Estimating grain-scale fluid effects on velocity dispersion in rocks

Abstract The magnitude of the grain-scale local flow effect on velocity dispersion in saturated rocks is quantified, by estimating the high-frequency unrelaxed shear and bulk frame moduli, which are then combined with the Biot formulation to predict total dispersion. The method is relatively independent of assumptions about idealized pore geometries and unknown parameters such as pore aspect ratios. The local flow effect depends on the heterogeneity of pore stiffness, in particular the presence of compliant cracks and grain contacts; the pressure dependence of the dry rock properties is shown to contain the essential information about the distribution of pore stiffnesses needed to estimate the high-frequency saturated behavior. To first order, the unrelaxed wet frame compressibility at any given pressure is shown to be approximately the dry frame compressibility at very high pressure; second order corrections add the additional compressibility gained by replacing an amount of mineral equal to the compliant pore volume with fluid. The method predicts that the difference between relaxed and unrelaxed shear compliance is simply proportional to that in bulk. The results for total dispersion (local flow plus Biot) explain quite well the measured P- and S-wave dispersion for a variety of saturated rocks.