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Autoregressive modeling of transfer functions in frequency domain to determine complex travel times

Earth, Planets and Space volume 53, pages 3–11 (2001)Cite this article

Abstract

We present a method to determine the complex travel times of impulses in the time domain on the basis of an autoregressive (AR) modeling of superimposed sinusoids in a finite complex series in the frequency domain. We assume that the complex frequency series consists of signals represented by a complex AR equation with additional noise. The AR model in the frequency domain corresponds to a complex Lorentzian in the time domain. In a similar way to the Sompi or extended Prony method, the complex travel times are given by solutions of a characteristic equation of complex AR coefficients, which are obtained as the eigenvector corresponding to a minimum eigenvalue in an eigenvalue problem of non-Toeplitz autocovariance matrix of the complex series. Our method is tested for synthetic frequency series of transfer functions, which show that (1) the complex travel times of closely adjacent pulses in the time domain are clearly resolved, and that (2) the frequency dependence of the complex travel times for physical and structural dispersions is precisely determined by the analysis within a narrow frequency window. These results demonstrate the usefulness of our method with high resolvability and accuracy in the analysis of impulse sequences.

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Author notes

  1. Hiroyuki Kumagai

    Present address: National Research Institute for Earth Science and Disaster Prevention, Tsukuba, Japan

Authors and Affiliations

  1. Department of Earth and Planetary Sciences, Nagoya University, Nagoya, Japan

    Yoko Hasada

  2. Research Center for Seismology and Volcanology, Nagoya University, Nagoya, Japan

    Hiroyuki Kumagai

  3. Tono Geoscience Center, Toki, Japan

    Mineo Kumazawa

Authors
  1. Yoko Hasada
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  2. Hiroyuki Kumagai
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  3. Mineo Kumazawa
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Correspondence to Yoko Hasada.

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Hasada, Y., Kumagai, H. & Kumazawa, M. Autoregressive modeling of transfer functions in frequency domain to determine complex travel times. Earth Planet Sp 53, 3–11 (2001). https://doi.org/10.1186/BF03352357

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