Journal of Seismology

, Volume 21, Issue 4, pp 837–855 | Cite as

The contribution of scattering to near-surface attenuation

  • Marco PilzEmail author
  • Donat Fäh


The rapid decrease of the acceleration spectral amplitude at high frequencies has widely been modeled by the spectral decay factor kappa (κ). Usually, the path-corrected component of κ, often called κ0, is believed to be a local and frequency-independent site characteristic, in turn representing attenuation related to waves propagating vertically through the very shallow layers beneath the study site. Despite the known relevance of κ0 in a wide range of seismological applications, most methods for its calculation do not fully consider the influence of the scattering component. To account for the scattering component, we present a summary of statistical observations of the seismic wavefield at sites of the Swiss seismic networks. The intrinsic properties of the wavefield show a clear dependency on the local shallow subsoil conditions with differences in the structural heterogeneity of the shallow subsoil layers producing different scattering regimes. Such deviations from the ballistic behavior (i.e., direct waves that sample only distinct directions) are indicative for local structural heterogeneities and the associated level of scatter. Albeit the attenuation term related to scattering depends nonlinearly on the intrinsic term, the results indicate that the commonly used explanation for the high-frequency decay spectrum might not be appropriate but involving the amount of scattering might allow better constrained estimates of κ0.


Attenuation Kappa Statistical methods 



We thank two anonymous reviewers for their very constructive reviews. The records used and the site characterization data regarding the stations were provided by the Swiss Seismological Service, ETH Zürich. The research was funded at different stages by the Swiss Federal Nuclear Safety Inspectorate (ENSI).


  1. Abercrombie RE (1997) Near-surface attenuation and site effects from comparison of surface and deep borehole recordings. Bull Seismol Soc Am 87:731–744Google Scholar
  2. Abercrombie RE (1998) A summary of attenuation measurements from borehole recordings of earthquakes: the 10 Hz transition problem. Pure Appl Geophys 153:475–487CrossRefGoogle Scholar
  3. Aki K (1980) Attenuation of shear-waves in the lithosphere for frequencies from 0.05 to 25 Hz. Phys Earth Planet Int 21:50–60CrossRefGoogle Scholar
  4. Anderson JG (1991) A preliminary descriptive model for the distance dependence of the spectral decay parameter in southern California. Bull Seismol Soc Am 81:2186–2193Google Scholar
  5. Anderson JG, Hough SE (1984) A model for the shape of the Fourier amplitude spectrum of acceleration at high frequencies. Bull Seismol Soc Am 74:1969–1993Google Scholar
  6. Aoi S, Kunugi T, Fujiwara H (2004) Strong-motion seismograph network operated by NIED: K-NET and KiK-net. J Japan Assoc Earthq Eng 4:65–74Google Scholar
  7. Aster RC, Shearer PM (1991) High-frequency borehole seismograms recorded in the san Jcinto fault zone, Southern California part 2. Attenuation and site effects. Bull Seismol Soc Am 81:1081–1100Google Scholar
  8. Atkinson GM, Boore DM (2006) Earthquake ground-motion prediction equations for eastern North America. Bull Seismol Soc Am 96:2181–2205CrossRefGoogle Scholar
  9. Bashan A, Bartsch R, Kantelhardt JW, Havlin S (2008) Comparison of detrending methods for fluctuation analysis. Physica A Stat Mech Appl 387:5080–5090CrossRefGoogle Scholar
  10. Bertero, M., P. Boccacci (1998). Introduction to inverse problems in imaging. CRC press, Bristol, UK.Google Scholar
  11. Bethmann F, Deichmann N, Mai PM (2012) Seismic wave attenuation from borehole and surface records in the top 2.5 km beneath the city of Basel, Switzerland. Geophys J Int 190:1257–1270CrossRefGoogle Scholar
  12. Boore DM (2003) Simulation of ground motion using the stochastic method. Pure Appl Geophys 160:635–676CrossRefGoogle Scholar
  13. Boore D (2005) On pads and filters: processing strong motion data. Bull Seismol Soc Am 95:745–750CrossRefGoogle Scholar
  14. Boore, D. M., K. W. Campbell (2017). Adjusting Central and eastern North America ground-motion intensity measures between sites with different reference-rock site conditions, manuscript in press, doi: 10.1785/0120160208.Google Scholar
  15. Boore DM, Joyner WB (1997) Site amplifications for generic rock sites. Bull Seismol Soc Am 87:327–341Google Scholar
  16. Campbell KW (2003) Prediction of strong ground motion using the hybrid empirical method and its use in the development of ground-motion (attenuation) relations in eastern North America. Bull Seismol Soc Am 93:1012–1033CrossRefGoogle Scholar
  17. Campbell KW (2009) Estimates of shear-wave Q and κ0 for unconsolidated and semiconsolidated sediments in eastern North America. Bull Seismol Soc Am 99:2365–2392CrossRefGoogle Scholar
  18. Campbell, K. W., Y. M. A. Hashash, B. Kim, A. R. Kottke, E. M. Rathje, W. J. Silva, J. R. Stewart (2014). Reference-rock site conditions for Central and Eastern North America. Part II: Attenuation (kappa) definition, Report PEER 2014–12, Pacific Earthquake Engineering Research Center, Berkeley, USA.Google Scholar
  19. Carpentier, S. F. A. (2007). On the estimation of stochastic parameters from deep seismic reflection data and its use in delineating lower crustal structure. PhD thesis, Utrecht University, Netherlands.Google Scholar
  20. Caserta A, Consolini G, De Michelis P (2007) Statistical features of the seismic noise field. Stud Geophys Geod 51:255–266CrossRefGoogle Scholar
  21. Chandler AM, Lam NTK, Tsang HH (2006) Near-surface attenuation modelling based on rock shear-wave velocity profile. Soil Dyn Earthq Eng 26:1004–1014CrossRefGoogle Scholar
  22. Chapman MC, Talwani P, Cannon RC (2003) Ground-motion attenuation in the Atlantic coastal plain near Charleston, South Carolina. Bull Seismol Soc Am 93:998–1011CrossRefGoogle Scholar
  23. Charrette, E. E. (1991). Elastic wave scattering in laterally inhomogeneous media, PhD thesis, Massachusetts Institute of Technology, Boston, USA.Google Scholar
  24. Chen Z, Ivanov PC, Hu K, Stanley HE (2002) Effect of nonstationarities on detrended fluctuation analysis. Phys Rev E 65:041107CrossRefGoogle Scholar
  25. Cormier VF (1982) The effect of attenuation on seismic body waves. Bull Seismol Soc Am 72:169–200Google Scholar
  26. Cotton F, Scherbaum F, Bommer JJ, Bungum H (2006) Criteria for selecting and adjusting ground-motion models for specific target regions: application to Central Europe and rock sites. J Seismol 10:137–156CrossRefGoogle Scholar
  27. Dainty AM (1981) A scattering model to explain seismic Q observations in the lithosphere between 1 and 30 Hz. Geophys Res Lett 8:1126–1128CrossRefGoogle Scholar
  28. Diehl T, Deichmann N, Clinton J, Kästli P, Cauzzi C, Kraft T, Behr Y, Edwards B, Guilhem A, Korger E, Hobiger M, Haslinger F, Fäh D, Wiemer S (2015) Earthquakes in Switzerland and surrounding regions during 2014. Swiss J Geosci 108:425–443CrossRefGoogle Scholar
  29. Douglas J, Bertil D, Roullé A, Dominique P, Jousset P (2006) A preliminary investigation of strong-motion data from the French Antilles. J Seismol 10:271–299CrossRefGoogle Scholar
  30. Douglas J, Gehl P, Bonilla LF, Scotti O, Régnier J, Duval AM, Bertrand E (2009) Making the most of available site information for empirical ground-motion prediction. Bull Seismol Soc Am 99:1502–1520CrossRefGoogle Scholar
  31. Douglas J, Gehl P, Bonilla LF, Gélis C (2010) A κ model for mainland France. Pure Appl Geophys 167:1303–1315CrossRefGoogle Scholar
  32. Edwards B, Fäh D, Giardini D (2011) Attenuation of seismic shear wave energy in Switzerland. Geophys J Int 185:967–984CrossRefGoogle Scholar
  33. Edwards B, Ktenidou OJ, Cotton F, Abrahamson N, Van Houtte C, Fäh D (2015) Epistemic uncertainty and limitations of the κ0 model for near-surface attenuation at hard rock sites. Geophys J Int 202:1627–1645CrossRefGoogle Scholar
  34. Einstein A (1905) Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen. Ann Phys 322:549–560CrossRefGoogle Scholar
  35. Faccioli, E., A. Tagliani (1987). Attenuation analysis of high frequency seismic waves in randomly heterogeneous rock media by finite difference simulations. In: Ground Motion and Engineering Seismology, A. S. Cakmak (ed.), 325–337.Google Scholar
  36. Faccioli E, Tagliani A, Paolucci R (1989) Effects of wave propagation in random earth media on the seismic radiation spectrum. In: Structural dynamics and soil-structure interaction. Proc. 4th int. Conf. on Soil Dyn. and Earthq. Eng 1:197–208Google Scholar
  37. Fernández AI, Castro RR, Huerta CI (2010) The spectral decay parameter kappa in northeastern Sonora, Mexico. Bull Seismol Soc Am 100:196–206CrossRefGoogle Scholar
  38. Frankel A (1982) The effects of attenuation and site response on the spectra of microearthquakes in the northeastern Caribbean. Bull Seismol Soc Am 72:1379–1402Google Scholar
  39. Frankel A, Clayton RW (1986) Finite difference simulations of seismic scattering: implications for the propagation of short-period seismic waves in the crust and models of crustal heterogeneity. J Geophys Res 91:6465–6489CrossRefGoogle Scholar
  40. Fu L, Li XJ (2016) The characteristics of high-frequency attenuation of shear waves in the Longmen Shan and adjacent regions. Bull Seismol Soc Am 106Google Scholar
  41. Gentili S, Franceschina G (2011) High frequency attenuation of shear waves in the southeastern alps and northern Dinarides. Geophys J Int 185:1393–1416CrossRefGoogle Scholar
  42. Gibson B (1991) Analysis of lateral coherency in wide-angle seismic images of heterogeneous targets. J Geophys Res 96:261–273Google Scholar
  43. Goff J, Jordan T (1988) Stochastic modeling of seafloor morphology: inversion of sea beam data for second-order statistics. J Geophys Res 93:589–608Google Scholar
  44. Hanks TC (1982) fmax. Bull Seismol Soc Am 72:1867–1879Google Scholar
  45. Hashash YM, Kottke AR, Stewart JP, Campbell KW, Kim B, Moss C, Nikolaou S, Rathje EM, Silva WJ (2014) Reference rock site condition for central and eastern North America. Bull Seismol Soc Am 104(2):684–701Google Scholar
  46. Hillers G, Ben-Zion Y, Landes M, Campillo M (2013) Interaction of microseisms with crustal heterogeneity: a case study from the San Jacinto fault zone area. Geochem Geophys Geosys 14:2182–2197CrossRefGoogle Scholar
  47. Holliger K, Carbonell R, Levander A (1992) Sensitivity of the lateral correlation function in deep seimic reflection data. Geophys Res Lett 19:2263–2266CrossRefGoogle Scholar
  48. Hough SE, Anderson JG (1988) High-frequency spectra observed at Anza, California: implications for Q structure. Bull Seismol Soc Am 78:692–707Google Scholar
  49. Hough SE, Anderson JG, Brune J, Vernon F, Berger J, Fletcher J, Haar L, Hanks T, Baker L (1988) Attenuation near Anza, California. Bull Seismol Soc Am 78:672–691Google Scholar
  50. Hurich C (1996) Statistical description of seismic reflection wavefields: a step towards quantitative interpretation of deep seismic reflection profiles. Geophys J Int 125:719–728CrossRefGoogle Scholar
  51. Hurst HE (1951) Long-term storage capacity of reservoirs. Trans Amer Soc Civil Eng 116:770–808Google Scholar
  52. Husen S, Kissling E, von Deschwanden A (2012) Induced seismicity during the construction of the Gotthard Base tunnel, Switzerland: hypocenter locations and source dimensions. J Seismol 16:195–213CrossRefGoogle Scholar
  53. Jin A, Mayeda K, Adams D, Aki K (1994) Separation of intrinsic and scattering attenuation in southern California using TERRAscope data. J Geophys Res 99:835–848Google Scholar
  54. Kanamori H (1967) Spectrum of short-period core phases in relation to the attenuation in the mantle. J Geophys Res 72:2181–2186CrossRefGoogle Scholar
  55. Kantelhardt JW, Zschiegner SA, Koscielny-Bunde E, Havlin S, Bunde A, Stanley HE (2002) Multifractal detrended fluctuation analysis of nonstationary time series. Phys A Stat Mech Appl 316:87–114CrossRefGoogle Scholar
  56. Kilb D, Biasi G, Anderson J, Brune J, Peng Z, Vernon FL (2012) A comparison of spectral parameter kappa from small and moderate earthquakes using southern California ANZA seismic network data. Bull Seismol Soc Am 102:284–300CrossRefGoogle Scholar
  57. Kinoshita S (2008) Deep-borehole-measured QP and QS attenuation for two Kanto sediment layer sites. Bull Seismol Soc Am 98:463–468CrossRefGoogle Scholar
  58. Knopoff L (1964) Q Rev Geophys Space Phys 2:625–660CrossRefGoogle Scholar
  59. Konno K, Ohmachi T (1998) Ground-motion characteristics estimated from spectral ratio between horizontal and vertical components of microtremor. Bull Seismol Soc Am 88:228–241Google Scholar
  60. Ktenidou OJ, Gélis C, Bonilla LF (2013) A study on the variability of kappa (κ) in a borehole: implications of the computation process. Bull Seismol Soc Am 103:1048–1068CrossRefGoogle Scholar
  61. Ktenidou OJ, Cotton F, Abrahamson NA, Anderson JG (2014) Taxonomy of κ: a review of definitions and estimation approaches targeted to applications. Seismol Res Lett 85:135–146CrossRefGoogle Scholar
  62. Ktenidou OJ, Abrahamson NA, Drouet S, Cotton F (2015) Understanding the physics of kappa (κ): insights from a downhole array. Geophys J Int 203:678–691CrossRefGoogle Scholar
  63. Lai TS, Mittal H, Chao WA, Wu YM (2016) A study on kappa value in Taiwan using borehole and surface seismic Array. Bull Seismol Soc Am 106:1509–1517CrossRefGoogle Scholar
  64. Laurendeau, A., P. Y. Bard, F. Hollender, V. Perron, L. Foundotos, O. J. Ktenidou, B. Hernandez (2016). Deviation of consistent hard rock (1000 < vs < 3000 m/s) GMPEs from surface and downhole recordings: Analysis of KiK-net data, Bull. Earthq. Eng., accepted manuscript.Google Scholar
  65. Lavallée, D., D. Schertzer, S. Lovejoy (1991). Non-Linear Variability in Geophysics, Scaling and Fractals, Kluwer Academic Publishers, Dordrecht, Netherlands.Google Scholar
  66. Lay, T., T. C. Wallace (1995). Modern global seismology. 521 pp., Academic press, San Diego, USA.Google Scholar
  67. Mandelbrot BB, Van Ness JW (1968) Fractional Brownian motions, fractional noises and applications. SIAM Rev 10:422–437CrossRefGoogle Scholar
  68. Mayor J, Margerin L, Calvet M (2014) Sensitivity of coda waves to spatial variations of absorption and scattering: radiative transfer theory and 2-D examples. Geophys J Int 197:1117–1137CrossRefGoogle Scholar
  69. Mehta K, Snieder R, Graizer V (2007a) Extraction of near-surface properties for a lossy layered medium using the propagator matrix. Geophys J Int 169:271–280CrossRefGoogle Scholar
  70. Mehta K, Snieder R, Graizer V (2007b) Downhole receiver function: a case study. Bull Seismol Soc Am 97:1396–1403CrossRefGoogle Scholar
  71. Menke W, Chen R (1984) Numerical studies of the coda falloff rate of multiply scattered waves in randomly layered media. Bull Seismol Soc Am 74:1605–1621Google Scholar
  72. O’Connell DR (1999) Replication of apparent nonlinear seismic response with linear wave propagation models. Science 283:2045–2050CrossRefGoogle Scholar
  73. Parolai S, Bindi D (2004) Influence of soil-layer properties on k evaluation. Bull Seismol Soc Am 94:349–356CrossRefGoogle Scholar
  74. Parolai S, Bindi D, Ansal A, Kurtulus A, Strollo A, Zschau J (2010) Determination of shallow S-wave attenuation by down-hole waveform deconvolution: a case study in Istanbul (Turkey). Geophys J Int 181:1147–1158Google Scholar
  75. Parolai S, Bindi D, Pilz M (2015) k0: the role of intrinsic and scattering attenuation. Bull Seismol Soc Am 105:1049–1052CrossRefGoogle Scholar
  76. Peng CK, Buldyrev SV, Goldberger AL, Havlin S, Sciortino F, Simons M, Stanley HE (1992) Long-range correlations in nucleotide sequences. Nature 356:168–170CrossRefGoogle Scholar
  77. Peng CK, Buldyrev SV, Havlin S, Simons M, Stanley HE, Goldberger AL (1994) Mosaic organization of DNA nucleotides. Phys Rev E 49:1685CrossRefGoogle Scholar
  78. Pilz M, Parolai S (2014) Statistical properties of the seismic noise field: influence of soil heterogeneities. Geophys J Int 199:430–440CrossRefGoogle Scholar
  79. Poggi V, Edwards B, Fäh D (2013) Reference S-wave velocity profile and attenuation models for ground-motion prediction equations: application to Japan. Bull Seismol Soc Am 103:2645–2656CrossRefGoogle Scholar
  80. Purvance MD, Anderson JG (2003) A comprehensive study of the observed spectral decay in strong-motion accelerations recorded in Guerrero, Mexico. Bull Seismol Soc Am 93:600–611CrossRefGoogle Scholar
  81. Rebollar CJ (1990) Estimates of shallow attenuation of the San Miguel fault, Baja California. Bull Seismol Soc Am 80:743–746Google Scholar
  82. Richards PG, Menke W (1983) The apparent attenuation of a scattering medium. Bull Seismol Soc Am 73:1005–1022Google Scholar
  83. Risken H (1989) The Fokker-Planck equation. Appl Opt 28:4496–4497Google Scholar
  84. Safak E (1997) Models and methods to characterize site amplification from a pair of records. Earthq Spec 13:97–129CrossRefGoogle Scholar
  85. Sato H, Fehler M, Wu RS (2002) Scattering and attenuation of seismic waves in the lithosphere. Int Geophys Series 81:195–208CrossRefGoogle Scholar
  86. Sato H, Fehler M, Maeda T (2012) Attenuation of high-frequency seismic waves. In: Seismic wave propagation and scattering in the heterogeneous earth. Springer, Berlin, Heidelberg, pp 153–184CrossRefGoogle Scholar
  87. SED, Swiss Seismological Service at ETH Zurich (2015). The site characterization database for seismic stations in Switzerland, Zurich, Federal Institute for Technology. doi:  10.12686/sed-stationcharacterizationdb (retrieved on 13 January 2016 from
  88. Shin, T. C. (1985). Lg and coda wave studies of Eastern Canada, PhD dissertation, Saint Louis University, Saint Louis, Missouri, USA.Google Scholar
  89. Silva, W. J. (1997), Characteristics of vertical strong ground motion for applications to engineering design, Proc. FHWA/NCEER workshop on the national representation of seismic ground motion for new and existing highway facilities, Technical Report NCEER-97-0010, National Center for Earthquake Engineering Research, Buffalo, New York, USA.Google Scholar
  90. Sivaji C, Nishizawa O, Kitagawa G, Fukushima Y (2002) A physical-model study of the statistics of seismic waveform fluctuations in random heterogeneous media. Geophys J Int 148:575–595CrossRefGoogle Scholar
  91. Tikhonov, A. N., V. I. Arsenin (1977). Solutions of ill-posed problems. Winston, Washington, DC, USA.Google Scholar
  92. Toro GR, Abrahamson NA, Schneider JF (1997) Model of strong ground motions from earthquakes in central and eastern North America: best estimates and uncertainties. Seismol Res Lett 68:41–57CrossRefGoogle Scholar
  93. Tsai CCP, Chen KC (2000) A model for the high-cut process of strong-motion accelerations in terms of distance, magnitude, and site condition: an example from the SMART 1 array, Lotung, Taiwan. Bull Seismol Soc Am 90:1535–1542CrossRefGoogle Scholar
  94. Van Houtte C, Drouet S, Cotton F (2011) Analysis of the origins of κ (kappa) to compute hard rock to rock adjustment factors for GMPEs. Bull Seismol Soc Am 101:2926–2941CrossRefGoogle Scholar
  95. Wang R (1999) A simple orthonormalization method for stable and efficient computation of Green’s functions. Bull Seismol Soc Am 89:733–741Google Scholar
  96. Witt A, Malamud BD (2013) Quantification of long-range persistence in geophysical time series: conventional and benchmark-based improvement techniques. Surv Geophys 34:541–651CrossRefGoogle Scholar
  97. Wu RS, Aki k (1988) Seismic wave scattering in three-dimensionally heterogeneous earth. In: Scattering and attenuations of seismic waves. Birkhäuser, Basel, pp1–6Google Scholar
  98. Zhang ZQ, Jones IP, Schriemer HP, Page JH, Weitz DA, Sheng P (1999) Wave transport in random media: the ballistic to diffusive transition. Phys Rev E 60:4843–4850CrossRefGoogle Scholar

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© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.Swiss Seismological ServiceSwiss Federal Institute of TechnologyZurichSwitzerland

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