Dispersion of elastic moduli in a porous-cracked rock: Theoretical predictions for squirt-flow

Crustal rocks contain variable amount of both cracks and equant pores depending on tectonic and thermal stresses but also on their geological origin. Crack damage and porosity change result in effects on elastic waves velocities. When rocks are fluid saturated, dispersion of the P- and S-waves should be taken into account. This paper deals with frequency dispersion of elastic moduli in a fluid saturated porous and cracked rock with the assumption that squirt-flow is the dominant process. We develop a theoretical approach to calculate both high (HF) and low (LF) frequency bulk and shear moduli. The HF moduli are derived from a new effective medium model, called CPEM, with an isotropic distribution of pores or cracks with idealized geometry, respectively spheres and ellipsoids. LF moduli are obtained by taking HF dry moduli from the CPEM and substituting into Gassmann's equations. In the case of a porosity only supported by equant pores, the calculated dispersion in elastic moduli is equal to zero. In the case of a crack porosity, no bulk dispersion is predicted but a shear dispersion appears. Finally in the general case of a mixed porosity (pores and cracks), dispersion in bulk and in shear is predicted. Our results show that the maximum dispersion is predicted for a mixture of pores and spheroidal cracks with a very small aspect ratio (≤ 10 − 3 ). Our theoretical predictions are compared to experimental data obtained during hydrostatic experiment performed on a basaltic rock and a good agreement is observed. We also used our theoretical model to predict elastic waves velocities and Vp/Vs ratio dispersion. We show that the P-waves dispersion can reach almost 20% and the Vp/Vs dispersion a maximum value of 9% for a crack porosity of about 1%. Since laboratory data are ultrasonic measurements and field data are obtained at much lower frequencies, these results are useful for geophysicists to interpret seismic data in terms of fluid and rock interactions. ► Squirt-flow is one of the main process involved in frequency dispersion. ► Elastic moduli are dependent on the frequency strain when cracks and pores are both present in the microstructure. ► P-waves are more sensitive to squirt-flow than S-waves.