Estimating seismic velocities at ultrasonic frequencies in partially saturated rocks

Seismic velocities in rocks at ultrasonic frequencies depend not only on the degree of saturation but also on the distribution of the fluid phase at various scales within the pore space. Two scales of saturation heterogeneity are important: (1) saturation differences between thin compliant pores and larger stiffer pores, and (2) differences between saturated patches and undersaturated patches at a scale much larger than any pore. We propose a formalism for predicting the range of velocities in partially saturated rocks that avoids assuming idealized pore shapes by using measured dry rock velocity versus pressure and dry rock porosity versus pressure. The pressure dependence contains all of the necessary information about the distribution of pore compliances for estimating effects of saturation at the finest scales where small amounts of fluid in the thinnest, most compliant parts of the pore space stiffen the rock in both compression and shear (increasing both Pand S-wave velocities) in approximately the same way that confining pressure stiffens the rock by closing the compliant pores. Large-scale saturation patches tend to increase only the high-frequency bulk modulus by amounts roughly proportional to the saturation. The pore-scale effects will be most important at laboratory and logging frequencies when pore-scale pore pressure gradients are unrelaxed. The patchysaturation effects can persist even at seismic field frequencies if the patch sizes are sufficiently large and the diffusivities are sufficiently low for the larger-scale pressure gradients to be unrelaxed.