12/15MR22B-01 1 Some remarks on seismic wave attenuation and tidal dissipation Shun-ichiro Karato Yale University Department of Geology & Geophysics

12/15MR22B-01 2 Why Q? orbital evolution tidal heatingQ -> internal state T, water, grain-size-----

12/15MR22B-01 3 What is the relation between seismological Q and tidal energy dissipation? –frequency, T-dependence of microscopic Q and tidal energy dissipation (phenomenology) Q and internal structure of a planet –What controls Q? T, water, strain, grain-size, ?? –Why is tidal dissipation of the Moon so large ? –What controls the Q of a giant planet (what controls the tidal evolution of extra-solar planets)?

12/15MR22B-01 4 Conditions of deformation (tele-)seismic wave propagation tidal deformation

12/15MR22B-01 5 Depth variation of tidal dissipation Energy dissipation occurs in most part in the deep interior of a planet. High-temperature non-elastic properties control tidal Q (similar to seismic waves but at lower frequencies and higher strain amplitude). (Peale and Cassen, 1978)

12/15MR22B-01 6 Phenomenology

12/15MR22B-01 7 Absorption band model log  t models of anelasticity

12/15MR22B-01 8 (for small Q )

12/15MR22B-01 9 Most of actual results for minerals, oxides and metals at high-T and low frequencies show weak frequency dependence of Q. (absorption band model) olivine MgO Fe (Jackson et al., 2002)(Getting et al. 1997) (Jackson et al., 2000)) Experimental observations on Q

12/15MR22B “wet” “dry” Aizawa et al. (2008) Tan et al. (2001)

12/15MR22B Non-linear anelasticity Amplitude of anelasticity increases with stress at high T (above a critical stress (strain)). This tendency is stronger at lower frequencies --> enhanced anelasticity for tidal dissipation? (Lakki et al. (1998))

12/15MR22B Non-linear anelasticity? For, energy dissipation increases with strain (stress). Linear anelasticity for seismic wave propagation, but non-linear anelasticity for tidal dissipation?

12/15MR22B Frequency dependence of Q from geophysical/astronomical observations tide (Goldreich and Soter, 1966) seismic waves (+ Chandler wobble, free oscil.) (Karato and Spetzler, 1990)

12/15MR22B Lunar Q model lunar T-z (selenotherm) model (Hood, 1986) Water-rich (Earth-like) deep mantle ? (Saal et al., 2008) Due to non-linear anelasticity ? Williams et al. (2001)

12/15MR22B conclusions Tidal energy dissipation and seismic Q are related but follow different frequency and temperature dependence (for some models). Tidal Q is likely smaller than seismic Q because of low frequency and high strain (no data on strain-dependent Q for Earth materials). Solid part of a planet can have large energy dissipation (low Q) at high temperatures. Influence of grain-size is modest, but the influence of water is likely very large (not confirmed yet). Low tidal Q of the Moon is likely due to high water content (+ high strain amplitude).

12/15MR22B Tidal Q lower Q than seismological Q low frequency, high strain non-linear anelasticity, distant- dependent Q ( )? time-dependent Q (t) (due to cooling of planets)?

12/15MR22B MgO (Getting et al., 1997)

12/15MR22B Deformation (generation of dislocations) enhances anelasticity

12/15MR22B Q in terrestrial planets Liquid portion –Small dissipation (Q~10 5 ) Liquid-solid mixture –Not large because a mixture is not stable under the gravitational field (liquid and solid tend to be separated) Solid portion –Large dissipation (Q~ )

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12/15MR22B Laboratory studies of Q (on mantle minerals, olivine)

12/15MR22B Conclusions Significant energy dissipation (Q -1 ) occurs in the solid part of terrestrial planets (due to thermally activated motion of crystalline defects). The degree of energy dissipation depends on temperature (pressure), water content (and grain-size) and frequency. Seismological observations on the distribution of Q can be interpreted by the distribution of temperature (pressure) and water content. Energy dissipation for tidal deformation is larger (smaller Q) than that for seismic waves. The degree of tidal dissipation depends on temperature (T/T m ) and water content of a terrestrial planet.

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12/15MR22B Jackson et al. (2002)

12/15MR22B Orbital evolution and Q (Jeffreys, 1976)

12/15MR22B Macroscopic processes causing Q Giant planets –Dynamic, wave-like mode of deformation –Very small energy dissipation (Q~10 5 ) Terrestrial planets –Quasi-static deformation –Elastic deformation, plastic flow, anelasticity –Large energy dissipation (Q~ )

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12/15MR22B Depth variation of Q in Earth’s mantle