Synthesis of a scalar wavelet intensity propagating through von Kármán-type random media: Radiative transfer theory using the Born and phase-screen approximations

Haruo Sato, Kentaro Emoto

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


In high-frequency seismograms of a small earthquake, coda waves continue for a long time and the S-wavelet is broadened as travel distance increases. Those phenomena can be interpreted as results of scattering by random inhomogeneities distributed in the solid earth. Recent measurements show that the power spectrum of the random medium heterogeneities decreases according to some power of wavenumber. As a mathematical model, we study the propagation of a scalar wavelet through von Kármán-type random media. Our objective is to propose a stochastic method to synthesize intensity time traces, the mean square amplitude traces, by using a few number of parameters statistically characterizing the random media. The most conventional method is known to use the Born approximation in the radiative transfer equation. However, as the centre wavenumber of a wavelet increases higher than the corner wavenumber, the Born approximation becomes inapplicable because the phase shift increases. We proposed a spectrum division method to avoid the difficulty in our previous papers. Taking the centre wavenumber as a reference, we divide the power spectrum into two components. The short-scale component is chosen to satisfy the applicable condition of the Born approximation, which leads to wide-angle scattering per volume. Here, we newly propose to use the phase screen approximation for the long-scale component, which leads to narrow-angle ray bending per length. We simultaneously introduce both the wide-angle scattering due to the short-scale component and the narrow-angle ray bending due to the long-scale component into the Monte Carlo simulation code in the framework of the radiative transfer theory. Synthesized wavelet intensity time traces show envelope broadening and peak delay with increasing travel distance and long lasting coda waves at a short distance. If the power spectrum is properly divided, synthesized intensity time traces well explain the averaged intensity time traces calculated by the finite difference simulation of wavelets in random media from the onset through the peak to coda for a wide dynamic range. The proposed method has a potential to adopt easily the spatial variation of randomness and intrinsic absorption.

Original languageEnglish
Pages (from-to)909-923
Number of pages15
JournalGeophysical Journal International
Issue number2
Publication statusPublished - 2018 Nov 1
Externally publishedYes


  • Seismic attenuation
  • Theoretical seismology
  • Wave propagation
  • Wave scattering and diffraction

ASJC Scopus subject areas

  • Geophysics
  • Geochemistry and Petrology


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