Introduction/ Theory

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