Performance and convergence of the non-periodic homogenization for the 3D elastic wave equation

Paul Cupillard and Yann Capdeville. ( 2017 )
in: 79th EAGE Conference & Exhibition, EAGE, Paris, France

Abstract

Seismic waves propagating in the Earth are affected by different sizes of heterogeneities. When modelling these waves using numerical methods, taking into account small heterogeneities is a challenge because it often requires important meshing efforts and leads to high, sometimes prohibitive, numerical costs. In the recent years, this problem has been overcome by applying the so-called homogenization technique to the elastic wave equation in non-periodic media. This technique allows to upscale the small heterogeneities and yields a smooth effective medium. In the present paper, we describe a 3D implementation of the method and we show that it can handle large and highly heterogeneous models with an acceptable speed and a good accuracy. This development opens the path to the correct account of the effect of small scale structures on the seismic wave propagation in complex 3D models of the subsurface.

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BibTeX Reference

@INPROCEEDINGS{,
    author = { Cupillard, Paul and Capdeville, Yann },
     title = { Performance and convergence of the non-periodic homogenization for the 3D elastic wave equation },
     month = { "jun" },
 booktitle = { 79th EAGE Conference & Exhibition },
      year = { 2017 },
  location = { Paris, France },
organization = { EAGE },
       doi = { 10.3997/2214-4609.201700524 },
  abstract = { Seismic waves propagating in the Earth are affected by different sizes of heterogeneities. When modelling these waves using numerical methods, taking into account small heterogeneities is a challenge because it often requires important meshing efforts and leads to high, sometimes prohibitive, numerical costs. In the recent years, this problem has been overcome by applying the so-called homogenization technique to the elastic wave equation in non-periodic media. This technique allows to upscale the small heterogeneities and yields a smooth effective medium. In the present paper, we describe a 3D implementation of the method and we show that it can handle large and highly heterogeneous models with an acceptable speed and a good accuracy. This development opens the path to the correct account of the effect of small scale structures on the seismic wave propagation in complex 3D models of the subsurface. }
}