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Some remarks on seismic wave attenuation and tidal dissipation

Shun-ichiro Karato

Yale University

Department of Geology & Geophysics

12/15 MR22B-012

Why Q?orbital evolution tidal heatingQ -> internal state

T, water, grain-size-----

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• 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)?

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Conditions of deformation (tele-)seismic wave propagation

tidal deformation

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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)

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Phenomenology

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Absorption band model

log t

models of anelasticity

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(for small Q )-1

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• 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

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“wet”

“dry”

Aizawa et al. (2008)Tan et al. (2001)

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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))

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Non-linear anelasticity?

• For , energy dissipation increases with strain (stress).

• Linear anelasticity for seismic wave propagation, but non-linear anelasticity for tidal dissipation?

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Frequency dependence of Q from geophysical/astronomical observations

tide (Goldreich and Soter, 1966)

seismic waves (+ Chandler wobble, free oscil.)

(Karato and Spetzler, 1990)

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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)

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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).

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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)?

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MgO (Getting et al., 1997)

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Deformation (generation of dislocations) enhances anelasticity

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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)

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Laboratory studies of Q

(on mantle minerals, olivine)

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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.

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Jackson et al. (2002)

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Orbital evolution and Q(Jeffreys, 1976)

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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)

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Depth variation of Q in Earth’s mantle