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Alternative interpretations of horizontal to vertical spectral ratios of ambient vibrations: new insights from theoretical modeling

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Abstract

Different positions exist about the physical interpretation of horizontal to vertical spectral ratios (HVSR) deduced from ambient vibrations. Two of them are considered here: one is based on the hypothesis that HVSR are mainly conditioned by body waves approaching vertically the free surface, the other one assumes that they are determined by surface waves (Rayleigh and Love, with relevant upper modes) only. These interpretations can be seen as useful approximations of the actual physical process, whose reliability should be checked case-by-case. To this purpose, a general model has been here developed where ambient vibrations are assumed to be the complete wave field generated by a random distribution of independent harmonic point sources acting at the surface of a flat stratified visco-elastic Earth. Performances of the approximate interpretations and complete wave field models have been evaluated by considering a simple theoretical subsoil configuration and an experimental setting where measured HVSR values were available. These analyses indicate that, at least as concerns the subsoil configurations here considered, the surface-waves approximation seems to produce reliable results for frequencies larger than the fundamental resonance frequency of the sedimentary layer. On the other hand, the body waves interpretation provides better results around the resonance frequency. It has been also demonstrated that the HVSR curve is sensitive to the presence of a source-free area around the receiver and that most energetic contribution of the body waves component comes from such local sources. This dependence from the sources distribution implies that, due to possible variations in human activities in the area where ambient vibrations are carried on, significant variations are expected to affect the experimental HVSR curve. Such variations, anyway, only weakly affect the location of HVSR maximum that confirms to be a robust indicator (in the range of 10%) of the local fundamental resonance frequency.

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References

  • Aki K (1957) Space and time spectra of stationary stochastic waves, with special reference to microtremors. Bull Earthq Res Inst XXXV(3): 415–457

    Google Scholar 

  • Aki K, Richards PG (1980) Quantitative seismology—theory and methods, vol I. Freeman Company, San Francisco (USA)

  • Arai H, Tokimatsu K (2004) S-wave velocity profiling by inversion of microtremor H/V spectrum. Bull Seism Soc Am 94(1): 53–63

    Article  Google Scholar 

  • Arai H, Tokimatsu K (2005) S-wave velocity profiling by joint inversion of microtremor dispersion curve and horizontal-to-vertical (H/V) spectrum. Bull Seism Soc Am 95(5): 1766–1778

    Article  Google Scholar 

  • Bard P-Y (1999) Microtremor measurements: a tool for site effect estimation?. In: Irikura K, Kudo K, Okada H, Sasatani T (eds) The effects of surface geology on seismic motion. Balkema, Rotterdam, pp 1251–1279

    Google Scholar 

  • Ben-Menahem A, Singh SJ (2000) Seismic waves and sources. Dover Publications Inc, New York, p 1102

    Google Scholar 

  • Bonnefoy-Claudet S, Cotton F, Bard P-Y (2006a) The nature of noise wavefield and its applications for site effects studies: a literature review. Earth Sci Rev 9(2006): 205–227

    Article  Google Scholar 

  • Bonnefoy-Claudet S, Cornou C, Bard P-Y, Cotton F, Moczo P, Kristek J, Fäh D (2006b) H/V ratios: a tool for site effects evaluation. Results from 1-D noise simulations. Geoph J Int 167: 827–837

    Article  Google Scholar 

  • Bonnefoy-Claudet S, Köhler A, Cornou C, Wathelet M, Bard P-Y (2008) Effects of love waves on microtremor H/V ratio. Bull Seism Soc Am 98(1): 288–300

    Article  Google Scholar 

  • Chatelain J-L, Guillier B, Cara F, Duval A-M, Atakan K, Bard P-Y, The WP02 SESAME team (2008) Evaluation of the influence of experimental conditions on H/V results from ambient noise recordings. Bull Earthq Eng 6:33–74

    Google Scholar 

  • D’Amico V, Picozzi M, Baliva F, Albarello D (2008) Ambient noise measurements for preliminary site-effects characterization in the urban area of florence. Bull Seism Soc Am 98(3): 1373–1388. doi:10.1785/0120070231

    Article  Google Scholar 

  • Fäh D, Kind F, Giardini D (2001) A theoretical investigation of average H/V ratios. Geoph J Int 145: 535–549

    Article  Google Scholar 

  • Ferrari G, Albarello D, Martinelli G (2000) Tromometric measurements as a tool for crustal deformation monitoring. Seism Res Lett 71(5): 562–569

    Google Scholar 

  • Foti S (2003) Small-strain stiffness and damping ratio of Pisa clay from surface wave test. Geotechnique 53: 455–461

    Google Scholar 

  • Gallipoli MR, Mucciarelli M, Vona M (2008) Empirical estimate of fundamental frequencies and damping for Italian buildings. Earthq Eng Struct Dyn (in press)

  • Haghshenas E, Bard P-Y, Theodulis N, SESAME WP04 Team (2008) Empirical evaluation of microtremor H/V spectral ratio. Bull Earthq Eng 6: 75–108

    Article  Google Scholar 

  • Harkrider DG (1964) Surface waves in multilayered elastic media, part 1. Bull Seism Soc Am 54(2): 627–679

    Google Scholar 

  • Herak M (2008) ModelHVSR—a Matlab tool to model horizontal-to-vertical spectral ratio of ambient noise. Comp Geosci 34: 1514–1526

    Article  Google Scholar 

  • Hisada Y (1994) An efficient method for computing green’s functions for a layered half-space with sources and receivers at close depths. Bull Seism Soc Am 84(5): 1456–1472

    Google Scholar 

  • Jamiolowski M, Pepe MC (2001) Vertical yield stress for Pisa clay from piezocone tests. J Geotech Geoenv Eng ASCE 127: 893–897

    Article  Google Scholar 

  • Konno K, Ohmachi T (1998) Ground-motion characteristics estimated from spectral ratio between Horizontal and Vertical components of microtremor. Bull Seism Soc Am 88(1): 228–241

    Google Scholar 

  • Kramer SL (1996) Geotechnical earthquake engineering. Prentice Hall, New Jersey, p 653

    Google Scholar 

  • Lachet C, Bard P-Y (1994) Numerical and theoretical investigations on the possibilities and limitations of Nakamura’s technique. J Geophys Earth 42: 377–397

    Google Scholar 

  • Lamb H (1904) On the propagation of tremors over the surface of an elastic solid. Phil Trans R Soc Lond A 203: 1–42

    Article  Google Scholar 

  • Lai CG, Rix GJ (2002) Solution of the Rayleigh eigen problem in viscoelastic media. Bull Seism Soc Am 92(6): 2297–2309

    Article  Google Scholar 

  • Lo Presti DCF, Pallaro O, Cavallaro A, (1997) Damping ratio of soils from laboratory and in-situ tests. In: Proceedings of the 14th international conference on soil mechanics and fundamental engineering, pp 391–400

  • Lunedei E, Albarello D (2009a) On the seismic noise wave field in a weakly dissipative layered earth. Geophys J Int (in press)

  • Lunedei E, Albarello D (2009b) Theoretical HVSR curves from the complete wave field modelling of ambient vibrations in a weakly dissipative layered earth. Geophys J Int (submitted)

  • Malischewsky PG, Scherbaum F (2004) Love’s formula and H/V-ratio (ellipticity) of Rayleigh waves. Wave Motion 40: 57–67

    Article  Google Scholar 

  • Malischewsky PG, Scherbaum F, Lomnitz C, Thanh Tuan T, Wuttke F, Shamir G (2008) The domain of existence of prograde Rayleigh-wave particle motion for simple models. Wave Motion 45: 556–564

    Article  Google Scholar 

  • Mucciarelli M (1998) Reliability and applicability of Nakamura’s technique using microtremors: an experimental approach. J Earthq Eng 2: 625–638

    Article  Google Scholar 

  • Mucciarelli M, Gallipoli MR (2001) A critical review of 10 years of microtremor HVSR technique. Boll Geof Teor Appl 42: 255–266

    Google Scholar 

  • Nakamura Y (1989) A method for dynamic characteristics estimation of subsurface using microtremor on the ground surface. QR of RTRI 30(1): 25–33

    Google Scholar 

  • Nakamura Y (2000) Clear identification of fundamental idea of Nakamura’s technique and its applications. In: Proceedings of the 12th world conference on earthquake engineering. Auckland, New Zealand, paper 2656

  • Okada H (2003) The microtremor survey method. In: Geophysical monograph series 12. Society of Exploration Geophysicists, 135 pp

  • Parolai S, Facke A, Richwalski SM, Stempniewski L (2005a) Assessing the vibrational frequencies of the Holweide hospital in the city of Cologne (Germany) by means of ambient seismic noise analysis and FE modelling. Natural Hazard 34: 217–230

    Article  Google Scholar 

  • Parolai S, Picozzi M, Richwalski SM, Milkereit C (2005b) Joint inversion of phase velocity dispersion and H/V ratio curves from seismic noise recordings using a genetic algorithm, considering higher modes. Geophys Res Lett 32. doi:10.1029/2004GL021115

  • Peterson J (1993) Observation and modeling of background seismic noise. US Geol Survey, open file report. Albuquerque, pp 93–322

  • Picozzi M, Albarello D (2007) Combining genetic and linearized algorithms for a two-step joint inversion of Rayleigh wave dispersion and H/V spectral ratio curves. Geoph J Int 169: 189–200

    Article  Google Scholar 

  • Picozzi M, Parolai S, Albarello D (2005) Statistical analysis of noise horizontal-to-vertical spectral ratios (HVSR). Bull Seism Soc Am 95(5): 1779–1786. doi:10.1785/0120040152

    Article  Google Scholar 

  • Scherbaum F, Hinzen K-G, Ohrnberger M (2003) Determination of shallow shear wave velocity profiles in the Cologne, Germany area using ambient vibrations. Geoph J Int 152: 597–612

    Article  Google Scholar 

  • Site Effects Assessment using Ambient Excitations (SESAME) European project (2005) Deliverable D23.12, Guidelines for the implementation of the H/V spectral ratio technique on ambient vibrations: measurements, processing and interpretation, http://sesame-fp5.obs.ujf-grenoble.fr/SESTechnicalDoc.htm. Accessed March 2008

  • Tokimatsu K (1997) Geotechnical site characterization using surface waves. In: Proceedings of the 1st international conference on earthquake geotechnical engineering, vol 3, pp 1333–1368

  • Tsai NC (1970) A note on the steady-state response of an elastic half-space. Bull Seism Soc Am 60: 795–808

    Google Scholar 

  • Wenzel H, Pichler D (2005) Ambient vibration monitoring. Wiley, The Atrium, Southern Gate, Chichester, West Sussex, England (UK), p 291

    Book  Google Scholar 

Download references

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Authors and Affiliations

  1. Dipatimento di Scienze della Terra, Università di Siena, Via Laterina 8, 53100, Siena, Italy

    Dario Albarello & Enrico Lunedei

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  1. Dario Albarello
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  2. Enrico Lunedei
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Correspondence to Dario Albarello.

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Albarello, D., Lunedei, E. Alternative interpretations of horizontal to vertical spectral ratios of ambient vibrations: new insights from theoretical modeling. Bull Earthquake Eng 8, 519–534 (2010). https://doi.org/10.1007/s10518-009-9110-0

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  • DOI: https://doi.org/10.1007/s10518-009-9110-0

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