Upscaling effective biot theory to poro-viscoelastic models

A method is suggested to express the effective bulk modulus of the solid frame of a poroelastic material as a function of the saturated bulk modulus. This method enables effective Biot theory to be described through the use of seismic dispersion measurements or other models developed for the effective saturated bulk modulus. The effective Biot theory is up-scaled to a poro-viscoelastic model for which the moduli are represented by the relaxation functions of the generalized fractional Zener model. The latter covers the general Zener and the Cole-Cole model as special cases. A global search method is described to determine the parameters of the relaxation functions. These methods enable poro-viscoelastic models to be constructed, which are based on measured seismic attenuation functions, and ensures that the model dispersion characteristics match the observations.