Homogenization for multi-scale problems in seismology: A treatment for seismic wave myopia in complex media, for tomography and for earthquake point sources
The Earth is heterogeneous on all scales, which has an impact on all the scientific disciplines involved, particularly seismology. The aim of this presentation is to show how this multi-scale aspect of the Earth affects the modelling of wave propagation, the modeling of the seismic source, seismic imaging methods and the interpretations of tomographic images. We will show that the two scale homogenization technique, extended to medium with no scale separation, is a good tool to deal with such a problem. It makes it possible to compute good quality effective media, to understand the link between tomographic images and possible fine scale elastic models as well as to understand the seismic source interactions with small heterogeneities (and more). In particular, we will show that homogenization can explain the strong difference between ground displacement and gradient of the displacement when it comes to sub-wavelength heterogeneities, which is an important topic in the light of the arrival of new seismic sensors such as rotational sensors or DAS (Distributed Acoustic sensors).