Generalized mechanical model analogies of linear viscoelastic behaviour

The description of wave propagation by a viscoelastic rheology allows for the introduction of two important phenomena: wave dissipation, i.e., the conversion of motion into heat, and velocity dispersion, the phenomenon in which two different Fourier components travel with different velocities. In this work, we consider a mechanical representation of viscoelastic media, which in virtue of its simplicity constitutes a useful tool to model the variety of dissipation mechanisms present in real media. Examples of simulated wavefields in these types of media can be found, for instance, in the works of Carcione et al. (1988 a,b), where the equations are based on the standard linear solid model. Here we analyze in detail the physical properties and capabilities of different mechanical models, and give some hints to obtain realistic models of attenuation and velocity dispersion; for example, the constant Q phenomenon and the set of relaxation peaks over a given frequency band.