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Source spectral phases of surface waves recovered from observed spectral amplitudes by using Hilbert transforms

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Spectral phases of surface waves radiated at the seismic source are recovered by means of the Hilbert transform of spectral amplitudes. Through numerical simulations as well as the study of an earthquake with well known focal mechanism, it is shown that the recovered phases satisfy a criterion of coherency, so that they can be used in an inversion process for the retrieval of the seismic moment tensor.

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  1. Aki, K. andRichards, P. G.,Quantitative Seismology. Theory and methods (Freeman, San Francisco, 1980).

  2. Bode, H. W.,Network Analysis and Feedback Amplifier Design (Van Nostrand, New York, 1945).

  3. Bolduc, P. M., Ellis, R. M. andRussell, R. D. (1972),Determination of the seismograph phase response from the amplitude response. Bull. Seism. Soc. Am.62, 1665–1672.

  4. Dziewonski, A. M. andAnderson, D. L. (1981),Preliminary reference earth model. Phys. Earth Planet. Int.25, 297–356.

  5. Forsyth, D. W. (1972),Mechanisms of earthquakes and plate motions in the East Pacific. Earth Planet. Sci. Letters17, 189–193.

  6. Lana, X. andCorreig, A. M. (1985),Determinación de mecanismos focales y profundidades focales mediante la inversión linealizada del tensor de momento sismico. Revista de Geofisica41, (In press).

  7. Lana, X. (1984),Càlcul dels elements del tensor de moment sismic, mitjangant tècniques d'inversiò de dades. Ph.D. Thesis, Universitat de Barcelona.

  8. McCowan, D. W. (1976),Moment tensor representation of surface waves. Geophys. J.R. Astr. Soc.44, 595–599.

  9. Melis, M. andAnasagasti, E. M.,Cálculo numérico. Métodos y aplicaciones (Rueda, Madrid, 1979).

  10. Mendiguren, J. A. (1977),Inversion of surface wave data in source mechanism studies. J. Geophys. Res.82, 889–894.

  11. Papoulis, A.,The Fourier integral and its applications (McGraw-Hill, New York, 1962).

  12. Patton, H. andAki, K. (1979),Bias in the estimate of the seismic moment tensor by the linear inversion method. Geophys. J.R. Astr. Soc. 59, 479–495.

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Lana, X., Correig, A.M. Source spectral phases of surface waves recovered from observed spectral amplitudes by using Hilbert transforms. PAGEOPH 123, 543–556 (1985). https://doi.org/10.1007/BF00877452

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  • Surface Wave
  • Focal Mechanism
  • Seismic Moment
  • Seismic Source
  • Moment Tensor