Synonyms
Seismic intrinsic attenuation
Definition
Linear viscoelastic attenuation. The fractional loss of seismic energy in a material in which elastic deformation (strain) induced by one cycle of a seismic wave or mode lags in time the applied stress associated with the wave or mode.
Apparent seismicattenuation. The loss of energy in a propagating seismic wave or standing mode due to viscoelasticity combined with the loss of scattered energy redistributed in time and space by heterogeneity.
Introduction
The amplitude of seismic waves decreases with increasing distance from earthquake, explosion, and impact sources. How this amplitude decrease occurs and how it depends on frequency of the seismic waves are fundamentally important to the efforts to describe Earth structure and seismic sources. The decay of amplitude of seismic waves with increasing distance of propagation through Earth is known as seismic wave attenuation. The attenuation occurring under high-temperature rheological...
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
Anderson DL (1989) Theory of the Earth. Blackwell Scientific Publications, Boston
Anderson DL, Given JW (1982) The absorption band Q model for the Earth. J Geophys Res 87:3893–3904
Bao X, Dalton CA, Jin G, Gaherty JB, Shen Y (2016) Imaging Rayleigh wave attenuation with USArray. Geophys J Int 206:241–259
Bataille K, Calisto I (2008) Seismic coda due to non-linear elasticity. Geophys J Int 172:572–580
Blanch JO, Robertsson JOA, Symes WW (1995) Optimally efficient constant Q modeling. Geophysics 60:176–184
Boatwright J, Choy G (1986) Teleseismic estimates of the energy radiated by shallow earthquakes. J Geophys Res 91:2095–2112
Calvet M, Margerin L (2008) Constraints on grain size and stable iron phases in the uppermost inner core from multiple scattering modeling of seismic velocity and attenuation. Earth Planet Sci Lett 267:200–212
Carpenter EW (1967) Teleseismic signal calculated for underground, underwater, and atmospheric explosions. Geophysics 32:17–32
Choy GL, Boatwright JL (1995) Global patterns of radiated seismic energy and apparent stress. J Geophys Res 100:18205–18228
Choy GL, Cormier VF (1986) Direct measurement of the mantle attenuation operator from broadband P and S waves. J Geophys Res 91:7326–7342
Cormier VF, Li X (2002) Frequency dependent attenuation in the inner core: Part II. A scattering and fabric interpretation. J Geophys Res 107(B12). https://doi.org/10.1029/2002JB1796
Cormier VF, Richards PG (1976) Comments on “The damping of core waves” by Anthony Qamar and Alfredo Eisenberg. J Geophys Res 81:3066–3068
Dalton CA, Ekstrom G, Dziewonski AM (2009) Global seismological shear velocity and attenuation: a comparison with experimental observations. Earth Planet Sci Lett 284:65–75
Delépine N, Lenti L, Bonnet G, Semblat J-F (2009) Nonlinear viscoelastic wave propagation: an extension of Nearly Constant Attenuation models. J Eng Mech (ASCE) 135(11):1305–1314
Der ZA, McElfresh TW, O’Dannell A (1982) An investigation of regional variations and frequency dependence of anelastic attenuation in the United States in the 0.5–4 Hz band. Geophys J R Astron Soc 69:67–100
Dziewonski AM, Anderson DL (1981) Preliminary reference Earth model. Phys Earth Planet Inter 24:297–356
Faul UH, Jackson I (2005) The seismological signature of temperature and grain size variations in the upper mantle. Earth Planet Sci Lett 234:119–134
Futterman WI (1962) Dispersive body waves. J Geophys Res 67:5279–5291
Gross B (1953) Mathematical structure of the theories of viscoelasticity. Hermann, Paris
Hong T-K, Wu R-S (2005) Scattering of elastic waves in geometrically anisotropic random media and its implication to sounding of heterogeneity in the Earth’s deep interior. Geophys J Int 163:324–338
Jackson I (1993) Progress in the experimental study of seismic attenuation. Annu Rev Earth Planet Sci 21:375–406
Jackson I (2007) Properties of rocks and minerals – physical origin of anelasticity and attenuation in rocks. In: Schubert G (ed) Treatise on geophysics, vol 2. Elsevier, Amsterdam, pp 493–525
Jackson DD, Anderson DL (1970) Physical mechanisms of seismic wave attenuation. Rev Geophys Space Phys 8:1–63
Jackson I, Webb S, Weston L, Boness D (2005) Frequency dependence of elastic wave speeds at high temperature: a direct experimental demonstration. Phys Earth Planet Inter 148:85–96
Kaelin B, Johnson LR (1998) Dynamic composite elastic medium theory. Part II. Three-dimensional media. J Appl Phys 84:5458–5468
Karato S-I, Jung H (1998) Water partial melting and the origin of the seismic low velocity zone in the upper mantle. Earth Planet Sci Lett 157:193–207
Knopoff L (1964) Q. Rev Geophys 2(4):625–660
Kohlstedt DL (2007) Properties of rocks and minerals – constitutive equations, rheological behavior, and viscosity of rocks. In: Schubert G (ed) Treatise on geophysics, vol 2. Elsevier, Amsterdam, pp 390–417
Lekić V, Matas J, Panning MP, Romanowicz B (2009) Measurement and implications of frequency dependence of attenuation. Earth Planet Sci Lett 282:295–203
Li X, Cormier VF (2002) Frequency dependent attenuation in the inner core: Part I. A viscoelastic interpretation. J Geophys Res 107(B12). https://doi.org/10.1029/2002JB001795
Liu H-P, Anderson DL, Kanamori H (1976) Velocity dispersion due to anelasticity: implications for seismology and mantle composition. Geophys J R Astron Soc 47:41–58
Makinen A, Deuss A, Redfern SAT (2014) Anisotropy of Earth’s inner core intrinsic attenuation from seismic normal mode models. Earth Planet Sci Lett 404:354–364
Margerin L (2013) Introduction to radiative transfer of seismic waves. In: Levander A, Nolet G (eds) Seismic Earth: array analysis of broadband seismograms. https://doi.org/10.1029/157GM14
Minster JB (1978) Transient and impulse responses of a one-dimensional linearly attenuating medium—I. Analytical results. Geophys J R Astron Soc 52:479–501
Minster B, Anderson DL (1981) A model of dislocation-controlled rheology for the mantle. Philos Trans R Soc Lond 299:319–356
Morozov IG (2015) On the relation between bulk and shear seismic dissipation. Bull Seismol Soc Am 105:3180–3188
Nowick AS, Berry BS (1972) Anelastic relaxation in crystalline solids. Academic, New York, p 677
O’Connell RJ, Budiansky B (1977) Viscoelastic properties of fluid-saturated cracked solids. J Geophys Res 82:5719–5735
O’Doherty RF, Anstey NA (1971) Reflections on amplitudes. Geophys Prospect 19:430–458
Panning MP, Romanowicz BA (2006) A three dimensional radially anisotropic model of shear velocity in the whole mantle. Geophys J Int 167:361–379
Ricard Y, Chambat F (2009) Seismic attenuation in a phase change coexistence loop. Phys Earth Planet Inter 176:124–131
Richards PG, Menke W (1983) The apparent attenuation of a scattering medium. Bull Seismol Soc Am 73:1005–1021
Robertsson JOA, Blanch JO, Symes WW (1994) Viscoelastic finite-difference modeling. Geophysics 59:1444–1456
Romanowicz B, Mitchell B (2015) Deep earth structure: Q of the earth from crust to core. In: Schubert G (ed) Treatise on Geophysics, vol 1. Elsevier, Amsterdam, pp 789–827
Roth EG, Wiens DA, Zhao D (2000) An empirical relationship between seismic attenuation and velocity anomalies in the upper mantle. Geophys Res Lett 27:601–604
Sato H, Fehler MC, Maeda T (2012) Seismic wave propagation and scattering in the heterogeneous Earth, 2nd edn. Springer, New York
Shearer, PM, Earle PS (2008) Observing and modeling elastic scattering in the deep Earth. Advances in geophysics, vol 50: Earth heterogeneity and scattering effects on seismic waves. 50 (Sato H, Fehler MC, Eds.)., Elsevier Academic, San Diego, pp 167–193. https://doi.org/10.1016/s0065-2687(08)00006-x
Silver PG (1996) Seismic anisotropy beneath the continents: probing the depths of geology. Annu Rev Earth Planet Sci 24:385–432
Stevenson DJ (1983) Anomalous bulk viscosity of two-phase fluids and implications for planetary interiors. J Geophys Res 88:2445–2455
Warren LM, Shearer PM (2000) Investigating the frequency dependence of mantle Q by stacking P and PP spectra. J Geophys Res 105(B11):25391–25402
Zener C (1960) Elasticity and anelasticity of metals. The University of Chicago Press, Chicago
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this entry
Cite this entry
Cormier, V.F. (2021). Seismic Viscoelastic Attenuation. In: Gupta, H.K. (eds) Encyclopedia of Solid Earth Geophysics. Encyclopedia of Earth Sciences Series. Springer, Cham. https://doi.org/10.1007/978-3-030-58631-7_55
Download citation
DOI: https://doi.org/10.1007/978-3-030-58631-7_55
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-58630-0
Online ISBN: 978-3-030-58631-7
eBook Packages: Earth and Environmental ScienceReference Module Physical and Materials ScienceReference Module Earth and Environmental Sciences