Statistical properties of reflection traveltimes in 3-D randomly inhomogeneous and anisomeric media

  1. Yu. A. Kravtsov1,
  2. T. M. Müller2,*,
  3. S. A. Shapiro2,
  4. S. Buske2

Article first published online: 20 AUG 2003

DOI: 10.1046/j.1365-246X.2003.02006.x

Issue

Geophysical Journal International

Geophysical Journal International

Volume 154, Issue 3, pages 841–851, September 2003

Additional Information

How to Cite

Kravtsov, Y. A., Müller, T. M., Shapiro, S. A. and Buske, S. (2003), Statistical properties of reflection traveltimes in 3-D randomly inhomogeneous and anisomeric media. Geophysical Journal International, 154: 841–851. doi: 10.1046/j.1365-246X.2003.02006.x

Author Information

  1. 1

    Space Research Institute, Russian Academy of Sciences, Profsoyuznaya 84/32, Moscow, 117997, Russia and Institute of Physics, Maritime University in Szczecin, Waly Chrobrego, 1/2, 70500 Szczecin, Poland. E-mail: kravtsov@wsm.szczecin.pl

  2. 2

    Fachrichtung Geophysik, Freie Universität Berlin, Malteserstr. 74-100, Haus D, 12249 Berlin, Germany. E-mails: shapiro@geophysik.fu-berlin.de; buske@geophysik.fu-berlin.de

* *Now at: Department of Exploration Geophysics, Curtin University of Technology, PO Box U1987, Perth, WA 6845, Australia. E-mail: tobias.muller@geophy.curtin.edu.au

Publication History

  1. Issue published online: 20 AUG 2003
  2. Article first published online: 20 AUG 2003
  3. Accepted 2003 April 3. Received 2003 January 6; in original form 2002 March 20

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Keywords:

  • double-passage effect;
  • random media;
  • regular refraction;
  • seismicity;
  • tomography;
  • traveltime

SUMMARY

We study the statistical properties of seismic reflection traveltimes in the presence of the double-passage effect (DPE) in order to characterize the inhomogeneities of the reflector overburden. A detailed analysis of the traveltime covariance function is presented for more general conditions than in the pioneering works by Touati, Iooss and Gaerets et al., namely 3-D geometry, quasi-homogeneous fluctuations of the medium parameters, anisomeric (i.e. statistically anisotropic fluctuations), longitudinal and transversal positions of receivers, and curved rays. The behaviour of the traveltime covariance function is elucidated by some numerical examples. It is shown, in particular, that at large offsets the effective longitudinal correlation scale associated with the ray trajectory is much larger than the transverse correlation scale and their product equals the product of the correlation lengths of the fluctuations of the medium.

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