Abstract

The modeling of 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 allow the use of seismic elastic wave full waveforms in a limited frequency band to image the elastic properties of the earth. Nevertheless, inhomogeneities of scale much smaller the minimum wavelength of the wavefield associated to the maximum frequency of the limited frequency band, are still a challenge for both forward and inverse problems. In this work, we tackle the problem of elastic properties and topography varying much faster than the minimum wavelength. Using a non periodic homogenization theory and a matching asymptotic technique, we show how to compute effective elastic properties and local correctors and how to remove the fast variation of the topography. The implications on the homogenization theory on the inverse problem will be presented.