Effective Biot theory and its generalization to poroviscoelastic 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 generalized to a poroviscoelastic model of 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 models as special cases. A global search method is described to determine the parameters of the relaxation functions, and a simple deterministic method is also developed to find the defining parameters of the single Cole-Cole model. These methods enable poroviscoelastic models to be constructed, which are based on measured seismic attenuation functions, and ensure that the model dispersion characteristics match the observations.