1 Seismic evidence for depth-dependent metasomatism in cratons Thomas Eeken 1 , Saskia Goes 1 , Helle A. Pedersen 2 , Nicholas T. Arndt 2 , Pierre Bouilhol 3 1 Department of Earth Science and Engineering, Imperial College London, U.K., 2 LGIT, Université Joseph Fourier, Grenoble, France, 3 CRPG, Université de Lorraine, UMR 7358, Vandoeuvre-Lès-Nancy, F-54501, France corresponding author: t.eeken14@imperial.ac.uk Submitted to EPSL October 2017, Revised March 2018, Accepted 12 March 2018 Abstract The long-term stability of cratons has been attributed to low temperatures and depletion in iron and water, which decrease density and increase viscosity. However, steady-state thermal models based on heat flow and xenolith constraints systematically overpredict the seismic velocity-depth gradients in cratonic lithospheric mantle. Here we invert for the 1-D thermal structure and a depth distribution of metasomatic minerals that fit average Rayleigh-wave dispersion curves for the Archean Kaapvaal, Yilgarn and Slave cratons and the Proterozoic Baltic Shield below Finland. To match the seismic profiles, we need a significant amount of hydrous and/or carbonate minerals in the shallow lithospheric mantle, starting between the Moho and 70 km depth and extending down to at least 100-150 km. The metasomatic component can consist of 0.5-1 wt% water bound in amphibole, antigorite and chlorite, ~0.2 wt% water plus potassium to form phlogopite, or ~5 wt% CO 2 plus Ca for carbonate, or a combination of these. Lithospheric temperatures that fit the seismic data are consistent with heat flow constraints, but most are lower than those inferred from xenolith geothermobarometry. The dispersion data require differences in Moho heat flux between individual cratons, and sublithospheric mantle temperatures that are 100-200°C less beneath Yilgarn, Slave and Finland than beneath Kaapvaal. Significant upward-increasing metasomatism by water and CO 2 -rich fluids is not only a plausible mechanism to explain the average seismic structure of cratonic lithosphere but such metasomatism may also lead to the formation of mid-lithospheric discontinuities and would contribute to the positive chemical buoyancy of cratonic roots. 1. Introduction The thermal and compositional structure of cratons, the stable continental cores that have survived for several billion years above a convecting mantle, is a long-standing enigma. Xenoliths brought up from the sub-cratonic lithospheric mantle have low contents of iron and incompatible elements, indicating that they represent residues left after the extraction of partial melts [Griffin et al., 1999a; Jordan, 1978]. The low compositional density resulting from the depletion in iron and garnet components may to a large extent balance out the high density due to low temperatures within the cratonic lithosphere. This makes the continental lithosphere, including the crust, close to neutrally buoyant with respect to the underlying mantle [Jordan, 1978; Mooney and Vidale, 2003; Poudjom Djomani et al., 2001]. However, buoyancy by itself cannot explain craton longevity [Doin et al., 1997; Lenardic and Moresi, 1999]. In addition, viscosities at least a factor 3-10 higher than surrounding mantle, often attributed to low contents of volatiles, are required to stabilise cratons against erosion by