Power law attenuation of shear waves in fractal media

There are two mechanisms for attenuation of mechanical waves: absorption and multiple scattering. We explore the second mechanism for shear waves in the context of MR elastography. The theory for attenuation was first given in the seismic field (O’Doherty u0026 Anstey, Geophys. Prosp. 1971). Later phase was included, and the mean field concept was applied (Banik et al., Geophys. 1985). Then, a more rigorous theory which also deals with random fractals was developed (Solna, SIAM J ApplMath, 2003; Garnier u0026 Solna, Multiscale Model Simul, 2009). We have developed this theory further by allowing fractality over a limited length scale and also shown that it gives results that are indistinguishable from those of power law absorption models like the fractional Kelvin-Voigt model (Holm u0026 Sinkus, JASA, 2010). This makes it a challenge to understand whether attenuation in a real medium is due to one or the other mechanism or both. Measurement of dispersion has been done for polystyrene microspheres embedded in agarose ...