Skip to content


  • Article
  • Open Access

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

Earth, Planets and Space201453:BF03352357

  • Received: 14 January 2000
  • Accepted: 11 September 2000
  • Published:


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.


  • Rayleigh Wave
  • Inverse Fourier Transform
  • Impulse Response Function
  • Narrow Frequency Band
  • Wave Element