On the use of upscaled models in Finite Difference wave simulators

in: 2017 RING Meeting, pages 4, ASGA

Abstract

The homogenization technique developed in mechanics in the late seventies enables to compute the e ective properties of nely-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 di erent sizes of heterogeneities) elastic models. The resulting homogenized media only hold smooth variations of elastic properties which considerably ease the numerical computation of 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 estimate the bene t of using homogenized models within Finite Di erence (FD) seismic wave simulations. We rst apply our homogenization code to com- plex subsurface models and we then compute reference (i.e accurate) seismic waveforms within the obtained smooth models using SW4. To quantify the bene t of this work ow in terms of compu- tation cost, we go back to the initial complex models and perform FD simulations by progressively re ning the grid until getting the reference waveforms. The bene t varies from one to three orders of magnitude depending on the set up.

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BibTeX Reference

@INPROCEEDINGS{Cupillard2017,
    author = { Cupillard, Paul and Mazuyer, Antoine and Irakarama, Modeste and Schuh-senlis, Melchior },
     title = { On the use of upscaled models in Finite Difference wave simulators },
 booktitle = { 2017 RING Meeting },
      year = { 2017 },
     pages = { 4 },
 publisher = { ASGA },
  abstract = { The homogenization technique developed in mechanics in the late seventies enables to compute the e ective properties of nely-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 di erent sizes of heterogeneities) elastic models. The resulting homogenized media only hold smooth variations of elastic properties which considerably ease the numerical computation of 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 estimate the bene t of using homogenized models within Finite Di erence (FD) seismic wave simulations. We rst apply our homogenization code to com- plex subsurface models and we then compute reference (i.e accurate) seismic waveforms within the obtained smooth models using SW4. To quantify the bene t of this work ow in terms of compu- tation cost, we go back to the initial complex models and perform FD simulations by progressively re ning the grid until getting the reference waveforms. The bene t varies from one to three orders of magnitude depending on the set up. }
}