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 saturatio n 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 t han any pore. We propose a formalism for predicting the range of veloc ities in partially saturated rocks that avoids assuming idealized pore shapes by using measured dry rock velocity versus pressure and dry ro ck porosity versus pressure. The pressure dependence contains all of t he necessary information about the distribution of pore compliances fo r estimating effects of saturation at the finest scales where small am ounts of fluid in the thinnest, most compliant parts of the pore space stiffen the rock in both compression and shear (increasing both P- an d S-wave velocities) in approximately the same way that confining pres sure stiffens the rock by closing the compliant pores. Large-scale sat uration patches tend to increase only the high-frequency bulk modulus by amounts roughly proportional to the saturation. The pore-scale effe cts will be most important at laboratory and logging frequencies when pore-scale pore pressure gradients are unrelaxed. The patchy-saturatio n effects can persist even at seismic field frequencies if the patch s izes are sufficiently large and the diffusivities are sufficiently low for the larger-scale pressure gradients to be unrelaxed.