No, spectral analysis won't tell you anything about anisotropy of surface waves.

The best way is to inverse separately Love waves and Rayleigh waves (which implies at first to be able to separate them with three-component sensors) and to extract the anisotropy from the differences between the two Shear-wave maps. There are papers that detail the techniques.

Hi Philippe, 

Indeed Nasser is referring to the inclusion of shear waves into the inversion process (we used 3D sensors), we observed anomalies in some datasets that could be explained by anisotropy. Can you point out any of these papers? Thank You so much.

I suggest you look at:

Yao, Van der Hilst, Montagner (JGR, 2010);

Huang, Yao, and Van der Hilst (GRL, 2010)

Thank you so much, Philippe