Experimental results on the combined effects of frequency, pressure and pore fluid on the dispersion of elastic waves in porous rock

A model is proposed for the frequency dependence of elastic wave velocities in porous rocks using the spheroidal geometry for the pores. The model is based on the assumption that the rock contains a distribution of « closable» cracks having small aspect ratios, and one family of «non-closable» pores. At a given wave frequency, some pores obey the Gassmann equation and others are isolated, with a critical aspect ratio demarcating the two families that depens on frequency and fluid viscosity. An effective medium model is used to add the compliances of the individual pores, so as to yield effective moduli. The model also allows for calculation of «intrinsic» seismic attenuation by applying the Kramers-Kronig relations to the velocities. By considering the crack closure process, the model is capable of describing the frequency dispersion of both the compressional and shear velocities at each pressure. The predictions, for some sandstones datasets taken from the literature, show that P and S-wave velocities generally increase in a relatively similar manner with frequency, and that dispersion of both velocities rapidly decreases with pressure. Attenuation values are consistent with typical values found in the literature.