Validity of the acoustic approximation for elastic waves in heterogeneous media

International audienceThe acoustic approximation of elastic waves is a very common approximation in exploration geophysics. The interest of the acoustic approximation in the inverse problem context lies in the fact that it leads to a much lower numerical cost than for the elastic problem. Nevertheless , the Earth is not an acoustic body and it has been shown in the past that this approximation is not without drawbacks mainly because P to S energy conversion and anisotropy cannot be easily modelled. Here, we study a different issue of this approximation related to small size heterogeneities with respect to the minimum wavelength of the wavefield. We first numerically show that elastic and acoustic waves behave differently with respect to small scale heterogeneities, introducing not only differences in amplitudes but also in phase between elastic and acoustic signals. We give then physical and mathematical interpretations of this phenomenon, showing the different nature of elastic and acoustic wave propagation and leading to the conclusion that, in rough media, acoustic waves can only be a poor quality approximation of elastic waves. Interestingly , we also show that, in the acoustic case, small scale heterogeneities give rise to natural acoustic effective anisotropic media through an anisotropic effective mass matrix. Unfortunately, this anisotropy is of different nature compared to the elastic effective anisotropy and cannot be used to mimic elastic anisotropy