Backus and Wyllie Averages for Seismic Attenuation

Backus and Wyllie equations are used to obtain average seismic velocities at zero and infinite frequencies, respectively. Here, these equations are generalized to obtain aver- ages of the seismic quality factor (inversely proportional to attenuation). The results indicate that the Wyllie velocity is higher than the corresponding Backus quantity, as expected, since the ray velocity is a high-frequency limit. On the other hand, the Wyllie quality factor is higher than the Backus one, following the velocity trend, i.e., the higher the velocity (the stiffer the medium), the higher the attenuation. Since the quality factor can be related to properties such as porosity, permeability, and fluid viscosity, these averages can be useful for evaluating reservoir properties.