Seismic full waveform inversion models are homogenized models
The modelling of the seismic elastic wave full waveform in a limited frequency band is now well established with a set of efficient numerical methods like the spectral element, the discontinuous Galerking or the finite difference methods. The constant increase of computing power with time has now allowed the use of seismic elastic wave full waveforms in a limited frequency band to image the elastic properties of the earth. Nevertheless, heterogeneities of scale much smaller than the minimum wavelength are still a challenge for both forward and inverse problems.
In the first part of work, we tackle the problem of elastic properties varying much faster than the minimum wavelength for the forward problem in seismology. Using a non periodic homogenization theory we show how to compute effective elastic properties and local correctors, allowing to release the meshing problem and to reduce significantly the forward problem cost.
In the second part of the talk, we show in the simple layered model case, that the obtained elastic model from a full waveform inversion in a limited frequency band and the homogenized