1. Thomas, P. C. et al. Enceladus’s measured physical libration requires a global subsurface ocean. Icarus 264, 37–47 (2016).

2. Čadek, O. et al. Enceladus’s internal ocean and ice shell constrained from Cassini gravity, shape, and libration data. Geophys. Res. Lett. 43, 5653–5660 (2016).

3. Beuthe, M., Rivoldini, A. & Trinh, A. Enceladus’s and Dione’s floating ice shells supported by minimum stress isostasy. Geophys. Res. Lett. 43, 10088–10096 (2016).

4. Le Gall, A. et al. Thermally anomalous features in the subsurface of Enceladus’s south polar terrain. Nat. Astron 1, 0063 (2017).

5. Postberg, F. et al. Sodium salts in E-ring ice grains from an ocean below the surface of Enceladus. Nature 459, 1098–1101 (2009).

6. Hsu, H.-W. et al. Ongoing hydrothermal activities within Enceladus. Nature 519, 207–210 (2015).

7. Sekine, Y. et al. High-temperature water–rock interactions and hydrothermal environments in the chondrite-like core of Enceladus. Nat. Commun 6, 8604 (2015).

8. Waite, J. H. et al. Cassini finds molecular hydrogen in the Enceladus plume: evidence for hydrothermal processes. Science 356, 155–159 (2017).

9. Porco, C. C. et al. Cassini observes the active south pole of Enceladus. Science 311, 1393–1401 (2006).

10. Spencer, J. R. et al. Cassini encounters Enceladus: background and the discovery of a south polar hot spot. Science 311, 1401–1405 (2006).

11. Souček, O., Hron, J., Běhounková, M. & Čadek, O. Effect of the tiger stripes on the deformation of Saturn’s moon Enceladus. Geophys. Res. Lett. 43, 7417–7423 (2016).

12. Běhounková, M., Souček, O., Hron, J. & Čadek, O. Plume activity and tidal deformation on Enceladus influenced by faults and variable ice shell thickness. Astrobiology 17, 941–954 (2017).

13. McKinnon, W. B. The shape of Enceladus as explained by an irregular core: implications for gravity, libration, and survival of its subsurface ocean. J. Geophys. Res. 118, 1775–1788 (2013).

14. Monteux, J., Collins, G. S., Tobie, G. & Choblet, G. Consequences of large impacts on Enceladus’ core shape. Icarus. 264, 300–310 (2016).

15. Neveu, M. & Rhoden, A. R. The origin and evolution of a differentiated Mimas. J. Geophys. Res. 296, 183–196 (2015).

16. Travis, B. J. & Schubert, G. Keeping Enceladus warm. Icarus 250, 32–42 (2015).

17. Roberts, J. H. The fluffy core of Enceladus. Icarus 258, 54–66 (2015).

18. Rollins, K. M., Evans, M. D., Diehl, N. B. & Daily, W. D. Shear modulus and damping relationships for gravels. J. Geotech. Geoenviron. Eng 124, 396–405 (1998).

19. Hedman, M. M. et al. An observed correlation between plume activity and tidal stresses on Enceladus. Nature 500, 182–184 (2013).

20. Nimmo, F., Porco, C. C. & Mitchell, C. Tidally modulated eruptions on Enceladus: Cassini ISS observations and models. Astron. J. 148, 46 (2014).

21. Běhounkovà, M. et al. Timing of water plume eruptions on Enceladus explained by interior viscosity structure. Nat. Geosci 8, 601 (2015).

22. Monnereau, M. & Dubuffet, F. Is Io’s mantle really molten? Icarus 158, 450–459 (2002).

23. Soderlund, K. M., Schmidt, B. E., Wicht, J. & Blankenship, D. D. Ocean-driven heating of Europa’s icy shell at low latitudes. Nat. Geosci 7, 16–19 (2014).

24. Grannan, A. M., Favier, B., Le Bars, M. & Aurnou, J. M. Tidally forced turbulence in planetary interiors. Geophys. J. Int. 208, 1690–1703 (2016).

25. Lainey, V. et al. New constraints on Saturn’s interior from Cassini astrometric data. Icarus 281, 286–296 (2017).

26. Fuller, J., Luan, J. & & Quataert, E. Resonance locking as the source of rapid tidal migration in the Jupiter and Saturn moon systems. Mon. Not. R. Astr. Soc. 458, 3867–3879 (2016).

27. Postberg, F. et al. The E ring in the vicinity of Enceladus. II. Probing the moon’s interior—the composition of E-ring particles. Icarus 193, 438–454 (2008).

28. Iess, L. et al. The gravity field and interior structure of Enceladus. Science 344, 78–80 (2014).

29. McKinnon, W. B. Effect of Enceladus’s rapid synchronous spin on interpretation of Cassini gravity. Geophys. Res. Lett. 42, 2137–2143 (2015).

30. Fountain, A. G. & Walder, J. S. Water flow through temperate glaciers. Rev. Geophys. 36, 299–328 (1998).

31. Johnson, J. W., Oelkers, E. H. & Helgeson, H. C. SUPCRT92: a software package for calculating the standard molal thermodynamic properties of minerals, gases, aqueous species, and reactions from 1 to 5000 bar and 0 to 1000 °C. Chem. Geol. 18, 899–947 (1992).

32. Johnson, J. W. & Norton, D. Critical phenomena in hydrothermal systems; state, thermodynamic, electrostatic, and transport properties of H 2 O in the critical region. Am. J. Sci. 291, 541–648 (1991).

33. Ishibashi, I. & Zhang, X. Unified dynamic shear moduli and damping ratios of sand and clay. Soils Found. 33, 182–191 (1993).

34. Fiscina, J. E. et al. Dissipation in quasistatically sheared wet and dry sand under confinement. Phys. Rev. E 86, 020103 (2012).

35. Wulff, A. M., Hashida, T., Watanabe, K. & Takahashi, H. Attenuation behaviour of tuffaceous sandstone and granite during microfracturing. Geophys. J. Int. 139, 395–409 (1999).

36. Brennan, A. J., Thusyanthan, N. I. & Madabhushi, S. P. Evaluation of shear modulus and damping in dynamic centrifuge tests. J. Geotech. Geoenviron. Eng 131, 1488–1497 (2005).

37. Seed, H. B., Wong, R. T., Idriss, I. M. & Tokimatsu, K. Moduli and damping factors for dynamic analyses of cohesionless soils. J. Geotech. Geoenviron. Eng 112, 1016–1032 (1986).

38. Segatz, M., Spohn, T., Ross, M. N. & Schubert, G. Tidal dissipation, surface heat flow, and figure of viscoelastic models of Io. Icarus 75, 187–206 (1988).

39. Tobie, G., Mocquet, A. & Sotin, C. Tidal dissipation within large icy satellites: Appli- cations to Europa and Titan. Icarus 177, 534–549 (2005).

40. Shibuya, S., Mitachi, T., Fukuda, F. & Degoshi, T. Strain rate effects on shear modulus and damping of normally consolidated clay. Geotech. Test. J. 18, 365–375 (1995).

41. Sun, J. I., Golesorki, R. & Seed, H. B. Dynamic Moduli and Damping Ratios for Cohesive Soils. (Earthquake Engineering Research Center, Univ, California, Berkeley, 1988). Report no. UCB/EERC-88/15.

42. Araei, A. A., Razeghi, H. R., Tabatabaei, S. H. & Ghalandarzadeh, A. Loading fre- quency effect on stiffness, damping and cyclic strength of modeled rockfill materials. Soil Dyn. Earthq. Eng. 33, 1–18 (2012).

43. Zhou, W., Chen, Y., Ma, G., Yang, L. & Chang, X. A modified dynamic shear modulus model for rockfill materials under a wide range of shear strain amplitudes. Soil Dyn. Earthq. Eng 92, 229–238 (2017).

44. Wichtmann, T., Niemunis, A. & Triantafyllidis, T. Strain accumulation in sand due to cyclic loading: drained triaxial tests. Soil Dyn. Earthq. Eng 25, 967–979 (2005).

45. Raad, L., Minassian, G. H. & Gartin, S. Characterization of saturated granular bases under repeated loads. Transp. Res. Rec. 369, 73–82 (1992).

46. 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).

47. Cole, D. M. A model for the anelastic straining of saline ice subjected to cyclic loading. Phil. Mag. A 72, 231–248 (1995).

48. Castillo-Rogez, J. C., Efroimsky, M. & Lainey, V. The tidal history of Iapetus: spin dynamics in the light of a refined dissipation model. J. Geophys. Res. 116, E09008 (2011).

49. Takeushi H., Saito M. in Methods in Computational Physics Vol. 1 (ed. Bolt, B. A.)217–295 (Academic, New York, 1972).

50. Saito, M. Some problems of static deformation of the Earth. J. Phys. Earth 22, 123–140 (1974).

51. Ricard, Y. in Mantle Dynamics. Treatise on Geophysics Vol. 7 (ed. Schubert, G.) 23–71 (Elsevier, Amsterdam, The Netherlands, 2015).

52. Kalousová, K., Souček, O., Tobie, G., Choblet, G. & Čadek, O. Ice melting and down- ward transport of meltwater by two-phase flow in Europa’s ice shell. J. Geophys. Res. 119, 532–549 (2014).

53. Palme, H. & O’Neill, H. S. C. in Mantle and Core. Treatise on Geochemistry Vol. 2 (ed. Carlson, R. W.) 1–38 (Elsevier, Amsterdam, The Netherlands, 2003).

54. Choblet, G. Modelling thermal convection with large viscosity gradients in one block of the cubed sphere. J. Comput. Phys. 205, 269–291 (2005).

55. Choblet, G., Čadek, O., Couturier, F. & Dumoulin, C. ŒDIPUS: a new tool to study the dynamics of planetary interiors. Geophys. J. Int 170, 9–30 (2007).

56. Goodman, J. C., Collins, G. C., Marshall, J. & Pierrehumbert, R. T. Hydrothermal plume dynamics on Europa: implications for chaos formation. J. Geophys. Res. 109, E03008 (2004).