Upscaling of geological elastic models for seismology – mémé

The approach is based on the non-periodic homogenization method. It can handle small scale inhomogeneities in any dimension and for any type of contrast. It is coupled with the spectral element method for the wave propagation part.

The main results to be expected is a 3D homogenization tool available to the scientific community.

The next perspective is, once the forward homogenization problem solved, to wok on the inverse problem to improve seismic imaging technique.

N.A.

Seismic waves are widely used to study the Earth interior at all scales, from the exploration geophysics one to the global earth scale, and to study seismic sources. Thanks to the introduction of powerful wave equation solvers like the Spectral Element Method (SEM) and the increasing power of computers, more and more efforts toward the use of the full waveform seismic signal in the seismic exploration industry and in the academic community are performed. In that context, the inhomogeneities of scales smaller or much smaller than the minimum wavelength used to explore the soil are a challenge. For the direct modeling, small scales are a problem because, for many modern numerical modeling techniques like the SEM, the necessary mesh of the fine structures is just impossible to design or lead to very high numerical costs. This mesh design problem is currently a major challenge in seismology and the strongest limitation to the use of SEM. For the inverse problem, small scales are a problem because they lead to local effects around the sources, around the receivers and around the free surface that are difficult to take into account with regular inversion of imaging techniques. Finally, for the interpretation aspect, small scales, by leading to effects like apparent anisotropy, smoothing of interfaces or source distortions, can lead to wrong interpretations of the inversion results. Different groups and scientific communities have been working on solutions to that problem for decades. In seismology solutions were found for layered media and research in solid mechanics has lead to the so-called two scale homogenization for periodic media theory. Nevertheless, no general solution for realistic non periodic media existed until the work of the leading team of this project (IPGP) during the ANR MUSE project (2006-2009) to extend the classical two scale homogenization from periodic to general non-periodic media. A patent on the results of this ANR has been filed by the CNRS. During the ANR MUSE project, a prototype program has been developed for the 2D case and has shown excellent results.
The objective of the first part of the present ANR proposal is to develop a complete 3D non-periodic homogenization solution and program able to upscale (or homogenize) any complex geological model, to adapt our existing SEM tool and to deliver these programs available to the research community.
The second objective is to apply the non-periodic homogenization to three interesting geophysical problems:
1) Source correction from local structures. One of the interest of the two scale homogenization is that it gives more than just an effective medium, it also gives correctors that take account of the local effects of the structure close to a receiver or to a source. We plan to apply this work to nuclear explosion monitoring.
2) Application to thin shallow structure effects on surface waves. The near surface has a large influence on the quality of land exploration-seismic data, mainly due to significant surface-wave energy and local structural complexity. By providing an effective view of complex thin shallow structures, the non periodic homogenization is a good solution for the direct and inverse problems involving such shallow structures.
3) Application to study the effective versus intrinsic anisotropy.
The 3 applications will be funded by each partners and the QUEST European training network.
This project will involve 4 complementary partners: the IPGP which has developed the non-periodic homogenization, the École polythechnique will bring its deep knowledge on periodic homogenization and especially on boundary layers, Schlumberger Cambridge Research will bring industrial perspectives and problematics and the CEA its knowledge on explosion monitoring.