Efficient Implementation of the 3D Homogenization for the Seismic Wave Equation

Paul Cupillard and Yann Capdeville and Arnaud Botella. ( 2014 )
in: Proc. 34th Gocad Meeting, Nancy

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 heterogeneities) 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. In this paper, we detail an efficient implementation of the non-periodic homogenization for 3D media. By efficient we here mean i) accurate and ii) fast. This second aspect has been honored in the recent months and therefore distinguishes the present implementation from the one showed last year. The current performance has been reached by implementing efficient search algorithms within our Finite Element code, by using OpenMP to speed up some time-consuming loops and by improving our distributed-memory calculation with a well-balanced domain decomposition. Therefore, computing the effective properties of a given complex medium and using these properties in a wave propagation solver is now much faster (possibly several orders of magnitude) than performing the wave propagation in the original medium directly. The efficiency of our code is illustrated by calculations in a finely-layered model (for which an analytical solution is available to compare with) and in a geological model extracted from gOcad.

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BibTeX Reference

@inproceedings{RUNKJRM28,
 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 heterogeneities) 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.
In this paper, we detail an efficient implementation of the non-periodic homogenization for 3D media. By efficient we here mean i) accurate and ii) fast. This second aspect has been honored in the recent months and therefore distinguishes the present implementation from the one showed last year. The current performance has been reached by implementing efficient search algorithms within our Finite Element code, by using OpenMP to speed up some time-consuming loops and by improving our distributed-memory calculation with a well-balanced domain decomposition. Therefore, computing the effective properties of a given complex medium and using these properties in a wave propagation solver is now much faster (possibly several orders of magnitude) than performing the wave propagation in the original medium directly. The efficiency of our code is illustrated by calculations in a finely-layered model (for which an analytical solution is available to compare with) and in a geological model extracted from gOcad. },
 author = { Cupillard, Paul AND Capdeville, Yann AND Botella, Arnaud },
 booktitle = { Proc. 34th Gocad Meeting, Nancy },
 title = { Efficient Implementation of the 3D Homogenization for the Seismic Wave Equation },
 year = { 2014 }
}