Some remarks on seismic wave attenuation and tidal

Some remarks on seismic wave attenuation and tidal dissipation Shun-ichiro Karato Yale University Department of Geology & Geophysics 12/15 MR 22 B-01 1

Why Q? orbital evolution tidal heating. Q -> internal state T, water, grain-size----- 12/15 MR 22 B-01 2

• 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)? 12/15 MR 22 B-01 3

Conditions of deformation (tele-)seismic wave propagation tidal deformation 12/15 MR 22 B-01 4

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) 12/15 MR 22 B-01 5

Phenomenology 12/15 MR 22 B-01 6

models of anelasticity Absorption band model log t 12/15 MR 22 B-01 7

-1 (for small Q ) 12/15 MR 22 B-01 8

Experimental observations on Q olivine (Jackson et al. , 2002) Mg. O (Getting et al. 1997) Fe (Jackson et al. , 2000)) • Most of actual results for minerals, oxides and metals at high-T and low frequencies show weak frequency dependence of Q. (absorption band model) 12/15 MR 22 B-01 9

“wet” “dry” Aizawa et al. (2008) Tan et al. (2001) 12/15 MR 22 B-01 10

Non-linear anelasticity (Lakki et al. (1998)) 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? 12/15 MR 22 B-01 11

Non-linear anelasticity? • For strain (stress). , energy dissipation increases with • Linear anelasticity for seismic wave propagation, but non-linear anelasticity for tidal dissipation? 12/15 MR 22 B-01 12

Frequency dependence of Q from geophysical/astronomical observations tide (Goldreich and Soter, 1966) seismic waves (+ Chandler wobble, free oscil. ) (Karato and Spetzler, 1990) 12/15 MR 22 B-01 13

lunar T-z (selenotherm) model (Hood, 1986) Lunar Q model Water-rich (Earth-like) deep mantle ? (Saal et al. , 2008) Due to non-linear anelasticity ? Williams et al. (2001) 12/15 MR 22 B-01 14

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). 12/15 MR 22 B-01 15

Tidal Q • lower Q than seismological Q • low frequency, high strain • non-linear anelasticity, distantdependent Q ( )? • time-dependent Q (t) (due to cooling of planets)? 12/15 MR 22 B-01 16

Mg. O (Getting et al. , 1997) 12/15 MR 22 B-01 17

Deformation (generation of dislocations) enhances anelasticity 12/15 MR 22 B-01 18

Q in terrestrial planets • Liquid portion – Small dissipation (Q~105) • 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~10 -103) 12/15 MR 22 B-01 19

12/15 MR 22 B-01 20

Laboratory studies of Q (on mantle minerals, olivine) 12/15 MR 22 B-01 21

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/Tm) and water content of a terrestrial planet. 12/15 MR 22 B-01 22

12/15 MR 22 B-01 23

Jackson et al. (2002) 12/15 MR 22 B-01 24

Orbital evolution and Q (Jeffreys, 1976) 12/15 MR 22 B-01 25

Macroscopic processes causing Q • Giant planets – Dynamic, wave-like mode of deformation – Very small energy dissipation (Q~105) • Terrestrial planets – Quasi-static deformation – Elastic deformation, plastic flow, anelasticity – Large energy dissipation (Q~10 -103) 12/15 MR 22 B-01 26

12/15 MR 22 B-01 27

Depth variation of Q in Earth’s mantle 12/15 MR 22 B-01 28