Deschamps, F. & Trampert, J. Mantle tomography and its relation to temperature and composition. Phys. Earth Planet. Inter. 140, 277–291 (2003).
Romanowicz, B. & Gung, Y. Superplumes from the core-mantle boundary to the lithosphere: implications for heat flux. Science 296, 513–516 (2002).
Dalton, C. A., Ekström, G. & Dziewonski, A. M. The global attenuation structure of the upper mantle. J. Geophys. Res. Solid Earth 113, B09303 (2008).
Karaoğlu, H. & Romanowicz, B. Inferring global upper-mantle shear attenuation structure by waveform tomography using the spectral element method. Geophys. J. Int. 213, 1536–1558 (2018).
Adenis, A., Debayle, E. & Ricard, Y. Attenuation tomography of the upper mantle. Geophys. Res. Lett. 44, 7715–7724 (2017).
Karato, S.-I. Importance of anelasticity in the interpretation of seismic tomography. Geophys. Res. Lett. 20, 1623–1626 (1993).
Faul, U. H. & Jackson, I. The seismological signature of temperature and grain size variations in the upper mantle. Earth Planet. Sci. Lett. 234, 119–134 (2005).
Faul, U. H. & Jackson, I. Transient creep and strain energy dissipation: an experimental perspective. Annu. Rev. Earth Planet. Sci. 43, 541–569 (2015).
Dannberg, J. et al. The importance of grain size to mantle dynamics and seismological observations. Geochem. Geophys. Geosyst. 18, 3034–3061 (2017).
Torsvik, T. H. et al. Deep mantle structure as a reference frame for movements in and on the Earth. Proc. Natl Acad. Sci. USA 111, 8735–8740 (2014).
Koelemeijer, P., Ritsema, J., Deuss, A. & van Heijst, H. J. SP12RTS: a degree-12 model of shear-and compressional-wave velocity for Earth’s mantle. Geophys. J. Int. 204, 1024–1039 (2016).
Trampert, J., Deschamps, F., Resovsky, J. & Yuen, D. Probabilistic tomography maps chemical heterogeneities throughout the lower mantle. Science 306, 853–856 (2004).
Lau, H. C. P. et al. Tidal tomography constrains Earth’s deep-mantle buoyancy. Nature 551, 321 (2017).
van Tent, R. et al. Reconciling 3-D mantle density models using recent normal-mode measurements and thermochemical convection modelling. In AGU Fall Meeting Abstracts, Vol. 2021, DI14A-05 (2021).
Richards, F. D., Hoggard, M. J., Ghelichkhan, S., Koelemeijer, P. & Lau, H. C. Geodynamic, geodetic, and seismic constraints favour deflated and dense-cored LLVPs. Earth Planet. Sci. Lett. 602, 117964 (2023).
Zhang, N., Zhong, S., Leng, W. & Li, Z.-X. A model for the evolution of the Earth’s mantle structure since the early Paleozoic. J. Geophys. Res. Solid Earth 115, B06401 (2010).
Cline II, C. J., Faul, U. H., David, E. C., Berry, A. J. & Jackson, I. Redox-influenced seismic properties of upper-mantle olivine. Nature 555, 355–358 (2018).
Qu, T., Jackson, I. & Faul, U. H. Low-frequency seismic properties of olivine-orthopyroxene mixtures. J. Geophys. Res. Solid Earth 126, e2021JB022504 (2021).
Romanowicz, B. Attenuation tomography of the Earth’s mantle: a review of current status. Pure Appl. Geophys. 153, 257–272 (1998).
Lawrence, J. F. & Wysession, M. E. Seismic evidence for subduction-transported water in the lower mantle. Geophys. Monogr. AGU 168, 251 (2006).
Hwang, Y. K. & Ritsema, J. Radial Qμ structure of the lower mantle from teleseismic body-wave spectra. Earth Planet. Sci. Lett. 303, 369–375 (2011).
Liu, C. & Grand, S. P. Seismic attenuation in the African LLSVP estimated from PcS phases. Earth Planet. Sci. Lett. 489, 8–16 (2018).
Deuss, A., Ritsema, J. & van Heijst, H. J. A new catalogue of normal-mode splitting function measurements up to 10 mHz. Geophys. J. Int. 193, 920–937 (2013).
Talavera-Soza, S. & Deuss, A. Constraining 3-D variations in mantle attenuation using normal modes: forward modelling and sensitivity tests. Geophys. J. Int. 233, 1097–1112 (2023).
Durek, J. J. & Ekström, G. A radial model of anelasticity consistent with long-period surface-wave attenuation. Bull. Seismol. Soc. Am. 86, 144–158 (1996).
Debayle, E., Bodin, T., Durand, S. & Ricard, Y. Seismic evidence for partial melt below tectonic plates. Nature 586, 555–559 (2020).
Connolly, J. A. 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).
Lau, H. C. & Faul, U. H. Anelasticity from seismic to tidal timescales: theory and observations. Earth Planet. Sci. Lett. 508, 18–29 (2019).
Barnhoorn, A., Jackson, I., Fitz Gerald, J., Kishimoto, A. & Itatani, K. Grain size-sensitive viscoelastic relaxation and seismic properties of polycrystalline MgO. J. Geophys. Res. Solid Earth 121, 4955–4976 (2016).
Webb, S., Jackson, I. & Gerald, J. F. Viscoelasticity of the titanate perovskites CaTiO3 and SrTiO3 at high temperature. Phys. Earth Planet. Inter. 115, 259–291 (1999).
Webb, S. & Jackson, I. Anelasticity and microcreep in polycrystalline MgO at high temperature: an exploratory study. Phys. Chem. Miner. 30, 157–166 (2003).
Glišović, P., Forte, A. M. & Ammann, M. W. Variations in grain size and viscosity based on vacancy diffusion in minerals, seismic tomography, and geodynamically inferred mantle rheology. Geophys. Res. Lett. 42, 6278–6286 (2015).
Ballmer, M. D., Houser, C., Hernlund, J. W., Wentzcovitch, R. M. & Hirose, K. Persistence of strong silica-enriched domains in the Earth’s lower mantle. Nat. Geosci. 10, 236–240 (2017).
Fei, H. et al. Variation in bridgmanite grain size accounts for the mid-mantle viscosity jump. Nature 619, 794–799 (2023).
Murakami, M., Ohishi, Y., Hirao, N. & Hirose, K. A perovskitic lower mantle inferred from high-pressure, high-temperature sound velocity data. Nature 485, 90–94 (2012).
Deschamps, F., Cobden, L. & Tackley, P. J. The primitive nature of large low shear-wave velocity provinces. Earth Planet. Sci. Lett. 349, 198–208 (2012).
Fei, H., Faul, U. H. & Katsura, T. The grain growth kinetics of bridgmanite at the topmost lower mantle. Earth Planet. Sci. Lett. 561, 116820 (2021).
Boioli, F. et al. Pure climb creep mechanism drives flow in Earth’s lower mantle. Sci. Adv. 3, e1601958 (2017).
Murakami, M., Hirose, K., Kawamura, K., Sata, N. & Ohishi, Y. Post-perovskite phase transition in MgSiO3. Science 304, 855–858 (2004).
Oganov, A. R. & Ono, S. Theoretical and experimental evidence for a post-perovskite phase of MgSiO3 in Earth’s D″ layer. Nature 430, 445–448 (2004).
Goryaeva, A. M., Carrez, P. & Cordier, P. Low viscosity and high attenuation in MgSiO3 post-perovskite inferred from atomic-scale calculations. Sci. Rep. 6, 34771 (2016).
Cobden, L., Thomas, C. & Trampert, J. in The Earth’s Heterogeneous Mantle (eds Khan, A. & Deschamps, F.) 391–440 (Springer, 2015).
Lekić, V., Cottaar, S., Dziewonski, A. M. & Romanowicz, B. Cluster analysis of global lower mantle tomography: a new class of structure and implications for chemical heterogeneity. Earth Planet. Sci. Lett. 357, 68–77 (2012).
Woodhouse, J. H. & Dahlen, F. A. The effect of a general aspherical perturbation on the free oscillations of the Earth. Geophys. J. Int. 53, 335–354 (1978).
Woodhouse, J. H. The coupling and attenuation of nearly resonant multiplets in the Earth’s free oscillation spectrum. Geophys. J. Int. 61, 261–283 (1980).
Masters, G., Laske, G. & Gilbert, F. Autoregressive estimation of the splitting matrix of free-oscillation multiplets. Geophys. J. Int. 141, 25–42 (2000).
Mäkinen, A. M. & Deuss, A. Normal mode splitting function measurements of anelasticity and attenuation in the Earth’s inner core. Geophys. J. Int. 194, 401–416 (2013).
Jagt, L. & Deuss, A. Comparing one-step full-spectrum inversion with two-step splitting function inversion in normal mode tomography. Geophys. J. Int. 227, 559–575 (2021).
Woodhouse, J. H. & Giardini, D. Inversion for the splitting function of isolated low order normal mode multiplets. Eos Trans. AGU 66, 300 (1985).
Dziewonski, A. M. & Anderson, D. L. Preliminary reference Earth model. Phys. Earth Planet. Inter. 25, 297–356 (1981).
Tarantola, A. & Valette, B. Generalized nonlinear inverse problems solved using the least squares criterion. Rev. Geophys. 20, 219–232 (1982).
Ritsema, J., van Heijst, H. J. & Woodhouse, J. H. Complex shear wave velocity structure imaged beneath Africa and Iceland. Science 286, 1925–1928 (1999).
Mooney, W., Laske, G. & Masters, G. CRUST5.1: a global model at 5 degrees by 5 degrees. J. Geophys. Res 102, 727–748 (1998).
Talavera-Soza, S. Observing Seismic Attenuation in the Earth’s Mantle and Inner Core Using Normal Modes. PhD thesis, Utrecht Univ. (2021); https://doi.org/10.33540/738.
Mégnin, C. & Romanowicz, B. The three-dimensional shear velocity structure of the mantle from the inversion of body, surface and higher-mode waveforms. Geophys. J. Int. 143, 709–728 (2000).
Dalton, C. A. & Faul, U. H. The oceanic and cratonic upper mantle: clues from joint interpretation of global velocity and attenuation models. Lithos 120, 160–172 (2010).
Irifune, T. & Ringwood, A. Phase transformations in a harzburgite composition to 26 GPa: implications for dynamical behaviour of the subducting slab. Earth Planet. Sci. Lett. 86, 365–376 (1987).
Palme, H. & Nickel, K. CaAl ratio and composition of the Earth’s upper mantle. Geochim. Cosmochim. Acta. 49, 2123–2132 (1985).
Perrillat, J.-P. et al. Phase transformations of subducted basaltic crust in the upmost lower mantle. Phys. Earth Planet. Inter. 157, 139–149 (2006).
Cobden, L., Goes, S., Cammarano, F. & Connolly, J. A. Thermochemical interpretation of one-dimensional seismic reference models for the upper mantle: evidence for bias due to heterogeneity. Geophys. J. Int. 175, 627–648 (2008).
Houser, C., Hernlund, J., Valencia-Cardona, J. & Wentzcovitch, R. Discriminating lower mantle composition. Phys. Earth Planet. Inter. 308, 106552 (2020).
Cobden, L. et al. Thermochemical interpretation of 1-D seismic data for the lower mantle: The significance of nonadiabatic thermal gradients and compositional heterogeneity. J. Geophys. Res. Solid Earth 114, B11309 (2009).
Stixrude, L. & Lithgow-Bertelloni, C. Thermodynamics of mantle minerals — I. Physical properties. Geophys. J. Int. 162, 610–632 (2005).
Stixrude, L. & Lithgow-Bertelloni, C. Thermodynamics of mantle minerals – II. Phase equilibria. Geophys. J. Int. 184, 1180–1213 (2011).
Raj, R. & Ashby, M. On grain boundary sliding and diffusional creep. Metall. Trans. 2, 1113–1127 (1971).
Raj, R. Transient behavior of diffusion-induced creep and creep rupture. Metall. Trans. 6, 1499–1509 (1975).
Kanamori, H. & Anderson, D. L. Importance of physical dispersion in surface wave and free oscillation problems. Rev. Geophys. 15, 105–112 (1977).
Beyreuther, M. et al. ObsPy: a Python toolbox for seismology. Seismol. Res. Lett. 81, 530–533 (2010).
Schneider, S., Talavera-Soza, S., Jagt, L. & Deuss, A. FrosPy: free oscillation Python toolbox for seismology. Seismol. Res. Lett. 93, 967–974 (2022).
Van Rossum, G. & Drake, F. L. Python 3 Reference Manual (CreateSpace, 2009).
Wessel, P., Smith, W. H. F., Scharroo, R., Luis, J. & Wobbe, F. Generic mapping tools: improved version released. Eos 94, 409–410 (2013).
Talavera-Soza, S. & Deuss, A. QS4L3: global 3D model of mantle attenuation using seismic normal modes. Zenodo https://doi.org/10.5281/zenodo.8247621 (2023).
Bird, P. An updated digital model of plate boundaries. Geochem. Geophys. Geosyst. 4, 1027 (2003).
Widmer-Schnidrig, R., Masters, G. & Gilbert, F. Spherically symmetric attenuation within the Earth from normal mode data. Geophys. J. Int. 104, 541–553 (1991).
Resovsky, J., Trampert, J. & van der Hilst, R. D. Error bars for the global seismic Q profile. Earth Planet. Sci. Lett. 230, 413–423 (2005).
Jordan, T. H. Global tectonic regionalization for seismological data analysis. Bull. Seismol. Soc. Am. 71, 1131–1141 (1981).
