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Nonstationary ray decomposition in a homogeneous half space

Abstract

Amethod for decomposing an SH-wave at the surface into the instantaneous power of shearing strain associated with rays in a homogeneous half space as a function of lapse time t and depth time τ, which is the travel time for the depth direction, is demonstrated. The instantaneous power in the (t, τ) space shows local maxima at the intersections of up-coming and down-going rays, which correspond to the velocity boundaries of the real layered structure beneath the site. Thus, the proposed method provides a tool for estimating the velocity boundaries of real layered structure from only surface recordings. The estimated results obtained by applying the proposed method to strong-motion data recorded at two Kanto sediment sites are in good agreement with the velocity boundaries previously determined by means of down-hole methods.

References

  • Claasen, T. A. C. M. and W. F. G. Mecklenbrauker, The Wigner distribution—A tool for time-frequency signal analysis. Part I: Continuous-time signals, Philips J. Res., 35, 217–250, 1980a.

    Google Scholar 

  • Claasen, T. A. C. M. and W. F. G. Mecklenbrauker, The Wigner distribution—A tool for time-frequency signal analysis. Part II: Discrete-time signals, Philips J. Res., 35, 276–300, 1980b.

    Google Scholar 

  • Claerbout, J., Synthesis of a layered medium from its acoustic transmission response, Geophysics, 33, 264–269, 1968.

    Article  Google Scholar 

  • Goupillaud, P., An approach to inverse filtering of near surface layer effects from seismic records, Geophysics, 25, 754–760, 1961.

    Article  Google Scholar 

  • Huang, N. E., Z. Shen, S. R. Long, M. C. Wu, H. H. Shin, Q. Zheng, N. Yen, C. C. Tung, and H. H. Liu, The empirical mode decomposition and Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. R. Soc. Lond., A454, 903–995, 1998.

    Article  Google Scholar 

  • Huang, N. E., C. C. Chen, K. Huang, L. W. Salvino, S. R. Long, and K. L. Fan, A new spectral representation of earthquake data: Hilbert spectral analysis of Station TCU129, Chi-Chi, Taiwan, 21 September 1999, Bull. Seismol. Soc. Am., 91, 1310–1338, 2001.

    Article  Google Scholar 

  • Kinoshita, S., A statistical method for the estimation of wave transfer function, Proc. JSCA, 313, 1–11, 1981 (in Japanese).

    Google Scholar 

  • Kinoshita, S., Propagation of total reflected plane SH pulses in a dipping layer, Zisin, 38, 597–608, 1985 (in Japanese).

    Google Scholar 

  • Kinoshita, S., A stochastic method for investigating site effects by means of a borehole array—SH and Love waves, Bull. Seismol. Soc. Am., 89, 484–500, 1999.

    Google Scholar 

  • Kinoshita, S., Deep-borehole-measured Qp and Qs attenuation for two Kanto sediment layer site, Bull. Seismol. Soc. Am., 98, 463–468, 2008a.

    Article  Google Scholar 

  • Kinoshita, S., Tilt measurement using broadband velocity seismograms, Bull. Seismol. Soc. Am., 98, 1887–1897, 2008b.

    Article  Google Scholar 

  • Kinoshita, S. and M. Ohike, Coherency characteristics of body waves traveling in a sedimentary layer—basement system in the Kanto region, Japan, Bull. Seismol. Soc. Am., 96, 165–175, 2006.

    Article  Google Scholar 

  • Kinoshita, S., H. Ishikawa, and T. Satoh, Tilt motions recorded at two WISE sites for the 2003 Tokachi-Oki earthquake (M8.3), Bull. Seismol. Soc. Am., 99, 1251–1260, 2009.

    Article  Google Scholar 

  • Kobori, T. and R. Minai, One-dimensional wave-transfer functions of linear visco-elastic multi-layered half-space, Bull. Disas. Prev. Res. Inst., Kyoto Univ., 18, 27–64, 1969.

    Google Scholar 

  • Levinson, N., The Wiener RMS error criterion in filter design and prediction, J. Math. Phys., 25, 261–278, 1947.

    Article  Google Scholar 

  • Nakahara, H., Theoretical background of retrieving Green’s function by cross-correlation: one-dimensional case, Geophys. J. Int., 165, 719–728, 2006.

    Article  Google Scholar 

  • Okada, Y., K. Kasahara, S. Hori, K. Obara, S. Sekiguchi, H. Fujiwara, and S. Aoi, Recent progress of seismic observation networks in Japan—Hinet, F-net, K-NET and KiK-net—, Earh Planets Space, 56, xv–xxviii, 2004.

    Article  Google Scholar 

  • Yamamizu, F., Seismic wave velocity structures in Kanto area as revealed by the crustal activity observation well VSP, Technical note of the National Research Institute for Earth Science and Disaster Prevention, 251, 1–75, 2004 (in Japanese).

    Google Scholar 

  • Yamamizu, F., H. Takahashi, N. Goto, and Y. Ohta, Shear wave velocities in deep soil deposits. Part 3, Zisin, 34, 465–479, 1980 (in Japanese).

    Google Scholar 

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Correspondence to Shigeo Kinoshita.

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Kinoshita, S. Nonstationary ray decomposition in a homogeneous half space. Earth Planet Sp 61, 1297–1312 (2009). https://doi.org/10.1186/BF03352983

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  • DOI: https://doi.org/10.1186/BF03352983

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