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12/15 MR22B-011
Some remarks on seismic wave attenuation and tidal dissipation
Shun-ichiro Karato
Yale University
Department of Geology & Geophysics
12/15 MR22B-013
• 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 MR22B-015
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 MR22B-019
• 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
12/15 MR22B-0111
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))
12/15 MR22B-0112
Non-linear anelasticity?
• For , energy dissipation increases with strain (stress).
• Linear anelasticity for seismic wave propagation, but non-linear anelasticity for tidal dissipation?
12/15 MR22B-0113
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 MR22B-0114
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)
12/15 MR22B-0115
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 MR22B-0116
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)?
12/15 MR22B-0119
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 MR22B-0122
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 MR22B-0126
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)