Tomographic inversion of the peak delay times to reveal random velocity fluctuations in the lithosphere: Method and application to northeastern Japan

Tsutomu Takahashi, Haruo Sato, Takeshi Nishimura, Kazushige Obara

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46 Citations (Scopus)


This study proposes a new approach to estimate a 3-D distribution of power spectral density function (PSDF) of random velocity inhomogeneities in the lithosphere and applies this method to northeastern Japan. Our approach analyses the peak delay times of high-frequency S wave for microearthquakes at plural frequency bands on the basis of the Markov approximation for the parabolic wave equation, where the peak delay time is measured as the time lag from the S-wave onset to the maximal amplitude arrival. This peak delay time is appropriate to quantify the accumulated scattering effects due to random inhomogeneities without significant effect of the intrinsic absorption. The target region is divided into many blocks, each of which is characterized by a von Kármán-type PSDF with two parameters. One of the two parameters characterizes the spectral decay and another one constrains the absolute values of the PSDF at wavelengths shorter than the correlation distance. The peak delay times are calculated with these parameters along the unperturbed ray path by means of a recursive formula that is based on the Markov approximation for the parabolic wave equation. According to this formula, the spatial variation of spectral decay can be identified only by the frequency dependence of the peak delay times. Considering this characteristic, we propose a two-step approach to achieve a stable estimation of both parameters. The first step constructs an initial model with an explicit constraint for the spatial variation of frequency dependence of the peak delay times. The second step improves the first-step result by minimizing the residual of the peak delay times at all frequency bands. In the synthetic test, this two-step approach successfully improves the estimation of both parameters. We apply this method for seismograms (2-4 Hz, 4-8 Hz, 8-16 Hz and 16-32 Hz) observed in northeastern Japan and reveal that strongly inhomogeneous regions are related to the Quaternary volcano distribution and seismicity. We investigate the PSDFs of random inhomogeneities P(m) for the case in which the correlation distance is 5 km, where m is the wavenumber. At the depth of 40-60 km beneath most of the Quaternary volcanoes, P (m) are estimated as 0.017 m-3.5 km3 ∼0.035 m-4.0 km3 at 0.5 < m < 50 km-1. A remarkable characteristic of these PSDFs is the weak spectral decay in the study area. This characteristic means that lateral variation of the PSDF becomes significant at large wavenumbers. On the other hand, a high seismicity area in the western Hidaka region in Hokkaido is characterized by a steep spectral gradient as P(m) = 0.023 m-4.2 ∼ 0.050 m-4.2 km3 at 0.5 < m < 50 km-1. The PSDF in this region is larger than in its neighbours, regardless of the wavenumbers. From the comparison with other geophysical observations, we speculate that these strong inhomogeneities are generated by liquid inclusions and/or fractured structures. These regions commonly indicate stronger inhomogeneities than those in their surrounding regions for large wavenumbers (m > 15 km-1), and our approach detects that they are described by different combinations of the two parameters. It implies that the parameters of random inhomogeneities estimated by our approach are useful to examine the earth medium in relation to seismotectonic conditions in the crust and uppermost mantle.

Original languageEnglish
Pages (from-to)1437-1455
Number of pages19
JournalGeophysical Journal International
Issue number3
Publication statusPublished - 2009


  • Seismic tomography
  • Wave propagation
  • Wave scattering and diffraction

ASJC Scopus subject areas

  • Geophysics
  • Geochemistry and Petrology


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