile-lid regime. It is generally accepted that the other terrestrial planets are currently in a stagnant-lid regime, with the possible exception of Venus that may be in an episodic-lid regime. In this study, we use numerical simulations to address the question of whether melting-induced crustal production changes the critical yield stress needed to obtain mobile-lid behaviour (plate tectonics). Our results show that melting-induced crustal production strongly influences plate tectonics on Earth-like planets by strongly enhancing the mobility of the lid, replacing a stagnant lid with an episodic lid, or greatly extending the time in which a smoothly evolving mobile lid is present in a planet. Finally, we show that our results are consistent with analytically predicted critical yield stress obtained with boundary layer theory, whether melting-induced crustal production is considered or not

The Tectonics and Volcanism of Venus: New Modes Facilitated by Realistic Crustal Rheology and Intrusive Magmatism

To explain Venus' young surface age and lack of plate tectonics, Venus' tectonic regime has often been proposed to be either an episodic-lid regime with global lithospheric overturns, or an equilibrium resurfacing regime with numerous volcanic and tectonic activities. Here, we use global 2-D thermochemical convection models with realistic parameters, including rheology (dislocation creep, diffusion creep, and plastic yielding), an experiment-based plagioclase (An$_{75}$) crustal rheology, and intrusive magmatism, to investigate the tectonics and mantle evolution of Venus. We find that surface tectonics is strongly affected by crustal rheology. With a ''weak'' plagioclase-rheology crust, models exhibit episodic overturns but with continuously high surface mobility and high distributed surface strain rates between overturns, leading to a new tectonic regime that we name ''deformable episodic lid''. On the other hand, olivine-crustal-rheology models exhibit either standard episodic-lid tectonics, i.e. with mobility that is high during overturns and near zero between overturns, or stagnant-lid tectonics, i.e. with near-zero mobility over the entire model time. Also, a combination of plagioclase crustal rheology and dislocation creep can weaken the lithosphere sufficiently to facilitate lithospheric overturns without applying plastic yielding. Internally, the composition-dependent density profile results in a ''basalt barrier'' at the mantle transition zone, which strongly affects Venus' mantle evolution. Only strong plumes can penetrate this basalt barrier and cause global lithospheric overturns. This basalt barrier also causes global internal episodic overturns that generate global volcanic resurfacing in stagnant-lid models, which suggests a new resurfacing mechanism (we name it ''stagnant episodic-volcanic-resurfacing'') that does not involve lithospheric overturns.Comment: Minor changes to previous version. Accepted by Icarus. Main text 54 pages, 17 figures, abstract abbreviate

A sequential data assimilation approach for the joint reconstruction of mantle convection and surface tectonics

International audienceWith the progress of mantle convection modelling over the last decade, it now becomes possible to solve for the dynamics of the interior flow and the surface tectonics to first order. We show here that tectonic data (like surface kinematics and seafloor age distribution) and mantle convection models with plate-like behaviour can in principle be combined to reconstruct mantle convection. We present a sequential data assimilation method, based on suboptimal schemes derived from the Kalman filter, where surface velocities and seafloor age maps are not used as boundary conditions for the flow, but as data to assimilate. Two stages (a forecast followed by an analysis) are repeated sequentially to take into account data observed at different times. Whenever observations are available, an analysis infers the most probable state of the mantle at this time, considering a prior guess (supplied by the forecast) and the new observations at hand, using the classical best linear unbiased estimate. Between two observation times, the evolution of the mantle is governed by the forward model of mantle convection. This method is applied to synthetic 2-D spherical annulus mantle cases to evaluate its efficiency. We compare the reference evolutions to the estimations obtained by data assimilation. Two parameters control the behaviour of the scheme: the time between two analyses, and the amplitude of noise in the synthetic observations. Our technique proves to be efficient in retrieving temperature field evolutions provided the time between two analyses is 10 Myr. If the amplitude of the a priori error on the observations is large (30 per cent), our method provides a better estimate of surface tectonics than the observations, taking advantage of the information within the physics of convection

Assessing the role of slab rheology in coupled plate-mantle convection models

International audienceAssessing the role of slab rheology in coupled plate-mantle convection models. Earth and Planetary Science Letters 430, 191-201. Abstract Reconstructing the 3D structure of the Earth's mantle has been a challenge for geodynamicists for about 40 years. Although numerical models and computational capabilities have substantially progressed, parameterizations used for modeling convection forced by plate motions are far from being Earth-like. Among the set of parameters, rheology is fundamental because it defines in a non-linear way the dynamics of slabs and plumes, and the organization of lithosphere deformation. In this study, we evaluate the role of the temperature dependence of viscosity (variations up to 6 orders of magnitude) and the importance of pseudo-plasticity on reconstructing slab evolution in 3D spherical models of convection driven by plate history models. Pseudo-plasticity, which produces plate-like behavior in convection models, allows a consistent coupling between imposed plate motions and global convection, which is not possible with temperature-dependent viscosity alone. Using test case models, we show that increasing temperature dependence of viscosity enhances vertical and lateral coherence of slabs, but leads to unrealistic slab morphologies for large viscosity contrasts. Introducing pseudo-plasticity partially solves this issue, producing thin laterally and vertically more continuous slabs, and flat subduction where trench retreat is fast. We evaluate the differences between convection reconstructions employing different viscosity laws to be very large, and similar to the differences between two models with the same rheology but using two different plate histories or initial conditions