Non periodic homogenisation for wave propagation and full waveform inverse problem in the earth

Yann Capdeville (Universite de Nantes)

G.205, Alan Turing Building,

The modelling of seismic elastic wave full waveform in a limited frequency
band is now well established with a set of efficient numerical methods
such as 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,
inhomogeneities of scale much smaller than the minimum wavelength are still
a challenge for both forward and inverse problems. In the first part of the presentation, we tackle the problem of elastic
properties varying much faster than the minimum wavelength for the forward problem in
seismology.
Using a non periodic homogenisation 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 and the homogenised model are
the same.

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