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Surface wave analysis with beamforming


It is well known that off-great-circle path propagation causes a technical difficulty for surface wave analysis in higher frequency ranges. We propose a new approach that combines a beamforming technique and two-station phase velocity measurement to resolve this problem. Beamforming allows us to determine the correct azimuth of incoming surface waves which can be taken into account in phase velocity measurement. Beamforming results also support that a plane-wave approximation is mostly acceptable for frequencies up to about 50–60 mHz (millihertz), although evidence of multipathing is occasionally recognized in beamforming results as multiple peaks. Application of this correction scheme for Rayleigh-wave data in Southern California seems to make the largest impact on the results of azimuthal anisotropy. Effects are not large for frequencies up to 30 mHz but fast velocity axes in azimuthal anisotropy maps change significantly for higher frequencies.


  • Aki, K. and P. G. Richards, Quantitative Seismology, W. H. Freeman and Company, San Francisco, 1980.

    Google Scholar 

  • Baumont, D., A. Paul, G. Zandt, S. Beck, and H. Pedersen, Lithospheric structure of the central Andes based on surface wave dispersion, J. Geophys. Res., 107 B12, 2371, doi:10.1029/2001JB000345, 2002.

    Article  Google Scholar 

  • Bourova, E., I. Kassaras, H. A. Pedersen, T. Yanovskaya, and D. Hatzfeld, Constraints o absolute S velocities beneath the Aegean Sea from surface wave analysis, Geophys. J. Int., 160, 1006–1019, doi:10.1111/j.1365-246X.2005.02565.x, 2005.

    Article  Google Scholar 

  • Bruneton, M., V. Farra, H. A. Pedersen, and teh SVEKALAPKO Seismic Tomography Working Group, Non-linear surface wave phase velocity inversion based on ray theory, Geophys. J. Int., 151, 583–596, 2002.

    Article  Google Scholar 

  • Cotte, N., H. A. Pedersen, M. Campillo, V. Farra, and Y. Cansi, Off-greatcircle propagation of intermediate-period surface waves observed on a dense array in the French Alps, Geophys. J. Int., 142, 825–840, 2000.

    Article  Google Scholar 

  • Friedrich, W., E. Wielandt, and S. Strange, Non-plane geometries of seismic surface wavefields and their implications for regional surface wave tomography, Geophys. J. Int., 119, 931–948, 1994.

    Article  Google Scholar 

  • Johnson, Don H. and D. E. Dudgeon, Array Signal Processing, P T R Prentice-Hall Inc., Upper Saddle River, New Jersey, 1993.

    Google Scholar 

  • Laske, G. and G. Masters, Constraints on global phase velocity maps by long-period polarization data, J. Geophys. Res., 101 B7, 16059–16075, 1996.

    Article  Google Scholar 

  • McGarr, A., Amplitude variations of Rayleigh waves—Across a continental margin, Bull. Seism. Soc. Am., 59, 1281–1305, 1969a.

    Google Scholar 

  • McGarr, A., Amplitude variations of Rayleigh waves—Horizontal refraction, Bull. Seism. Soc. Am., 59, 1307–1334, 1969b.

    Google Scholar 

  • Pedersen, H. A., Impacts of non-plane waves on two-station measurements of phase velocities, Geophys. J. Int., 165, 279–287, doi:10.1111/j.1365-246X.2006.02893.x, 2006.

    Article  Google Scholar 

  • Pollitz, F., Regional velocity structure in nortehrn California from inversion of scattered seismic surface waves, J. Geophys. Res., 104,B7, 15043–15072, 1999.

    Article  Google Scholar 

  • Prindle, K., Souther California Surface Wave Analysis: Recovery of Three-dimensional S-wave Velocity Structure, the Finite Frequency, Off Great-Circle Propagation and Azimuthal Anisotropy, Ph.D. thesis, University of California, Santa Barbara, 2006.

    Google Scholar 

  • Prindle, K. and T. Tanimoto, Teleseismic Surface Wave study for S-wave velocity structure under an array: Southern California, Geophys. J. Int., 166, 601–621, 2006.

    Article  Google Scholar 

  • Tanimoto, T. and Don L. Anderson, Lateral Heterogeneity and Azimuthal Anisotropy of the Upper Mantle: Love and Rayleigh Waves 100–250s, J. Geophys. Res., 90, 842–1858, 1985.

    Google Scholar 

  • Tanimoto, T. and K. Prindle, Three-dimensional S-wave velocity structure in Southern California, Geophys. Res. Lett., 29, 8, 1–4, doi:1029/ 2001GL013486, 2002.

    Article  Google Scholar 

  • Tape, C., Q. Liu, and J. Tromp, Finite-frequency tomography using adjoint methods—Methodology and examples using membrane surface waves. Geophys. J. Int., 2006 (in press).

    Google Scholar 

  • Yang, Y. and D. W. Forsyth, Rayleigh wave phase velocitiers, small-scale convection, and azimuthal anisotropy beneath souther California, J. Geophys. Res., 111, B07306, doi:10.1029/2005JB004180, 2006.

    Google Scholar 

  • Zhao, L. and T. Jordan, STructural sensitivity of finite-frequency seismic waves: A full-wave approach, Geophys. J. Int., 165, 981–990, 2006.

    Article  Google Scholar 

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Correspondence to Toshiro Tanimoto.

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Tanimoto, T., Prindle, K. Surface wave analysis with beamforming. Earth Planet Sp 59, 453–458 (2007).

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Key words

  • Surface wave
  • wave propagation
  • earth structure