Fitting observed seismic attenuation curves with the general fractional Zener model

As an extension of the single Zener element, which exhibits a rather narrow band attenuation peak, the fractional Zener model (or what is also called the Cole-Cole model) has been suggested to describe a lossy material having a broad attenuation spectrum. We have developed a new and simple deterministic method to extract the model parameters of the single fractional Zener solid from the attenuation observations. To approximate a more complicated seismic attenuation dispersion curves which exhibits multiple peaks, we suggest the general fractional Zener model which comprises multiple fractional Zener elements in parallel. The model parameters for the general fractional Zener model can be estimated using the simulated annealing inversion method. Such mechanical models can be used to construct viscoelastic and/or poro-viscoelastic models for simulating seismic wave propagation in dissipative media. The calculated seismic attenuation dispersion curves show a good match with the observations over the entire frequency range.