Approximations for the Quality Factor of the Interlayer-flow Model, its Minimum Value, and the Characteristic Frequency

The analytical solution of the 1D White’s model yields seismic attenuation (given by the inverse of quality factor) and velocity dispersion in layered poroelastic media. In this model, also called interlayer-flow model, frequency-dependent attenuation and velocity dispersion are caused by wave-induced fluid flow between saturated layers of different compliances. Different compliances in the layers can be due to differences in solid frame and/or fluid properties. We derive approximations for the frequency-dependent quality factor of the interlayer-flow model, its minimum value, and the characteristic frequency at which the minimum value of the quality factor occurs. The approximations are valid for any two alternating sets of petrophysical parameters for the layers. Approximations for the minimum value of the quality factor and for the characteristic frequency exist in the literature, but they are restricted to media of homogeneous solid frame saturated with two alternating fluids, one fluid being much more compressible than the other. Our approximations give insight into the dependence of attenuation on the physical properties of the rock and the saturating fluid(s).