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It has been proposed that a basal magma ocean (BMO) may have existed, or even still exists, at the base of the Martian mantle [1]. One formation scenario for such a BMO involves a mantle-scale overturn just after the crystallization of the main magma ocean. In this case, the BMO would be enriched in iron and heat-producing elements (HPE), and hence gravitationally stable at the base of the mantle, with potential effects on the efficiency of mantle convection. The Insight mission has allowed geophysical investigation of the Martian interior and has indeed provided seismic evidence of a basal liquid silicate layer just above the core-mantle boundary. It is thus crucial to understand the effect of such a layer on the long-term evolution of the interior of Mars.Here, we model thermochemical mantle convection and crust production for a Mars-sized planet in a 2D spherical annulus geometry using code StagYY. Assuming that the top of the BMO is at ~1800 km radius, we parameterize the basal magma ocean as a ‘primordial layer’ with a low viscosity and a high effective thermal conductivity to account for the enhanced effective heat flux in a liquid layer due to turbulent flow. HPE are preferentially partitioned into the silicate liquid layer following a mass balance equation assuming an interstitial porosity. We systematically vary BMO thickness and interstitial porosity in order to study the outcome of the different HPE distributions. The liquid density, which is attributed by the different degrees of iron enrichment, is also examined to explore the mechanical stability and entrainment of the BMO.We present results of our models, comparing our present-day temperature profiles with areotherms deduced from seismic observation [2,3]. We find that the interstitial porosity is an important factor that determines the thermal structure of the mantle throughout Martian evolution. A value of ~50% provides the best fit with crustal production history, crustal thickness, HPE enrichment in the crust, as well as the seismically-constrained present-day areotherm. This result suggests that the initial HPE partitioning has not been controlled by end-member fractional crystallization of the main magma ocean (for which interstitial porosity would be close to 0%), and/or that some re-equilibration occurred during subsequent overturn. Meanwhile, the BMO thickness, within the uncertainties from seismic inversion, does not strongly influence Mars thermal evolution. [1] Samuel et al. (2021) doi:10.1029/2020JE006613[2] Khan et al. (2021) doi: 10.1126/science.abf2966[3] Duran et al. (2022) doi: 10.1016/j.pepi.2022.10685

Terrestrial exoplanets, ranging in size up to approximately twice Earth-size (10 Earth masses), may have a range of characteristics that are not found in solar system planets, including but not limited to: larger size, different bulk composition (possibly resulting in being core-less), being tidally-locked to their host star, and being covered by water layers. Larger size has been proposed to result in sluggish deep-mantle convection and also (for stagnant-lid exoplanets) lower magmatism and outgassing, but internal differentiation is still expected to take place. Different bulk composition may lead to different viscosity (among other physical properties), modified melting behaviour and different core size (including the possibility of having no core). Tidally-locked exoplanets likely have hemispherical tectonics and internal structures, but the asymmetry would be reduced if they are continuously reorienting due to true polar wander. We are pursuing a range of studies investigating most of these different aspects using thermo-chemical convection models that include self-consistent lithospheric dynamics, partial melting and crustal production, using the code StagYY. Some of these studies are presented elsewhere at this meeting; this presentation will focus on additional interesting results.

The dawn of high-resolution observations with the James Webb Space Telescope will enable spatially resolved observations of ultrashort-period rocky exoplanets. Some of these planets orbit so closely to their star that they lack an atmosphere [1], which gives direct access to their surfaces and opens a window to infer their geodynamics [2]. The physical parameters of the ultrashort-period sub-Earth GJ 367b have been observationally constrained to a planetary radius of about 0.72 to 0.75 Earth-radii and a mass between 0.48 and 0.55 Earth-masses, implying a density of 6200 to 8500 kg/m3 [3, 4], which puts this planet in a Mercury-like interior regime with a thin mantle overlying a fractionally large core.The dayside temperature ranges between 1500 to 1800 K, thus suggesting the presence of a permanent magma ocean or dayside magma pond on the surface, induced by stellar irradiation. The large uncertainty on the age of the stellar system, between 30 Myr [4] and about 8 Gyr [3], however, introduce severe uncertainties related to the compositional and thermal evolution of the planetary mantle. In this study we perform global 2D spherical annulus StagYY simulations [5, 6] of solid state mantle convection and surface melting with the goal to constrain the geometric and compositional properties ofthe planet. Constraining the spatial dimensions of thermodynamic properties of partially molten, atmosphere-less planets like GJ 367b offers unique opportunities to constrain the compositional fractionation during magma ocean epochs and provides avenues to constrain the delivery and loss cycle of atmophile elements on strongly irradiated exoplanets.References:[1] L. Kreidberg and 18 co-authors. Absence of a thick atmosphere on the terrestrial exoplanet LHS 3844b. Nature, 573:87–90, August 2019.[2] T. G. Meier, D. J. Bower, T. Lichtenberg, P. J. Tackley, and B.-O. Demory. Hemispheric Tectonics on LHS 3844b. Astrophys. J. Lett., 908:L48, February 2021.[3] K.W.F. Lam and 78 co-authors. GJ 367b: A dense, ultrashort-period sub-earth planet transiting a nearby red dwarf star. Science, 374:1271–1275, 2021.[4] W. Brandner, P. Calissendorff, N. Frankel, and F. Cantalloube. High-contrast, high-angular resolution view of the GJ367 exoplanet system. Mon. Notices Royal Astron. Soc., 513:661–669, June 2022.[5] J. W. Hernlund and P. J. Tackley. Modeling mantle convection in the spherical annulus. Phys. Earth Planet. Int., 171:48–54, 2008.[6] P. J. Tackley. Modelling compressible mantle convection with large viscosity contrasts in a three-dimensional spherical shell using the yin-yang grid. Phys. Earth Planet. Int., 171:7–18, 2008.

Observations of Venus reveal tectonic expressions and recent volcanism, showing that the planet is still active. Tectonically deformed areas such as ridges or tesserae indicate surface mobility, however, no signs of active plate tectonics like on Earth have been found. The tectonics and volcanism of Venus and other terrestrial planets are defined by the active mantle convection mode. A key component of tectonics is rheology, which is affected by water as shown by numerous studies[1]. However, the effects of water have been mostly ignored when studying Venus because its interior has been assumed to be dry. This notion is being challenged by indications of strong hydrodynamic escape to space that requires volcanic replenishment[2]. Therefore, water should be present in Venus’ interior, even if its content is not known. Importantly, the potential effects of water in the dynamics and evolution of Venus are poorly understood. This calls for the consideration of complex dynamic thermo-magmatic models that track water and take into account intrusive and extrusive magmatism.In this study, we use the code StagYY to perform state-of-the-art 2D numerical models in a spherical annulus geometry to assess the effects of water on the tectono-magmatic evolution of Venus[3]. Particular attention will be given to changes in mantle viscosity, melt generation and crustal properties such as thickness and surface age. We explore model settings related to melting, intrusive magmatism, and water presence. Results show that intrusion depth influences the thermal evolution and related magmatism. Moreover, preliminary results show that the rate of water outgassing is directly related to changes in the thermo-magmatic evolution of Venus. Water outgassing rates have further implications on surface conditions and atmospheric compositions over time. In the future, coupling these improved mantle convection models to atmospheric evolution models may unveil new insights into the thermal and tectonic history that has shaped Venus into the planet we observe today.

The study of coupled Earth systems, and in particular the coupled interactions between the lithosphere, atmosphere, and biosphere, have received greater attention in recent years (Gerya et al. 2020). Interactions between these systems occur primarily at the surface, and are driven on the large scale by topographic and bathymetric evolution controlled by deep mantle processes. However, due to the large difference in length scales between the mantle and the surface, it is difficult to capture topographic evolution to a high degree of accuracy in existing global mantle convection models including a free surface boundary condition.Global mantle convection models incorporating a free surface often employ a marker-in-cell technique with a layer of “sticky air” (i.e. material with the density of the air and sufficiently low viscosity, which is still much higher than that of real air) to characterise the surface. However, accurate topographic evolution using this method requires a high density of markers near the surface. This need for additional computational resources motivates alternative methods of tracking the interface between the air and rock layers, as is done frequently in existing multiphase fluid flow codes. A volume of fluid method with piecewise-linear interface reconstruction provides a suitable method for tracking a surface in a performant way with the sub-grid level topographic resolution that is necessary for coupling global scale geodynamic models to models of other Earth systems.We demonstrate benchmarks of an implementation of a volume of fluid method within the existing advanced mantle convection code StagYY (Tackley, 2008). Our method is applicable to both 2D and 3D geometries, and on both Cartesian and non-Cartesian grids. Models of global scale topography and evolution produced using StagYY may later be used as a tool for further studies on the coupling of mantle dynamics with modelling of the landscape, and the evolution of the atmosphere and biosphere.

Grain-size evolution is a crucial controlling factor for the lower mantle rheology. Notably, one order of grain size change can produce a viscosity change of the order of 100-1000 times. As diffusion creep dominates in the lower mantle, grain growth of lower mantle mineral assemblages, e.g., bridgmanite and ferropericlase, increase viscosity considerably. It has been quite challenging to constrain the grain-size evolution parameters for lower mantle mineral assemblages until recently; a new high-pressure experimental study (27 GPa, cf. Fei et al, 2021, EPSL) parameterised them. The experimental data found a slower grain growth of bridgmanite-ferropericlase phases than of the upper mantle mineral phases, e.g., olivine and spinel. Using the most updated knowledge of grain-size evolution, we develop 2-D spherical annulus numerical models of self-consistent mantle convection using the finite volume code StagYY and explore how grain-size evolution affects the lower mantle dynamics. We test our models with different heterogeneous grain size evolution and composite rheology that evolve self-consistently for 4.5 billion years. Our preliminary models show the self-consistent formation of thermochemical piles at the base of the core-mantle boundary where the grain size is maximum (~3 times than the surroundings). Even though the bridgmanite-ferropericlase grain growth is slower, a slight increase in the grain size of thermochemical piles can make them ~100-1000 times viscous, subsequently helping them to achieve morphological stability over billion years. In some of our models, we find sweeping stability of the piles for ~500 million years.

Following the long-standing paradigm in HPC, computational geodynamic codes have been typically written in high-level statically typed and compiled languages, namely C/C++ and Fortran. The low productivity rates of these languages led to the so-called two-language problem, where dynamic languages such as Python or MATLAB are used for prototyping purposes, before porting the algorithms to high-performance languages. The Julia programming language aims at bridging the productivity and advantages of such dynamic languages without sacrificing the performance provided by static languages. The high performance of Julia, combined with high-productivity rates and other powerful tools, such as advanced meta-programming (i.e. code generation), make Julia a suitable candidate for the next generation of HPC-ready scientific software.We introduce the open-source and Julia-written package JustRelax.jl (https://github.com/PTsolvers/JustRelax.jl) as a way forward for the next generation of geodynamic codes. JustRelax.jl is a production-ready API for a collection of highly-efficient numerical solvers (Stokes equations, diffusion, etc.) based on the embarrassingly parallel pseudo-transient method. We rely on ParallelStencil.jl (https://github.com/omlins/ParallelStencil.jl), which leverages the advanced meta-programming capabilities of Julia to generate efficient computational kernels agnostic to the back-end system (i.e. Central Processing Unit (CPU) or Graphics Processing Unit (GPU)). Using ImplicitGlobalGrid.jl (https://github.com/eth-cscs/ImplicitGlobalGrid.jl) to handle the MPI and CUDA-aware MPI communication, these computational kernels run seamlessly in local shared-memory workstations and distributed memory and multi-GPU HPC systems with little effort for the front-end user.Efficient computation of the (local) physical properties of different materials is another key feature required in geodynamic codes, for which we employ GeoParams.jl (https://github.com/JuliaGeodynamics/GeoParams.jl). This package provides lightweight, optimised, and reproducible computation of different material properties (e.g. advanced rheological laws, density, seismic velocity, etc.), amongst other available features. GeoParams.jl is also carefully designed to support CPU and GPU devices, and be fully compatible with other external packages, such as ParallelStencil.jl and existing auto-differentiation packages.We finally show high-resolution examples of geodynamic models run on multi-GPU HPC systems employing the presented open-source Julia tools.

The short-lived isotope systems, including 146Sm-142Nd (half-life = 103 Ma) and 182Hf-182W (half-life = 8.9 Ma), provide evidence for mantle differentiation events in early Earth, as both the daughter nuclides are more incompatible than the parent nuclides. For the 146Sm-142Nd system, both positive and negative μ142Nd measurements are observed in Hadean-Archean mantle-derived rocks, which possibly indicates a major differentiation event of the silicate Earth before the extinction of 146Sm (e.g., Boyet and Carlson, 2005, Science). The diminishing trend of μ142Nd between Hadean and Archean, on the other hand, suggests continuous mantle mixing during this period. However, for the 182Hf-182W system, Hadean-Archean mantle-derived rocks often show positive μ182W anomalies followed by a decline in at 2.5~3.0 Ga ago without a mixing trend (e.g., Carlson et al., 2019, Chem. Geol.). Also, μ142Nd and μ182W often show no or negative correlation in Hadean-Archean mantle derived rocks (e.g., Rizo et al. 2016, Geochim. Cosmochim. Acta), which requires a mechanism to decouple these two isotopic systems.In this study, we implement both 182Hf-182W and 146Sm-142Nd system in a global thermochemical geodynamic model, StagYY (Tackley, 2008, PEPI), to track the evolution of these isotope systems through Earth’s mantle evolution. Based on the particle-in-cell method, the geodynamic model incorporates melting and magmatic crust production that allow us to track both fractionation (by melting and crustal production) and mixing (through mantle convection) of trace elements through time. We discuss in detail how (1) the ‘basalt barrier’ at the base of the mantle transition zone (Davies, 2008 EPSL), (2) crustal delamination from intrusive magmatism, or plutonic-squishy-lid tectonics (Lourenco et al., Nat. Geo. 2018; GCubed 2020), and (3) late accretion could affect the tectonics of early Earth, and the preservation of geochemical heterogeneities and decoupling of two isotopic systems in the mantle through time.

IntroductionThe catalog of known exoplanets has increased vastly since the first detection in 1995. In the era of JWST, this catalog is expected to grow even further, and especially the fraction of terrestrial exoplanets will grow due to the enhanced capabilities of next-generation instruments compared to its predecessors. Due to limited observation time with instruments such as JWST, target selection is an important process, especially for the difficult-to-observe terrestrial planets. This process can be improved by using readily available data, stellar abundances, by considering that a planet and its host star originate from material with the same composition. The composition of a terrestrial planet modulates many properties, including core size, mantle rheology, and mantle melting behaviour. This will determine whether the planet has a mobile surface, with plate tectonics-like behaviour, or an immobile surface, with e.g. stagnant-lid-like behaviour. Further, interaction between the interior and the atmosphere depends on interior properties, and interior composition may therefore leave its mark on the planet’s atmosphere. Finally, these compositional effects may have an influence on whether the surface is capable of forming and sustaining life-forms [1]. However, the full effect of compositional influence on terrestrial planet evolution has only recently reached a level of maturity that it can now be applied to planets orbiting other stars.Bulk compositions of terrestrial exoplanets can to some extent be estimated by considering them as devolatized stars. By applying devolatilization factors [2], we have determined the range of bulk terrestrial exoplanet compositions in the Solar neighbourhood (Spaargaren et al., in preparation) based on stellar abundances from the Hypatia catalog [3]. In this work, we identified 20 end-member bulk planet compositions that span the full range of compositional diversity. Here, we study these end-members in more detail, to investigate how compositional effects alter the evolutionary pathway of terrestrial planets. CompositionsWe study 20 planets of one Earth mass, with the previously established end-member bulk compositions, in more detail. Bulk composition is given in terms of the most common elements in rocky planets: Fe, Mg, Si, O, Ca, Al, Na, Ni, and S, where the latter two exclusively appear in the metallic iron core. The structure (i.e., relative sizes of the metallic iron core and silicate mantle) is determined by considering bulk iron, nickel, and sulphur abundances, assuming constant bulk planet oxygen fugacity. Core composition is subtracted from the bulk to determine mantle composition. To calculate mantle physical properties from bulk mantle composition, we employ the Gibbs energy minimization algorithm Perple_X [4]. This algorithm calculates mineralogy, based on a new thermodynamic database by Stixrude and Lithgow-Bertelloni (2022; [5]) and related physical properties for each of the 20 cases. Interior ModellingWe explore the effects of bulk planet composition on long-term interior evolution using a geodynamical model, StagYY [6]. We run this model for five billion years, to analyze the thermal evolution of our planetary test-cases. Adjustments are made to the melting calculation scheme based on the basalt fraction and iron abundance in the mantle, where the latter can change solidus temperature by up to 36 K per wt% FeO. Further, we explore the effects of yield stress for each of our compositional end-members, to determine the propensity of each planet towards plate tectonics-like behaviour, stagnant lid-like behaviour, or behaviour that falls under a different dynamic regime. In general, Earth tends to have an average composition for most elements, except for iron, which it is relatively rich in, and therefore it has an above average core size. Our preliminary results show that core size (and thus iron abundance) affects convective vigor, and thus thermal evolution of the interior. Interesting to note is that on average, due to galactic chemical evolution, the iron abundance and thus exoplanet core sizes tends to increase (e.g., [7]). Therefore, Earth will tend more towards being average in younger populations. We further find major differences for planets with different ratios of Mg-silicates, as these minerals control mantle viscosity, and thereby thermal evolution. Planets with lower Mg/Si than Earth will have a significantly stronger mantle, impeding cooling on planetary lifetimes, while planets with much higher Mg/Si have weaker upper mantles, impacting surface mobility. Stellar Mg/Si is a good indicator of the relative abundances of these minerals, and can be an important source of information. Therefore, the host stellar abundances seem to be an indicator of rocky planet properties, and can be used in the target selection for future missions. [1] Mojzsis, S.J. (2021). Geoastronomy: Rocky planets as the Lavosier-Lomonosov Bridge from the non-living to the living world. in Royal Society of Chemistry, Prebiotic Chemistry and the Origin of Life. arXiv:2112.04309 [2] Wang, H.S., Lineweaver, C.H., Ireland, T.R. (2019). The volatility trend of protosolar and terrestrial elemental abundances. Icarus, 328, 287-305. [3] Hinkel, N., Timmes, F., Young, P., et al. (2014). Stellar abundances in the Solar neighbourhood: the Hypatia Catalog. The Astronomical Journal, 148(3), 33 pp. [4] Connolly, J.A. (2005). Computation of phase equilibria by linear programming: a tool for geodynamic modeling and its application to subduction zone decarbonation. Earth and Planetary Science Letters, 236(1-2), 524-541. [5] Stixrude, L., Lithgow-Bertelloni, C. (2022). Thermal expansivity, heat capacity and bulk modulus of the mantle. Geophysical Journal International, 228(2), 1119-1149. [6] Tackley, P.J. (2008). Modelling compressible mantle convection with large viscosity contrasts in a three-dimensional spherical shell using the yin-yang grid. Physics of the Earth and Planetary Interiors, 171(1-4), 7-18. [7] Matteuci, F., Greggio, L. (1986). Relative roles of type I and II supernovae in the chemical enrichment of the interstellar gas. Astronomy & Astrophysics, 154, 279-287.

A tectonic regime is the surface expression of interior dynamics in a planet. With the help of numerical models, different tectonic regimes have been proposed. Some of these are: (1) plate tectonics or mobile lid, (2) stagnant lid, (3) episodic lid, (4) plutonic-squishy lid, (5) and heat pipe (e.g., Lourenço et al., G3 2020). Over time, a tectonic regime shapes the surface of a planet, including its surface topography. Using the numerical models, we can compute the topographies associated with different tectonic regimes including spatial and temporal measures of variations. In this study, we compute statistics for the topography formed by different tectonic regimes in numerical models and compare with the statistics of observed topography of different terrestrial planets, with the aim of linking a planet to a tectonic regime at the present-day. Venus’ topography is better matched by topography distributions obtained for plutonic-squishy lid models than those for stagnant- or episodic-lid models, while Earth’s oceanic topography is best matched by mobile-lid models.

Mars features a crustal dichotomy, with its southern hemisphere covered by a thicker basaltic crust than its northern hemisphere[1,2]. Additionally, the planet displays geologically recent volcanism only in its low latitude regions[3-5]. Previous giant impact models coupled with simulations of mantle convection have shown that the crustal dichotomy can be explained by post-impact melt crystallization that emplaced a thick crust in the southern hemisphere[6-8]. In this study, we show that the depleted residue left behind by the original post-impact crustal formation can spread laterally, potentially persisting beneath the northern hemisphere to the present day. Such a large-scale mantle province would concurrently explain both the prevalence of long-term magmatism on Mars and its strong preference for localised equatorial regions.

Poster for AGU 2022

The Martian dichotomy features a 5.5 km contrasts in topography and a potential ~ 25 km difference in crustal thickness [1], depending on the crustal density assumption [2], between the older southern highlands and the younger northern lowlands. It is thought to be the most ancient feature observed on Mars and have formed within the first 400-500 Myr of Martian history [3]. While the formation mechanism of the dichotomy is still under debate, our previous models [4] have successfully demonstrated that a southern giant impact does not only form a thicker crust on the impacted site, but also have a significant consequence in the location of magmatism in the next billions of years. In addition to the shock wave-generated impact melt, the temperature within the mantle after a giant impact is shown to be well above the silicate solidus. Therefore, deep mantle melting is expected to generate a local magma ocean. Shortly following the crystallization of the local magma ocean, depleted residues spread within the upper mantle from the southern impacted site northwards. This layering, deficient in heat producing elements, assists the faster formation of a thicker and more stable lithosphere in the North. This in turns maintains a lower crust production rate in the north. Rather, due to the north-south different in thermal and composition gradient, melt production and therefore magmatism are focused at low latitude regions of the planet and last until geologically recent times, which is consistent with observations. While our previous study can demonstrate the important interactions among impact-induced local magma ocean, crust formation and mantle flow, the impact scenario we used is rather simplified, as the associated thermal anomaly is parametrised and extrapolated from smaller head-on impact experiments. In order to account for a more realistic impact scenario, we use smoothed particle hydrodynamics (SPH) simulations [5] to model the first 24 hours of a giant impact between proto-Mars and its impactor. The SPH result is then transferred to the mantle convection code StagYY [6], as an initial thermal condition, to simulate the long-term evolution of the crust and mantle for the subsequent 4.5 billion years. We systematically vary the impactor size, angle, velocity and pre-impact Martian mantle temperature. Our result shows that a 45-degree impact does not form a Martian dichotomy-like crustal structure, and a 15-degree impact is a better match. While a 500 km-radius impactor may not generate crust extensive enough, a 750 km-radius impactor can form a thickened crust that covers the whole southern hemisphere. Resultant mantle flow from a larger impactor size is a key to suppressing multiple mantle plumes as well. Fig 1. Temperature field (result from SPH model) at the start of simulation t=0 Myr Fig 2. Compositional field at t=~500 Myr [1] Watters, T., McGovern, P., & Irwin III, R. (2007). Hemispheres Apart: The Crustal Dichotomy on Mars. Annual Review Of Earth And Planetary Sciences, 35(1), 621-652. [2] Wieczorek, M., Broquet, A., McLennan, S., Rivoldini, A., Golombek, M., & Antonangeli, D. et al. (2022). InSight constraints on the global character of the Martian crust. Journal Of Geophysical Research: Planets. doi: 10.1029/2022je007298 [3] Taylor, S., & McLennan, S. (2009). Planetary crusts. Cambridge, UK: Cambridge University Press. [4] Cheng, K.W., Tackley, P.J., Rozel, A.B., Golabek, G.J. (2021). Martian Dichotomy: Impact-induced Crustal Production in Mantle Convection Models, Abstract [DI35B-0023] presented at 2021 Fall Meeting, AGU, New Orleans, LA, 13-17 Dec. [5] Emsenhuber, A., Jutzi, M., Benz, W. (2018). SPH calculations of Mars-scale collisions: The role of the equation of state, material rheologies, and numerical effects. Icarus, 301, 247-257 [6] Tackley, P. (2008). Modelling compressible mantle convection with large viscosity contrasts in a three-dimensional spherical shell using the yin-yang grid. Physics Of The Earth And Planetary Interiors, 171(1-4), 7-18.

The evolution of surface conditions on Venus has recently made a return to the forefront of planetary sciences questions. Due to both the striking similarities and the obvious differences between Earth and Venus, understanding Venus might hold some of the keys to how terrestrial planets become habitable, either in our solar system or beyond. The question of the origin and persistence of water at the surface/in the atmosphere of Venus determines, in a large part what the planet's evolutionary path has been. The critical difference between Earth and Venus might even be settled during their primordial evolution. Since no sample of Venus can be studied yet, as would be the case for Earth, we turn on alternative methods of investigation. We track the evolution of volatiles at the surface of the planet during its history, since the end of the magma ocean phase. We compare these scenarios with present-day observation and derive limits on maximum amounts of volatiles in the atmosphere of Venus through time, on volatile exchanges, and on water delivery. We have developed coupled numerical simulations of the evolution of Venus, modeling mechanisms that govern its surface conditions and atmosphere composition. Currently, the simulations include modeling of mantle dynamics, core evolution, volcanism, surface alteration, atmospheric escape (both hydrodynamic and non-thermal), greenhouse effect, and the feedback mechanisms between the interior and the atmosphere of the planet. Focusing on Late Accretion, we have modeled the effects of large meteoritic impacts on long term evolution through three aspects: atmosphere erosion, volatile delivery and mantle dynamics perturbation due to energy transfer. The models are constrained by present-day observation and atmosphere composition, with the requirement that scenarios fit reasonnably the current state of the planet. We produce scenarios that fit present-day conditions and feature both early mobile lid regime (akin to plate tectonics) as well as late episodic lid regime with resurfacing events. However, water outgassing during late evolution could be dampened by high surface pressures. Therefore, it is during the early history of Venus, in particular, that we observe the largest volatile exchanges. That era seems to have large repercussions on long term evolution and present-day state, as it determines volatile inventories and repartition. The effects of impacts dominate the volatile and mantle evolution during Late Accretion. Large impacts are shown to have essential consequences for volatile repartition. The atmosphere erosion they cause is marginal and doesn’t deplete the atmosphere as much as swarms of smaller bodies, they instead act as a significant source of volatiles. Indeed, if Late Accretion is mainly composed of volatile-rich bodies; it is very difficult to reach the observed present-day state of Venus; instead the atmosphere may become too wet. Likewise, the likely mass received by Venus during volatile-rich Late Accretion, if completely outgassed into the planet's atmosphere, could lead to masses of CO2 and N2 3-6 times higher than observed at present-day. Simulations show that the maximum contribution of wet material impactors (carbon-chondrites-like) is about 5-10% (mass.) of the total accreted mass during Late Accretion (the larger portion of the Late accretion being composed of enstatite-chondrite-like bodies). In less volatile rich scenarios, water brought by collisions is then lost, either quickly or over billions of years. A small amount of water is then slowly reinserted in the atmosphere by volcanic outgassing. In wet scenarios, water is efficiently brought to the surface of Venus and loss mechanisms are not able to remove it later, through solid surface oxidation and atmospheric escape. This then leads to water-rich atmosphere, unlike what we observe today. Those results are consistent over a large range of simulations with variations of late accretion timing, impactors mass-size distribution, composition, efficiency, mantle parameters and so on. Water should have been delivered early to the terrestrial planets in the solar system, during main accretion, before the last giant impact, as is suggested for Earth from isotopic measurements. Acknowledgments: CG acknowledges support from the FNRS ET-HOME project and Brussels Free University. CG further acknowledges support from the CLEVER Planets group, supported by NASA.

From the observations on ~1000 recognizable impact craters on Venus’ surface, the average surface age for Venus is comparable to the average surface age for Earth, and is significantly younger than the surface ages of other solar terrestrial planets. To explain Venus’ young surface without plate tectonics, the global tectonics of Venus have often been proposed to be in an episodic-lid regime with catastrophic global overturns. Previous episodic-lid geodynamic models often assume an olivine-diffusion-creep rheology for Venus’ crust, resulting in global overturns followed by stagnant-lid phases with near-zero surface mobilities. However, some tectonic units on Venus’ surfaces show substantial tectonic deformation, such as tesserae and coronae. Recent analyses of satellite images on Venus' surface also suggest possible widespread lithospheric mobilities in the lowland basins. And these observations can hardly be explained by the stagnant-lid phases between overturns in the episodic-lid models.In this study, we test the influence of (1) a composite, experiment-based crustal rheology (including diffusion creep, dislocation creep, and plasticity), and (2) intrusive magmatism, on Venus’ surface tectonics, using the mantle convection code StagYY in a 2D spherical annulus geometry. Our results show that applying the experiment-based rheology and intrusive magmatism in the model results in (1) both global and regional overturns, (2) high and continuous surface mobilities that indicate substantial surface deformation between global overturns, and (3) a young and thinner crust that is consistent with current estimations. As for volcanic activities, contrary to olivine-diffusion-creep models, there is no persistent mantle plume in our models when the realistic crustal rheology is applied. The basalt cumulated between the upper and lower mantle affects convective flows in the mantle and mantle upwellings from the core-mantle boundary. Also, there are short-term, randomly located volcanisms within crust between global overturns, which are consistent with recent observations of active magmatism on Venus’ surface and the short-term plumes suggested by coronae formation models. The surface tectonics in our models are dependent on the heat transfer efficiency in the upper mantle. And the tectonic regime is different from both episodic-lid regime and plutonic-squishy-lid regime that are proposed in previous literature, and can provide insights on the tectonic style for Venus and early Earth.

The long-term evolution of the mantle is simulated using 2D spherical annulus geometry to examine the effect of heterogeneous conductivity on the stability of primordial thermo-chemical reservoirs. Conductivity of the mantle is often emulated in numerical models using purely depth-dependent profiles (e.g., taking on values between 3 and 9 W/m-K). This approach is meant to synthesize the mean conductivities of mantle materials at their respective conditions in-situ. However, because conductivity depends also on temperature and composition, their role in the conductivity of the mantle is masked. This issue is significant because dynamically evolving temperature and composition introduce lateral variations in conductivity, especially in the deep-mantle. Minimum and maximum variations in conductivity are due to the temperatures of plumes and slabs, respectively, and depth-dependence directly controls the amplitude of the conductivity (and its variations) across the mantle depth. Our simulations allow assessing the consequences of these variations on mantle dynamics, in combination with the reduction of thermo-chemical pile conductivity with iron composition, which has so far not been well examined. First, we examine the effect of depth (D)-dependence employing a linear profile and vary the bottom-to-top conductivity ratio. We find that increased conductivity ratio acts to reduce pile temperature. Greater conductivity in the lower mantle helps to efficiently extract heat from piles (at rates sufficient to overcome or suppress temperature increases due to enrichment in HPEs). This reduction in thermal buoyancy stabilizes the piles and may play a major role in organizing thermo-chemical reservoirs into two distinct piles. Next, the combined effects of temperature (T) and composition (C) are examined. A positive feedback occurs when the reduced conductivity of piles inhibits its cooling and the resulting increase in temperature further reduces its conductivity. Consequently, the augmented thermal buoyancy destabilizes piles (i.e., greater topography or enhanced erosion). Furthermore, the combined T and C-dependences can greatly underestimate typical mantle conductivities if D-dependence is also underestimated. By increasing the amplitude of D-dependence, the destabilizing effects of T and C-dependence can be suppressed. Finally, mineral physics data is employed to emulate a more realistic depth-dependent profile for the upper and lower mantle. Depth-dependence is no longer a linear profile and values range from 3 to 27.5 W/m-K. Buoyancy ratio and the enrichment in heat-producing elements in piles are examined for this conductivity model to determine potential evolution scenarios of primordial thermo-chemical piles. We find that this model produces stable piles for periods exceeding the age of the Earth. When B is reduced from 0.23 to 0.15, piles are destabilized earlier (by approx 1 Gyr) for cases with lesser depth-dependence. HPE enrichment in piles increases their temperature over time (and further reduces their conductivity). For HPE enrichment 10 times the mantle heat production, two distinct piles are formed with moderate topography. For greater enrichment, the piles become unstable and material becomes entrained by thin plume conduits.

Motions within the Earth mantle and tectonics constitute a single self-organized system which is cooling the planet over its geological history. Since the end of the XXth century, models of mantle convection self-generating plate tectonic behavior have progressed to a state that makes them applicable to global tectonic problems. The possibility of combining geological and geophysical data with dynamic models to retrieve the recent history of mantle flow and tectonics becomes realistic. Therefore, it is a challenge to build inverse methods to study inverse and sensitivity problems in the Earth's mantle convection. We have automatically generated the tangent-linear and the adjoint source code from the StaggYY code (Tackley, Phys. Earth Planet. Int. 171, 7-18, 2008). The Fortran code of the model was translated to the corresponding derivative codes using TAF (Transformation of Algorithms in Fortran), source-to-source translator. All codes run in parallel mode, using MPI (Message Passing Interface). The economic taping strategy of TAF, including re-computations, and checkpointing, helps to keep the memory footprint of the adjoint code low and the performance high. We highlight some key features of the automatic differentiation, evaluate the performance of the adjoint code, and show first results from 2D and 3D sensitivity fields, focusing on the relationships between temperature in the mantle and tectonics. Ultimately the addjoint code shall be applied to inversion and assimilation problems using a bayesian framework.

The timing of the onset of plate tectonics on Earth remains a topic of strong debate, as does the tectonic mode that preceded modern plate tectonics. Understanding possible tectonic modes and transitions between them is also important for other terrestrial planets such as Venus and rocky exoplanets. Recent two-dimensional modelling studies have demonstrated that impacts can initiate subduction during the early stages of terrestrial planet evolution - the Hadean and Eoarchean in Earth’s case (O’Neill et al. 2017). Here, we perform three-dimensional simulations of the influence of ongoing multiple impacts on early Earth tectonics and its effect on the distribution of compositional heterogeneity in the mantle, including the distribution of impactor material. We compare two-dimensional and three-dimensional simulations to determine when geometry is important. Results show that impacts can induce subduction in both 2-D and 3-D and thus have a great influence on the tectonic regime. The effect is particularly strong in cases that otherwise display stagnant-lid tectonics: impacts can shift them to having a plate-like regime. In such cases, however, plate-like behaviour is temporary: as the impactor flux decreases the system returns to what it was without impacts. Impacts result in both greater production of oceanic crust and greater recycling of it, increasing the build-up of subducted crust above the core-mantle boundary and in the transition zone. Impactor material is mainly located in the upper mantle, at least at the end of the modelled 500 million year period. This is modified when impactors are differentiated into metal and silicate: the dense metal blobs sink to the CMB. In 2-D simulations, in contrast to 3-D simulations, impacts are less frequent but each has a larger effect on surface mobility, making the simulations more stochastic. These stronger 2-D subduction events can mix both recycled basalt and impactor material into the lower mantle. These results thus demonstrate that impacts can make a first-order difference to the early tectonics and mantle mixing of Earth and other large terrestrial planets, and that three-dimensional simulations are important so that effects are not over- or under-predicted.

The rheological properties of­­­ Earth’s lower mantle materials are key for mantle dynamics and planetary evolution. The main rock-forming minerals in the lower mantle are bridgmanite (Br) and smaller amounts of ferropericlase (Fp). Bridgmanite minerals are intrinsically much stronger than ferropericlase minerals, resulting in significant variations in lower-mantle rheological behavior depending on the quantity and degree of interconnectivity of the weak phase. The resulting effective bulk rock viscosity decreases with accumulating strain when the weaker Fp minerals become elongated and eventually interconnected. This implies that strain localization may occur in Earth’s lower mantle, which would in turn influence the pattern of mantle flow and could potentially aid the preservation of compositionally distinct, “hidden” reservoirs. So far, there have been no studies on global-scale mantle convection in the presence of such strain-weakening (SW) rheology.Here, we present 2D numerical models of thermo-chemical convection in spherical annulus geometry including a new strain-weakening (SW) rheology formulation for lower-mantle materials. This macro-scale SW rheology is based on micro-scale rheological behavior found in prior studies, and combining rheological weakening and healing terms. We determine the effects of SW rheology on the planform of mantle flow, the mixing of chemical reservoirs, and the dynamics of mantle plumes.We find that, in particular, plume conduits are weakened and act as lubrication channels which allow for the rapid ascent of mantle material. Their thermal anomalies and geometries are significantly different than those of mantle plumes which are not rheologically weakened. Moreover, larger thermochemical piles at the base of the mantle are stabilized by SW rheology, with implications for preservation of chemically-distinct materials over long timescales. Finally, we put our results into context with observations and existing hypotheses on the style of Earth's mantle convection and mixing. Most importantly, we suggest that the new kind of plume dynamics may explain the discrepancy between expected and observed thermal anomalies of deep-seated mantle plumes on Earth.

The study of exoplanets can provide a more general understanding of planetary systems and terrestrial-planet evolution. How terrestrial exoplanets differ from Earth has so far mostly focused on planet size and orbital distance. In contrast, bulk planet composition has gained much less attention, even though it controls key physical properties of planetary interiors, and thus interior dynamics and long-term evolution. Bulk planet composition is related to core size as well as mantle chemistry and mineralogy. To better understand the variability of interior properties among terrestrial exoplanets, we attempt to constrain the range of bulk terrestrial exoplanet compositions. To constrain the compositional range of terrestrial exoplanets, we use the compositional link between rocky planets and their host stars. At least in the Solar System, planetary building blocks (chondrites) correspond to the devolatized star (Sun) composition. Accordingly, we apply devolatilization to stellar compositions in the galactic neighbourhood (i.e., within 500 pc) according to the approach of Wang et al. [1]. These bulk compositions are then split into core and mantle reservoirs by considering interior oxygen fugacity during core formation equal to that of Earth. We find compositional ranges of molar mantle Mg/Si-ratios from 0.9 to 2.0, core sizes between 18 and 35 wt%, and mantle molar MgO+FeO+SiO2 abundances between 88 and 94 mol%. We summarize our results by defining 20 end-member compositions that represent the full range of bulk terrestrial exoplanet compositions in the Solar neighbourhood. A Gibbs energy minimization algorithm, Perple_X, shows that these planets all have mantles dominated by Fe-Mg-Si minerals, such as olivine, pyroxene, bridgmanite and periclase. The relative abundances of these minerals control mantle viscosity, where Mg-rich minerals (periclase) are weaker than Si-rich minerals (olivine, bridgmanite). We continue by simulating mantle dynamics using a 2D geodynamic model. Most of our end-member planets have a lower mantle viscosity than Earth, and their mantles are more fertile than Earth's. Accordingly, we find that mantle cooling is more efficient than for Earth for most Earth-sized exoplanets in the solar neighborhood. Future work is needed to further constrain the coupled interior-atmosphere evolution of Earth-like exoplanets, and how bulk planet composition affects it. [1] Wang, H.S., Lineweaver, C.H., Ireland, T.R. (2019). The volatility trend of protosolar and terrestrial elemental abundances. Icarus, 328, 287-305

The Martian dichotomy features a ~25 km difference in crustal thickness and ~5 km contrast in topography between the southern highlands and northern lowlands [1]. Among various origin hypothesis, a southern impact [2,3] creates a magma pond which, upon cooling, induces crustal thickening and thereby forms the crustal dichotomy within 10s of million years. Our previous study [4], which utilizes a head-on parametrized impact in 2D geometry, shows that an impact-induced magma pond in the southern hemisphere is able to not only create a thickened crust in the south, but also a satisfying volcanic history with localized melt production in the equatorial region at geologically recent time. Depleted material, formed from crystallization of the magma pond, spreads and underplates the thicker and colder Northern lithosphere undisturbed by the impact, reinforcing the lesser extent of volcanism in the northern hemisphere. Our resultant mantle structure is consistent with existing simulation efforts that focus on the post-dichotomy formation evolution history [5], and in addition gives the context of how such thermochemical structure is developed. In order to include a more realistic impact scenario, we use smoothed particle hydrodynamics (SPH) simulations [6] to model the first 24-36 hours of a giant impact between proto-Mars and its impactor. The SPH result is then transferred to the mantle convection code StagYY [7], as an initial thermal condition, to simulate the long-term evolution of the crust and mantle for the subsequent 4.5 billion years. We systematically vary the impactor size, impact velocity and pre-impact Martian mantle temperature. Our preliminary results show that a 45-degree impact does not form a Martian dichotomy-like crustal structure, while a 15-degree impact is a better match. With a realistic impact, the mechanisms reported in our parametrized impact study still hold. References: [1] Watters, T., McGovern, P., & Irwin III, R. (2007). Hemispheres Apart: The Crustal Dichotomy on Mars. Annual Review Of Earth And Planetary Sciences, 35(1), 621-652. [2] Reese, C., Orth, C., & Solomatov, V. (2011). Impact megadomes and the origin of the martian crustal dichotomy. Icarus, 213(2), 433-442. [3] Golabek, G., Keller, T., Gerya, T., Zhu, G., Tackley, P., & Connolly, J. (2011). Origin of the martian dichotomy and Tharsis from a giant impact causing massive magmatism. Icarus, 215(1), 346-357. [4] Cheng, K.W., Tackley, P.J., Rozel, A.B., Golabek, G.J. (2021). Martian Dichotomy: Impact-induced Crustal Production in Mantle Convection Models, Abstract [DI35B-0023] presented at 2021 Fall Meeting, AGU, New Orleans, LA, 13-17 Dec. [5] Plesa, A., Padovan, S., Tosi, N., Breuer, D., Grott, M., & Wieczorek, M. et al. (2018). The Thermal State and Interior Structure of Mars. Geophysical Research Letters, 45(22), 12,198-12,209. [6] Emsenhuber, A., Jutzi, M., Benz, W. (2018). SPH calculations of Mars-scale collisions: The role of the equation of state, material rheologies, and numerical effects. Icarus, 301, 247-257 [7] Tackley, P. (2008). Modelling compressible mantle convection with large viscosity contrasts in a three-dimensional spherical shell using the yin-yang grid. Physics Of The Earth And Planetary Interiors, 171(1-4), 7-18.

The evolution of the system Earth is critically influenced by the long-term dynamics, composition and structure of the mantle. While cosmochemical and geochemical constraints indicate that the lower mantle hosts an ancient primordial reservoir that may be enriched in SiO2 with respect to the upper mantle, geophysical observations and models point to efficient mass transfer and convective mixing across the entire mantle. Recent hypotheses of primordial-material preservation in a convecting mantle involve delayed mixing of intrinsically dense and/or intrinsically strong heterogeneity. Yet, the effects of composition-dependent rheology and density upon heterogeneity preservation and the dynamics of mantle mixing remain poorly understood. Here, we present two-dimensional numerical models in spherical geometry, investigating the preservation styles of primordial material as a function of its physical properties (i.e., viscosity and density contrasts). We establish multiple regimes of primordial-material preservation that can occur in terrestrial planets. These include (1) efficient mixing, (2) double-layered convection with or without topography, and (3) variable styles of partial heterogeneity preservation (e.g., as diffuse domains, piles or viscous blobs in the lower mantle). Some of these regimes are here characterised for the first time, and all regimes are put into context with each other as a function of model parameters. The viscous-blobs and diffuse-domains regimes can reconcile the preservation of primordial domains in a convecting mantle, potentially resolving the discrepancy between geochemical and geophysical constraints for planet Earth. Several, if not all, regimes characterised here may be relevant to understand the long-term evolution of terrestrial planets in general.

The nature of compositional heterogeneity in Earth’s lower mantle remains a long-standing puzzle that can inform about the long-term thermochemical evolution and dynamics of our planet. Here, we use global-scale 2D models of thermo- chemical mantle convection to investigate the coupled evolution and mixing of (intrinsically-dense) recycled and (intrinsically- strong) primordial heterogeneity in the mantle. We explore the effects of ancient compositional layering of the mantle, as motivated by magma-ocean solidification studies, and of the physical parameters of primordial material. Depending on these physical parameters, our models predict various regimes of mantle evolution and heterogeneity preservation over 4.5 Gyrs. Over a wide parameter range, primordial and recycled heterogeneity are predicted to co-exist with each other in the lower mantle of Earth-like planets. Primordial material usually survives as mid-to-large scale blobs (or streaks) in the mid-mantle, around 1000-2000 km depth, and this preservation is largely independent on the initial primordial-material volume. In turn, recycled oceanic crust (ROC) persists as large piles at the base of the mantle and as small streaks everywhere else. In models with an additional dense FeO-rich layer initially present at the base of the mantle, the ancient dense material partially survives at the top of ROC piles, causing the piles to be compositionally stratified. Moreover, the addition of such an ancient FeO-rich basal layer significantly aids the preservation of the viscous domains in the mid-mantle. Finally, we find that primordial blobs are commonly directly underlain by thick ROC piles, and aid their longevity and stability. Based on our results, we propose an integrated style of mantle heterogeneity for the Earth, involving the preservation of primordial domains along with recycled piles. This style has important implications for early Earth evolution, and has the potential of reconciling geophysical and geochemical discrepancies on present-day lower-mantle heterogeneity.

Earth science has been heavily data-driven due to the abundance in data. Yet, when there are relatively a small number of hypotheses to verify, the inverse problem becomes a classification problem. It is then worth directly examining observed seismic data against predicted data. Concretely, we chain forward modelling from geodynamics to seismology. We call this process ‘waveform Seismic Low Filtering of Earth’s models’ (SeLFiE). We take seismic signals of the snapshots of forwardly generated Earth models with that of the actual Earth, as if we took a photo of ourselves. Although there have several studies on how the seismological tomographic technique can perceive the geodynamical models, there are few studies on the seismic waveform sensitivity to geodynamical or petrological parameters. A pilot test of our SeLFiE methodology was encouraging, since we used only one seismic station to constrain the melt transportation manner beneath the Réunion island (Franken et al. 2020). Here in this contribution we present our strategy and developed tools towards the waveform filtering that have been developed during and after the CLEEDI week in August, 2020.

Ariel, the Atmospheric Remote-sensing Infrared Exoplanet Large-survey, was adopted as the fourth medium-class mission in ESA's Cosmic Vision programme to be launched in 2029. During its 4-year mission, Ariel will study what exoplanets are made of, how they formed and how they evolve, by surveying a diverse sample of about 1000 extrasolar planets, simultaneously in visible and infrared wavelengths. It is the first mission dedicated to measuring the chemical composition and thermal structures of hundreds of transiting exoplanets, enabling planetary science far beyond the boundaries of the Solar System. The payload consists of an off-axis Cassegrain telescope (primary mirror 1100 mm x 730 mm ellipse) and two separate instruments (FGS and AIRS) covering simultaneously 0.5-7.8 micron spectral range. The satellite is best placed into an L2 orbit to maximise the thermal stability and the field of regard. The payload module is passively cooled via a series of V-Groove radiators; the detectors for the AIRS are the only items that require active cooling via an active Ne JT cooler. The Ariel payload is developed by a consortium of more than 50 institutes from 16 ESA countries, which include the UK, France, Italy, Belgium, Poland, Spain, Austria, Denmark, Ireland, Portugal, Czech Republic, Hungary, the Netherlands, Sweden, Norway, Estonia, and a NASA contribution., Comment: Ariel Definition Study Report, 147 pages. Reviewed by ESA Science Advisory Structure in November 2020. Original document available at: https://www.cosmos.esa.int/documents/1783156/3267291/Ariel_RedBook_Nov2020.pdf/

Since the first exoplanet detection in 1992, the study of exoplanets has received considerable attention. It is becoming apparent that the diversity of the general exoplanet population extends beyond that of the Solar System and includes a variety of structures and compositions. For instance, recent research suggests that if a terrestrial planet forms with substantially more Al and Ca than Earth, it may be entirely rocky and lack a metallic core. Two such planets have been tentatively identified (Dorn et al., 2018). Small-core and coreless planets are expected to differ significantly from Earth. Small cores may have fundamentally different dynamics compared to larger cores, which can affect the heat flow inside the planet and the generation and retention of a magnetic dynamo. Additionally, core size has been shown to affect the development of plate tectonics in numerical models (Osterloo et al. 2021; O'Neill et al., 2017), as well as carbon cycling on a planet. Investigating small-core and coreless planets therefore illustrates the potential diversity of exoplanets and offers insight into different regimes of mantle dynamics and plate tectonics. In this study, we use the code StagYY (Tackley, 2008, 2013) to model the evolution of planets with core mass fractions ranging from 10-1 to 10-6 and compare them to an Earth-like reference model. We use mantle reference viscosities of 1020, 1021, and 1022 Pa·s and crustal yield stresses of 30, 100, and 300 MPa. The planets are set to evolve for 4.5 Gyr. In planets with smaller cores, hot plumes rising from the core-mantle boundary (CMB) are reduced in number and develop slowly compared to large-core planets. In the models with a reference viscosity of 1021 Pa·s and a crustal yield stress of 30 MPa, all planets show subduction and plate tectonic-like behavior. The onset of subduction is delayed in small-core planets compared to the Earth-like reference model. Basalt-enriched material accumulates at the CMB and forms a continuous layer in all planet models; this layer is thicker in small-core planets. Due to insulation by the basalt layer, CMB temperature is significantly higher in small-core planets at the end of the 4.5 Gyr evolution period. For a lower reference viscosity of 1020 Pa·s, subduction is initiated earlier and the basalt layer surrounding the CMB is thicker, while the reverse is true for the higher reference viscosity of 1022 Pa·s. At higher yield stresses, some of the planet models undergo subduction and later transition to a stagnant-lid state. However, for a reference viscosity of 1021 Pa·s and a yield stress of 100 MPa, there is no consistent trend regarding this transition. For a yield stress of 300 MPa, planets with core fractions of 10-3 and larger do not show any subduction, but remain in stagnant-lid state throughout the evolution period. In planets with smaller core fractions, subduction events occur starting at 2.5 Gyr. This agrees with previous research suggesting that a small core size can favor the initiation of plate tectonics (Osterloo et al. 2021; O'Neill et al., 2017). In such cases, core size may crucially influence a planet's habitability, since a large-core planet may lack the plate tectonics that are sometimes considered essential to efficient carbon cycling, while a small-core planet may lack the gravity or magnetic dynamo necessary to sustain life. We conclude that core size influences the onset of subduction and plate tectonics on terrestrial planets, as well as their thermal evolution. Small-core planets tend to initiate subduction later than their large-core counterparts and can also be subject to interior heating due to the hot basalt layers insulating the core. For high crustal yield stresses, small-core planets are more likely to develop plate tectonics, while large-core planets remain in a stagnant-lid state. However, this tendency is not evident at yield stresses below 300 MPa. Figure 1: Interior differentiation of planets with a) Earth-like core size b) core mass fraction of 10-1 c) core mass fraction of 10-6 for a reference viscosity of 1021 Pa·s and crustal yield stress of 100 MPa. References: Dorn, C., Harrison, J. H. D., Bonsor, A. and Hands, T.O. A new class of Super-Earths formed from high-temperature condensates: HD219134 b,55 Cnc e, WASP-47 e, MNRAS, 484 (1), 712–727, doi:10.1093/mnras/sty3435.url:http://dx.doi.org/10.1093/mnras/sty3435, 2018. O'Neill, C., Lowman, J., Wasiliev, J. The effect of galactic chemical evolution on terrestrial exoplanet composition and tectonics, Icarus, 352, 114025, doi: 10.1016/j.icarus.2020.114025, 2020. Oosterloo, M., Höning, D., Kamp, I. E. E., van der Tak, F. F. S. The role of planetary interior in the long-term evolution of atmospheric CO2 on Earth-like exoplanets, A&A, 2021, doi:10.1051/0004-6361/202039664, 2021. Tackley, P. J. Modelling compressible mantle convection with large viscosity contrasts in a three-dimensional spherical shell using the yin-yang grid, Phys. Earth Planet. Inter, 171 (1-4), 7-18, doi: 10.1016/j.pepi.2008.08.005, 2008. Tackley, P. J., Ammann, M., Brodholt, J. P., Dobson, D. P. and Valencia, D. Mantle dynamics in super-Earths: Post-perovskite rheology and self-regulation of viscosity, Icarus 225 (1), 50-61, doi:10.1016/j.icarus.2013.03.013, 2013.

It is common to perform 2-dimensional simulations of mantle convection in spherical geometry, either with (r, theta) axisymmetry or the (r, phi) spherical annulus geometry (Hernlund and Tackley, PEPI 2008). A problem with both of these is that the geometrical restriction forces deformation that is not present in 3 dimensions. Specifically, in a 2-D spherical approximation, a downwelling is forced to contract in the plane-perpendicular direction, requiring it to extend in the 2 in-plane directions. In other words, it is "squeezed" in the plane-perpendicular direction. If the downwelling has a high viscosity, as a cold slab does, then it resists this forced deformation, sinking much more slowly than in three dimensions, in which it could sink with no deformation. This can cause unrealistic behaviour and scaling relationships for high viscosity contrasts. This problem can be solved by subtracting the geometrically-forced deformation ("squeezing") from the strain-rate tensor when calculating the stress tensor. Specifically, components of in-plane and plane-normal strain rate that are required by and proportional to the vertical (radial) velocity are subtracted, a procedure that is here termed "anti-squeeze". It is demonstrated here that this "anti-squeeze" correction results in sinking rates and scaling relationships that are similar to those in 3-D geometry whereas without it, abnormal and physically unrealistic results can be obtained for high viscosity contrasts. This correction has been used for 2-D geometries in the code StagYY (Tackley, PEPI 2008; Hernlund and Tackley, PEPI 2008) since 2010.

Seismic studies show two antipodal regions of lower shear velocity at the core-mantle boundary (CMB) called Large Low Shear Velocity Provinces (LLSVPs). They are thought to be thermally and chemically distinct, and therefore might have a different density and viscosity than the ambient mantle. Employing a composite rheology, using both diffusion and dislocation creep, we investigate the influence of grain size evolution on the dynamics of thermo-chemical piles in evolutionary geodynamic models. We consider a primordial layer and a time-dependent basalt production at the surface to dynamically form the present-day chemical heterogeneities, similar to earlier studies, e.g., by Nakagawa and Tackley (2014). We perform a parameter study which includes different densities and viscosities of the imposed primordial layer. Further, we test the influence of yield stress and parameters of the grain size evolution equation on the dynamics of piles and their interaction with the ambient mantle. Our results show that, relative to the ambient mantle, grain size is higher inside the piles, but due to the large temperature at the CMB, the viscosity is not remarkably different from ambient mantle viscosity. We further find, that although the average viscosity of the detected piles is buffered by both grain size and temperature, grain size dominates the viscosity development. However, depending on the convection regime, in the ambient mantle, viscosity can be dominated by temperature. All pile properties, except for temperature, show a self-regulating behaviour: although grain size, density and viscosity decrease when downwellings or overturns occur, these properties quickly recover and return to values prior to the downwelling. We compute the necessary recovery time and find, that it takes approximately 400 Myr for the properties to recover after a resurfacing event. Extrapolating to Earth-values, we estimate a much smaller recovery time. We observe that dynamic recrystallisation counteracts grain growth in the piles when the lithosphere is weakened and forms downwellings. Venus-type resurfacing episodes reduce the grain size in piles and ambient mantle to few millimetres. More continuous mobile-lid type downwellings limit the grain size to a centimetre. Consequently, we find that grain size-dependent viscosity does not increase the resistance of thermo-chemical piles to downgoing slabs. Mostly, piles deform in grain size- sensitive diffusion creep but they are not stiff enough to counteract the force of downwellings. Hence, we conclude that the location of subduction zones could be responsible for the location and stability of the thermo-chemical piles of the Earth because of dynamic recrystallisation.

Written as both a textbook and a handy reference, this text deliberately avoids complex mathematics assuming only basic familiarity with geodynamic theory and calculus. Here, the authors have brought together the key numerical techniques for geodynamic modeling, demonstrations of how to solve problems including lithospheric deformation, mantle convection and the geodynamo. Building from a discussion of the fundamental principles of mathematical and numerical modeling, the text moves into critical examinations of each of the different techniques before concluding with a detailed analysis of specific geodynamic applications. Key differences between methods and their respective limitations are also discussed - showing readers when and how to apply a particular method in order to produce the most accurate results. This is an essential text for advanced courses on numerical and computational modeling in geodynamics and geophysics, and an invaluable resource for researchers looking to master cutting-edge techniques. Links to supplementary computer codes are available online.

International audience

M30 M34