Garnero, E. J., McNamara, A. K. & Shim, S. H. Continent-sized anomalous zones with low seismic velocity at the base of Earth’s mantle. Nat. Geosci. 9, 481–489 (2016).
Google Scholar
Labrosse, S., Hernlund, J. W. & Coltice, N. A crystallizing dense magma ocean at the base of the Earth’s mantle. Nature 450, 866–869 (2007).
Google Scholar
Canup, R. M. & Asphaug, E. Origin of the Moon in a giant impact near the end of the Earth’s formation. Nature 412, 708–712 (2001).
Google Scholar
Kokubo, E. & Ida, S. Orbital evolution of protoplanets embedded in a swarm of planetesimals. Icarus 114, 247–257 (1995).
Google Scholar
Cameron, A. G. W. & Ward, W. R. The origin of the Moon. Abstr. Lunar Planet. Sci. Conf. 7, 120–122 (1976).
Ringwood, A. E. Volatile and siderophile element geochemistry of the Moon: a reappraisal. Earth Planet. Sci. Lett. 111, 537–555 (1992).
Google Scholar
Nie, N. X. & Dauphas, N. Vapor drainage in the protolunar disk as the cause for the depletion in volatile elements of the Moon. Astrophys. J. 884, L48 (2019).
Google Scholar
Lee, C. T. A. et al. Upside-down differentiation and generation of a primordial lower mantle. Nature 463, 930–933 (2010).
Google Scholar
Christensen, U. R. & Hofmann, A. W. Segregation of subducted oceanic crust in the convecting mantle. J. Geophys. Res. 99, 19867–19884 (1994).
Google Scholar
Williams, C. D., Mukhopadhyay, S., Rudolph, M. L. & Romanowicz, B. Primitive helium is sourced from seismically slow regions in the lowermost mantle. Geochem. Geophys. Geosyst. 20, 4130–4145 (2019).
Google Scholar
Mukhopadhyay, S. Early differentiation and volatile accretion recorded in deep-mantle neon and xenon. Nature 486, 101–104 (2012).
Google Scholar
Desch, S. J. & Robinson, K. L. A unified model for hydrogen in the Earth and Moon: no one expects the Theia contribution. Chemie der Erde 79, 125546 (2019).
Google Scholar
Pepin, R. O. & Porcelli, D. Origin of noble gases in the terrestrial planets. Rev. Mineral. Geochem. 47, 191–246 (2002).
Google Scholar
Burke, K., Steinberger, B., Torsvik, T. H. & Smethurst, M. A. Plume generation zones at the margins of large low shear velocity provinces on the core–mantle boundary. Earth Planet. Sci. Lett. 265, 49–60 (2008).
Google Scholar
Will, P., Busemann, H., Riebe, M. E. I. & Maden, C. Indigenous noble gases in the Moon’s interior. Sci. Adv. 8, 1–9 (2022).
Google Scholar
Stewart, S. et al. The shock physics of giant impacts: key requirements for the equations of state. AIP Conf. Proc. 2272, 080003 (2020).
Google Scholar
Kegerreis, J. A., Eke, V. R., Massey, R. J., Sandnes, T. D. & Teodoro, L. F. A. Immediate origin of the Moon as a post-impact satellite. Astrophys. J. Lett. 937, L40 (2022).
Google Scholar
Deng, H. et al. Enhanced mixing in Giant Impact simulations with a new Lagrangian method. Astrophys. J. 870, 127 (2019).
Google Scholar
Deng, H. et al. Primordial Earth mantle heterogeneity caused by the Moon-forming Giant Impact? Astrophys. J. 887, 211 (2019).
Google Scholar
Cottaar, S. & Lekic, V. Morphology of seismically slow lower-mantle structures. Geophys. J. Int. 207, 1122–1136 (2016).
Google Scholar
Kegerreis, J. A. et al. Planetary giant impacts: convergence of high-resolution simulations using efficient spherical initial conditions and SWIFT. Mon. Not. R. Astron. Soc. 487, 5029–5040 (2019).
Google Scholar
Deguen, R., Landeau, M. & Olson, P. Turbulent metal–silicate mixing, fragmentation, and equilibration in magma oceans. Earth Planet. Sci. Lett. 391, 274–287 (2014).
Google Scholar
Dauphas, N., Burkhardt, C., Warren, P. H. & Fang-Zhen, T. Geochemical arguments for an Earth-like Moon-forming impactor. Philos. Trans. R. Soc. A 372, 20130244 (2014).
Google Scholar
Pahlevan, K., Stevenson, D. J. & Eiler, J. M. Chemical fractionation in the silicate vapor atmosphere of the Earth. Earth Planet. Sci. Lett. 301, 433–443 (2011).
Google Scholar
Meier, M. M. M., Reufer, A. & Wieler, R. On the origin and composition of Theia: constraints from new models of the Giant Impact. Icarus 242, 316–328 (2014).
Google Scholar
Robinson, K. L. et al. Water in evolved lunar rocks: evidence for multiple reservoirs. Geochim. Cosmochim. Acta 188, 244–260 (2016).
Google Scholar
Connolly, J. A. D. Computation of phase equilibria by linear programming: a tool for geodynamic modeling and its application to subduction zone decarbonation. Earth Planet. Sci. Lett. 236, 524–541 (2005).
Google Scholar
Connolly, J. A. D. The geodynamic equation of state: what and how. Geochem. Geophys. Geosyst. 10, 1–19 (2009).
Google Scholar
Stixrude, L. & Lithgow-Bertelloni, C. Thermodynamics of mantle minerals – II. Phase equilibria. Geophys. J. Int. 184, 1180–1213 (2011).
Google Scholar
Nakajima, M. & Stevenson, D. J. Melting and mixing states of the Earth’s mantle after the Moon-forming impact. Earth Planet. Sci. Lett. 427, 286–295 (2015).
Google Scholar
Gurnis, M. The effects of chemical density differences on convective mixing in the Earth’s mantle. J. Geophys. Res., Solid Earth 91, 11407–11419 (1986).
Google Scholar
Tackley, P. J. in The Core‐Mantle Boundary Region (eds Gurnis, M., Wysession, M. E., Knittle, E. & Buffet, B. A.) 231–253 (American Geophysical Union, 1998).
Nakagawa, T., Tackley, P. J., Deschamps, F. & Connolly, J. A. D. The influence of MORB and harzburgite composition on thermo-chemical mantle convection in a 3-D spherical shell with self-consistently calculated mineral physics. Earth Planet. Sci. Lett. 296, 403–412 (2010).
Google Scholar
Gu, T., Li, M., McCammon, C. & Lee, K. K. M. Redox-induced lower mantle density contrast and effect on mantle structure and primitive oxygen. Nat. Geosci. 9, 723–727 (2016).
Google Scholar
Yuan, Q. & Li, M. Instability of the African large low-shear-wave-velocity province due to its low intrinsic density. Nat. Geosci. 15, 334–339 (2022).
Google Scholar
McNamara, A. K. & Zhong, S. Thermochemical structures beneath Africa and the Pacific Ocean. Nature 437, 1136–1139 (2005).
Google Scholar
O’Neill, C., Marchi, S., Zhang, S. & Bottke, W. Impact-driven subduction on the Hadean Earth. Nat. Geosci. 10, 793–797 (2017).
Google Scholar
Hernlund, J. W. & Houser, C. On the statistical distribution of seismic velocities in Earth’s deep mantle. Earth Planet. Sci. Lett. 265, 423–437 (2008).
Google Scholar
Lei, W. et al. Global adjoint tomography – model GLAD-M25. Geophys. J. Int. 223, 1–21 (2020).
Google Scholar
Elkins-Tanton, L. T. Magma oceans in the inner Solar System. Annu. Rev. Earth Planet. Sci. 40, 113–139 (2012).
Google Scholar
Abe, Y. Thermal and chemical evolution of the terrestrial magma ocean. Phys. Earth Planet. Inter. 1, 27–39 (1997).
Google Scholar
Solomatov, V. S. in Treatise on Geophysics 1st edn, Vol. 9 (ed. Schubert, G.) 91–119 (Elsevier, 2007).
Maurice, M. et al. Onset of solid-state mantle convection and mixing during magma ocean solidification. J. Geophys. Res., Planets 122, 577–598 (2017).
Google Scholar
Boukaré, C. E., Parmentier, E. M. & Parman, S. W. Timing of mantle overturn during magma ocean solidification. Earth Planet. Sci. Lett. 491, 216–225 (2018).
Google Scholar
Labrosse, S., Morison, A., Deguen, R. & Alboussière, T. Rayleigh–Bénard convection in a creeping solid with melting and freezing at either or both its horizontal boundaries. J. Fluid Mech. 846, 5–36 (2018).
Google Scholar
Agrusta, R. et al. Mantle convection interacting with magma oceans. Geophys. J. Int. 220, 1878–1892 (2020).
Google Scholar
Morison, A., Labrosse, S., Deguen, R. & Alboussière, T. Timescale of overturn in a magma ocean cumulate. Earth Planet. Sci. Lett. 516, 25–36 (2019).
Google Scholar
Becker, T. W., Kellogg, J. B. & O’Connell, R. J. Thermal constraints on the survival of primitive blobs in the lower mantle. Earth Planet. Sci. Lett. 171, 351–365 (1999).
Google Scholar
Lock, S. J., Bermingham, K. R., Parai, R. & Boyet, M. Geochemical constraints on the origin of the Moon and preservation of ancient terrestrial heterogeneities. Space Sci. Rev. 216, 1–46 (2020).
Google Scholar
Ballmer, M. D., Lourenço, D. L., Hirose, K., Caracas, R. & Nomura, R. Reconciling magma-ocean crystallization models with the present-day structure of the Earth’s mantle. Geochem. Geophys. Geosyst. 18, 2785–2806 (2017).
Google Scholar
Maas, C. & Hansen, U. Dynamics of a terrestrial magma ocean under planetary rotation: a study in spherical geometry. Earth Planet. Sci. Lett. 513, 81–94 (2019).
Google Scholar
Williams, C. D. & Mukhopadhyay, S. Capture of nebular gases during Earth’s accretion is preserved in deep-mantle neon. Nature 565, 78–81 (2019).
Google Scholar
Mundl-Petermeier, A. et al. Temporal evolution of primordial tungsten-182 and 3He/4He signatures in the Iceland mantle plume. Chem. Geol. 525, 245–259 (2019).
Google Scholar
Li, M., McNamara, A. K. & Garnero, E. J. Chemical complexity of hotspots caused by cycling oceanic crust through mantle reservoirs. Nat. Geosci. 7, 366–370 (2014).
Google Scholar
Mulyukova, E., Steinberger, B., Dabrowski, M. & Sobolev, S. V. Survival of LLSVPs for billions of years in a vigorously convecting mantle: replenishment and destruction of chemical anomaly. J. Geophys. Res., Solid Earth 120, 3824–3847 (2015).
Google Scholar
Jackson, M. G. et al. Ancient helium and tungsten isotopic signatures preserved in mantle domains least modified by crustal recycling. Proc. Natl Acad. Sci. USA 117, 30993–31001 (2020).
Google Scholar
Brown, J. M. & Shankland, T. J. Thermodynamic parameters in the Earth as determined from seismic profiles. Geophys. J. R. Astron. Soc. 66, 579–596 (1981).
Google Scholar
Stacey, F. D. A thermal model of the earth. Phys. Earth Planet. Inter. 15, 341–348 (1977).
Google Scholar
Canup, R. M., Barr, A. C. & Crawford, D. A. Lunar-forming impacts: high-resolution SPH and AMR-CTH simulations. Icarus 222, 200–219 (2013).
Google Scholar
Hosono, N., Saitoh, T. R., Makino, J., Genda, H. & Ida, S. The Giant Impact simulations with density independent smoothed particle hydrodynamics. Icarus 271, 131–157 (2016).
Google Scholar
Reinhardt, C. & Stadel, J. Numerical aspects of Giant Impact simulations. Mon. Not. R. Astron. Soc. 467, 4252–4263 (2017).
Google Scholar
Ruiz-Bonilla, S. et al. Dealing with density discontinuities in planetary SPH simulations. Mon. Not. R. Astron. Soc. 512, 4660–4668 (2022).
Google Scholar
Hosono, N. & Karato, S. The influence of equation of state on the Giant Impact simulations. J. Geophys. Res., Planets 127, 1–18 (2022).
Google Scholar
Hosono, N. et al. Unconvergence of very-large-scale Giant Impact simulations. Publ. Astron. Soc. Jpn 69, 1–11 (2017).
Google Scholar
Meier, T., Reinhardt, C. & Stadel, J. G. The EOS/resolution conspiracy: convergence in proto-planetary collision simulations. Mon. Not. R. Astron. Soc. 1816, 1806–1816 (2021).
Google Scholar
Raskin, C. & Owen, J. M. Examining the accuracy of astrophysical disk simulations with a generalized hydrodynamical test problem. Astrophys. J. 831, 26 (2016).
Google Scholar
Gabriel, T. S. J. & Allen-Sutter, H. Dependencies of mantle shock heating in pairwise accretion. Astrophys. J. Lett. 915, L32 (2021).
Google Scholar
Frontiere, N., Raskin, C. D. & Owen, J. M. CRKSPH – a conservative reproducing kernel smoothed particle hydrodynamics scheme. J. Comput. Phys. 332, 160–209 (2017).
Google Scholar
Rosswog, S. Astrophysical smooth particle hydrodynamics. New Astron. Rev. 53, 78–104 (2009).
Google Scholar
Schaller, M. et al. SWIFT: SPH with inter-dependent fine-grained tasking. In Astrophysics Source Code Library, ascl-1805 (2018).
Ruiz-Bonilla, S., Eke, V. R., Kegerreis, J. A., Massey, R. J. &Teodoro, L. F. A. The effect of pre-impact spin on the Moon-forming collision. Mon. Not. R. Astron. Soc. 2870, 2861–2870 (2021).
Canup, R. M. Forming a Moon with an Earth-like composition via a giant impact. Science 338, 1052–1056 (2012).
Google Scholar
Hopkins, P. F. A new class of accurate, mesh-free hydrodynamic simulation methods. Mon. Not. R. Astron. Soc. 450, 53–110 (2015).
Google Scholar
Thompson, S. L. & Lauson, H. S. Improvements in the Chart D Radiation—Hydrodynamic Code. III. Revised Analytic Equation of State. Sandia Report SC-RR-71 0174 (1972).
Melosh, H. J. A hydrocode equation of state for SiO2. Meteorit. Planet. Sci. 42, 2079–2098 (2007).
Google Scholar
Fiquet, G. et al. Melting of peridotite to 140 gigapascals. Science 329, 1516–1518 (2010).
Google Scholar
Andrault, D. et al. Solidus and liquidus profiles of chondritic mantle: implication for melting of the Earth across its history. Earth Planet. Sci. Lett. 304, 251–259 (2011).
Google Scholar
Abe, Y. in Evolution of the Earth and Planets (eds Takahashi, E., Jeanloz, R. & Rubie, D.) 41–54 (American Geophysical Union, 1993).
Miyazaki, Y. & Korenaga, J. On the timescale of magma ocean solidification and its chemical consequences: 2. Compositional differentiation under crystal accumulation and matrix compaction. J. Geophys. Res., Solid Earth 124, 3399–3419 (2019).
Google Scholar
Nomura, R. et al. Spin crossover and iron-rich silicate melt in the Earth’s deep mantle. Nature 473, 199–202 (2011).
Google Scholar
Andrault, D. et al. Solid–liquid iron partitioning in Earth’s deep mantle. Nature 487, 354–357 (2012).
Google Scholar
Moresi, L. N. & Solomatov, V. S. Numerical investigation of 2D convection with extremely large viscosity variations. Phys. Fluids 7, 2154–2162 (1995).
Google Scholar
Farrell, K. A. O. & Lowman, J. P. Emulating the thermal structure of spherical shell convection in plane-layer geometry mantle convection models. Phys. Earth Planet. Inter. 182, 73–84 (2010).
Google Scholar
Tackley, P. J. & King, S. D. Testing the tracer ratio method for modeling active compositional fields in mantle convection simulations. Geochem. Geophys. Geosyst. 4, 1–15 (2003).
Google Scholar
Schaller, M. et al. Swift: a modern highly-parallel gravity and smoothed particle hydrodynamics solver for astrophysical and cosmological applications. Preprint at http://arxiv.org/abs/2305.13380 (2023).
Hirth, G. & Kohlstedt, D. L. Water in the oceanic upper mantle: implications for rheology, melt extraction and the evolution of the lithosphere. Earth Planet. Sci. Lett. 144, 93–108 (1996).
Google Scholar
Dziewonski, A. M. & Anderson, D. L. Preliminary reference Earth model. Phys. Earth Planet. Inter. 25, 297–356 (1981).
Google Scholar