Upscaling 3D Complex Geological Media for the Elastic Wave Equation

@inproceedings{RUNKJRM23,
 abstract = { Seismic waves propagating in the Earth are affected by different sizes of heterogeneities. When modeling 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 (originally developed in mechanics for periodic media) to the elastic wave equation in non-periodic media. This technique allows to upscale the small heterogeneities and yields a smooth effective medium and effective equations. In this paper, the non-periodic homogenization is implemented in 3D for the first time. We first recall the main theoretical results of the method. Then, the 3D implementation is detailed. We finally test this implementation on a highly diffractive non-geological medium. This test validates our code and shows the high accuracy of the homogenized solution. Such a result opens the path to promising applications in forward modeling (validation of complex geomodels, study of site effects) and inverse problem (correct account for fine-scale priors, interpretation of small-scale induced anisotropy). },
 author = { Cupillard, Paul AND Capdeville, Yann },
 booktitle = { Proc. 33rd Gocad Meeting, Nancy },
 title = { Upscaling 3D Complex Geological Media for the Elastic Wave Equation },
 year = { 2013 }
}