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Large-Scale Simulation of Acoustic Waves in Random Multiscale Media

  • Olga N. Soboleva
  • Ekaterina P. Kurochkina
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 231)

Abstract

The effective coefficients in the problem of the acoustic wave propagation have been calculated for a multiscale 3D medium by using a subgrid modeling approach. The density and the elastic stiffness have been represented by the Kolmogorov multiplicative cascades with a log-normal probability distribution. The wavelength is assumed to be large as compared with the scale of heterogeneities of the medium. We consider the regime in which the waves propagate over a distance of the typical wavelength in source. If a medium is assumed to satisfy the improved Kolmogorov similarity hypothesis, the term for the effective coefficient of the elastic stiffness coincides with the Landau-Lifshitz-Matheron formula. The theoretical results are compared with the results of a direct 3D numerical simulation.

Keywords

Propagation of acoustic waves Subgrid modeling Multiplicative cascades 

Notes

Acknowledgements

The work was supported by the RFBR N15-01-01458.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Novosibisk State Technical UniversityNovosibirskRussia
  2. 2.The Novosibisk State University - Baker Hughes Joint Laboratory of The Multi-Scale Geophysics and MechanicsNovosibirsk 90Russia

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