- Open Access
Nonstationary ray decomposition in a homogeneous half space
Earth, Planets and Space volume 61, pages1297–1312(2009)
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.
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.
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.
Claerbout, J., Synthesis of a layered medium from its acoustic transmission response, Geophysics, 33, 264–269, 1968.
Goupillaud, P., An approach to inverse filtering of near surface layer effects from seismic records, Geophysics, 25, 754–760, 1961.
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.
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.
Kinoshita, S., A statistical method for the estimation of wave transfer function, Proc. JSCA, 313, 1–11, 1981 (in Japanese).
Kinoshita, S., Propagation of total reflected plane SH pulses in a dipping layer, Zisin, 38, 597–608, 1985 (in Japanese).
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.
Kinoshita, S., Deep-borehole-measured Qp and Qs attenuation for two Kanto sediment layer site, Bull. Seismol. Soc. Am., 98, 463–468, 2008a.
Kinoshita, S., Tilt measurement using broadband velocity seismograms, Bull. Seismol. Soc. Am., 98, 1887–1897, 2008b.
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.
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.
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.
Levinson, N., The Wiener RMS error criterion in filter design and prediction, J. Math. Phys., 25, 261–278, 1947.
Nakahara, H., Theoretical background of retrieving Green’s function by cross-correlation: one-dimensional case, Geophys. J. Int., 165, 719–728, 2006.
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.
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).
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).
About this article
Cite this article
Kinoshita, S. Nonstationary ray decomposition in a homogeneous half space. Earth Planet Sp 61, 1297–1312 (2009). https://doi.org/10.1186/BF03352983
- Ray decomposition
- instantaneous power
- velocity discontinuity