Introduction/ Theory
Viscoelastic rheology and response/seismic signature
Maxwell solid
Kelvin-Voigt model
Standard linear solid
Burger’s model
Andrade model
Findlay, W.M., J.S. Lai, K. Onaran, (1989). Chapter 5. Linear viscoelastic constitutive
equations, in Creep and Relaxation of nonlinear viscoelastic materials, Dover Publications,
NY
Cooper, R.F. (2002), Seismic wave attenuation: Energy dissipation in viscoelastic
crystalline solids, in: Plastic Deformation of Minerals and Rocks, S.I. Karato and H.R. Wenk,
eds., Rev. Mineral. Geochem. 51, Chap. 9, pp 253-290.
Nowick, A.S., and B.S. Berry (1972) Anelastic Relaxation in Crystalline Solids, Academic
Press, San Diego CA.
Dispersion associated with attenuation
Liu, H.P., Anderson, D., Kanamori, H., (1976). Velocity dispersion due to anelasticity;
implications for seismology and mantle composition. Geophys. J. R. Astr. Soc. 47, 41–58.
Karato, S., (1993) The importance of anelasticity in the interpretation of seismic
tomography, Geophys. Res. Lett., 20, 1623-1626.
Transient – recoverable etc.
Seismological observations of attenuation
Coda Q
Lg
Phillips, W.W., and R.J. Stead (2008) Attenuation of Lg in the western US using the
USArray, Geophys. Res. Lett., 35, L07307, doi:10.1029/2007GL032926
Normal modes
Masters, G. and F. Gilbert, (1983) Attenuation in the Earth at low frequencies, Phil.
Trans. Roy. Soc. Lond. Series A, 308, 479-522.
Widmer, R., G. Masters, and F. Gilbert (1991) Spherically symmetric attenuation within
the Earth from normal mode data, Geophys. J. Int., 104, 541-553.
Roult, G. and E. Clevede, (2000) New refinements in attenuation measurements from
free-oscillation and surface-wave observations, Phys. Earth Planet. Int., 121, 1-37.
Surface waves – regional
Yang, Y., D.W. Forsyth, and D.S. Weeraratne, (2007) Seismic attenuation near the East
Pacific Rise and the origin of the low-velocity zone, Earth Planet. Sci. Lett., 258, 260-268,
doi:10.1016/j.epsl.2007.03.040.
Mitchell, B.J., (1995) Anelastic structure and evolution of the continental crust and
upper mantle from seismic surface wave attenuation, Rev. Geophys. 33, 441-462.
Lin, F.-C., V. C. Tsai, and M. H. Ritzwoller (2012a), The local amplification of surface
waves: a new observable to constrain elastic velocities, density, and anelastic attenuation,
J. Geophys. Res., 117, B06302.
Global surface waves
Dalton, C.A., and G. Ekstrom (2006), Global models of surface wave attenuation, J.
Geophys. Res., 111, B05317, doi:10.1029/2005JB003997.
Selby, N.D., and J.H. Woodhouse (2002) The Q structure of the upper mantle:
constraints from Rayleigh wave amplitudes, J. Geophys. Res., 107, 2097
Body waves
Ko, Y.-T., B.-Y. Kuo, and S-H. Hung, (2012) Robust determination of earthquake source
parameters and mantle attenuation, J. Geophys. Res., 117, B04304.
Doi:10.1029/2011JB008759
Ambient noise correlation
Lin, F.-C., M. H. Ritzwoller, and W. Shen (2011b), On the reliability of attenuation
measurements from ambient noise crosscorrelations, Geophys. Res. Lett., 38, L11303.
Lawrence, J. F., and G. A. Prieto (2011), Attenuation tomography of the western United
States from ambient seismic noise, J. Geophys. Res., 116, B06302.
Prieto, G. A., J. F. Lawrence, and G. C. Beroza (2009), Anelastic Earth structure from the
coherency of the ambient seismic field, J. Geophys. Res., 114, B07303.
Prieto, G. A., M. Denolle, J. F. Lawrence, and G. C. Beroza (2011), On amplitude
information carried by the ambient seismic field, C. R. Geosci., 343, 600-614.
Attempts at observing frequency dependence of Q
Anderson, D.L., and J.W. Given (1982) Absorption band Q model for the Earth, J
Geophys. Res., 87, 3893-3904.
Anderson, D.L., and J.B. Minster (1979) The frequency dependence of Q in the Earth
and implication for mantle rheology and Chandler wobble, Geophys. J. R. Astr. Soc., 58,
431-440.
Shito, A., S. Karato, and J. Park (2004) Frequency dependence of Q in Earth’s upper
mantle inferred from continuous spectra of body waves, Geophys. Res. Lett., 31, L12603,
doi:10.1029/2004GL019582.
Lekic, V., J. Matas, M. Panning, and B. Romanowicz, (2009) Measurement and
implications of frequency dependence of attenuation, Earth Planet. Sci. Lett., 282, 285-293.
Flanagan, M.P., and D.A. Wiens, (1998) Attenuation of broadband P and S waves in
Tonga: Observations of frequency dependent Q, Pure Appl. Geophys., 153, 345-375.
Scattering vs. intrinsic attenuation
Tectonic settings
Global – correlation with plate boundaries, cratons etc.
Resovsky, J., J. Trampert, R.D. Van der Hilst, (2005) Error bars for the global seismic Q
profile, Earth Planet. Sci. Lett., 230, 413-423.
Subduction zones – subducting plate, mantle wedge
Spreading centers
Lithosphere / asthenosphere
Karato, S., (2012) On the origin of the asthenosphere, Earth Planet. Sci. Lett., 321, 95-103,
doi:10.1016/j.epsl.2012.01.001
Laboratory measurements
McCarthy, C., Y. Takei, T. Hiraga, (2011) Experimental study of attenuation and dispersion
over a broad frequency range: 2. The universal scaling of polycrystalline materials, J.
Geophys. Res., 116, B09207, doi:10.1029/2011JB008384
Jackson, I., U.H. Faul, J.D. FitzGerald, B.H. Tan,(2004) Shear wave attenuation and
dispersion in melt-bearing olivine polycrystals: 1. Specimen fabrication and mechanical
testing, J. Geophys. Res., 109, B06201, doi:10.1029/2003JB002406.
Gribb, T.T., and R.F. Cooper (1998). Low-frequency shear attenuation in polycrystalline
olivine: Grain boundary diffusion and the physical significance of the Andrade model for
viscoelastic rheology, J. Geophys. Res. 103, 27267-27279.
Theory
Physical mechanisms of attenuation
Sundberg, M., and R.F. Cooper (2010) A composite viscoelastic model for incorporating
grain boundary sliding and transient diffusion creep; correlating creep and attenuation
responses for materials with a fine grain size, Philos. Mag. 90, 2817-2840,
doi:10.1080/14786431003746656.
Finite frequency kernels for attenuation
Temperature, melt, water content, grain size, viscosity
McCarthy, C. and Y. Takei, (2011) Anelasticity and viscosity of partially molten rock
analogue: Toward seismic detection of small quantities of melt, Geophys. Res. Lett., 38,
L18306, doi:10.1029/2011GL048776.
Hammond, W.C.,, and E.D. Humphreys, (2000) Upper mantle seismic wave attenuation:
effects of realistic partial melt distribution, J. Geophys. Res. 105, 10987-10999.
Schmeling, (1985) Numerical experiments on the influence of partial melt on elastic,
anelastic aand electric properties of rocks, part I., elasticity and anelasticity, Phys. Earth
Planet. Int., 41, 34-57.
Jackson, I., and U.H. Faul (2010), Grainsize-sensitive viscoelastic relaxation in olivine:
Towards a robust laboratory-based model for seismological application, Phys. Earth Planet.
Int., 183, 151-163, doi: 10.1016/j.pep.2010.09.005
Faul, U.H., J/D. Fitz Gerald, I. Jackson, (2004) Shear wave attenuation and dispersion in
melt-bearing olivine polycrystals: 2. Microstructrual interpretation and seismological
implications, J. Geophys. Res., 109 B06202, doi:10.1029/2003JB002407.
Faul, U.H., and I. Jackson, (2005) The seismological signature of temperature and grain
size variations in the upper mantle, Earth Planet. Sci. Lett., 234, 119-134.
Gribb, T.T., and R.F. Cooper, (2000) The effect of an equilibrated melt phase on the shear
creep and attenuation behavior of polycrystalline olivine, Geophys. Res. Lett., 27, 2341-2344.
Karato, S. and H. Jung (1998) Water, partial melting and the origin of seismic low velocity
and high attenuation zone in the upper mantle, Earth Planet. Sci. Lett., 157, 193-207.
Term Project
Comparison of coda Q estimates for old Pacific lithosphere vs. spectral shape
estimates vs. amplitude decay as function of distance