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

Abstract

We use a multivariate analysis to investigate the influence of effective pressure [Formula: see text], porosity ϕ, and clay content C on the compressional velocity [Formula: see text] and shear velocity [Formula: see text] 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 [Formula: see text] and [Formula: see text] have been determined. All samples were well fit by relationships that have an exponential increase in velocity at low [Formula: see text], tapering to a linear increase with [Formula: see text] for [Formula: see text] 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 ϕ or C. For the combined set of measurements from all samples, the best fitting formulations are [Formula: see text] and [Formula: see text]. While 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, ϕ, C, and [Formula: see text]. The model accounts for 95 percent of the variance and has rms error of 0.1 km/s. An increased value of [Formula: see text] can indicate a decrease in [Formula: see text], a decrease in porosity, or an increase in clay content or some combination thereof.