The non-periodic homogenization theory in a nutshell

Paul Cupillard. ( 2016 )
in: 2016 RING Meeting, ASGA

Abstract

The homogenization technique developed in mechanics in the late seventies enables to compute the effective properties of finely-periodic materials for the elastic wave equation. In the recent years, this technique has been adapted to non-periodic media, allowing for the determination of long-wavelength equivalent properties of complex (i.e containing many different sizes of hetero- geneities) geological models. The resulting homogenized media only hold smooth variations of elastic properties which considerably ease the numerical computation of seismic wave propagation. They indeed prevent from complex meshes and extremely small time-steps associated with small heterogeneities. The goal of the present paper is to provide a digest of the non-periodic homogenization theory. By skipping some technical details of the whole derivation to focus on the main ideas and concepts of the theory, we hope to make the method understandable by a large number of geoscientists.

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BibTeX Reference

@INPROCEEDINGS{,
    author = { Cupillard, Paul },
     title = { The non-periodic homogenization theory in a nutshell },
 booktitle = { 2016 RING Meeting },
      year = { 2016 },
 publisher = { ASGA },
  abstract = { The homogenization technique developed in mechanics in the late seventies enables to compute
the effective properties of finely-periodic materials for the elastic wave equation. In the recent
years, this technique has been adapted to non-periodic media, allowing for the determination of
long-wavelength equivalent properties of complex (i.e containing many different sizes of hetero-
geneities) geological models. The resulting homogenized media only hold smooth variations of
elastic properties which considerably ease the numerical computation of seismic wave propagation.
They indeed prevent from complex meshes and extremely small time-steps associated with small
heterogeneities.
The goal of the present paper is to provide a digest of the non-periodic homogenization theory.
By skipping some technical details of the whole derivation to focus on the main ideas and concepts
of the theory, we hope to make the method understandable by a large number of geoscientists. }
}