Empirical relationships among seismic velocity, effective pressure, porosity, and clay content in sandstone

We use a multivariate analysis to investigate the influence of effective pressure P e , porosity phi , and clay content C on the compressional velocity V p and shear velocity V s of sandstones. Laboratory measurements on water-saturated samples of 64 different sandstones provide a large data set that was analyzed statistically. For each sample, relationships between effective pressure and V p and V s have been determined. All samples were well fit by relationships that have an exponential increase in velocity at low P e , tapering to a linear increase with P e for P e greater than 0.2 kbar. There are differences in the pressure dependences of velocity for different rocks, particularly at very low pressures; however, the differences cannot be attributed to phi or C. For the combined set of measurements from all samples, the best fitting formulations areEquationandEquationWhile this is admittedly a very simplified parameterization, it is remarkable how well the velocity of the rocks considered here can be predicted based on only the three parameters, phi , C, and P e . The model accounts for 95 percent of the variance and has rms error of 0.1 km/s. An increased value of V p /V s can indicate a decrease in P e , a decrease in porosity, or an increase in clay content or some combination thereof.