Seismic velocities in unconsolidated sands: Measurements of pressure, sorting, and compaction effects

This dissertation presents measurements of compressional- and shear-wave velocities made on unconsolidated sand and glass-bead samples over a pressure range from 100 kPa to 20 MPa. These measurements demonstrate that the shear-wave velocity varies with the fourth root of the effective pressure over the entire pressure range, while the compressional-wave velocity demonstrates a slightly lower pressure dependence. These pressure dependences show no systematic variation with the porosity for porosities from 25 to 44%. The porosity-velocity trend at a given pressure is described by the isostress average between the moduli of the highest porosity sample and the moduli of quartz. The significant porosity dependence of the water-saturated, compressional-wave velocities, as modeled with Gassmann fluid substitution, is mostly contained in the zero-pressure bulk modulus. Preconsolidation produces only a slight increase in the velocities and a slight reduction in the pressure dependence. A comparison of the velocities measured at 150 kHz in water-saturated samples of four natural sands to velocities predicted by Biot and Mavko-Jizba models demonstrates that the squirt mechanism is the primary dispersion mechanism active in these sands at this frequency. The dispersion in the velocities demonstrates no significant change with compaction. The static bulk modulus calculated from the volumetric strains observed in the dry samples of these four natural sands and one glass bead sample is shown to be from 2 to 10 times lower than the dynamic bulk modulus for the normally consolidated samples, and drops from being equal to the dynamic modulus on the first unloading step to being approximately 3 times lower on complete unloading. A Preisach-Mayergoyz space analysis adapted to include plastic-strain effects demonstrates that both the strain-magnitude dependence of elastic strains and the occurrence of plastic strain contribute to these differences between the static and dynamic moduli. A compilation of this data with velocity data from dry and water-saturated rocks from a number of published sources demonstrates that the sensitivity of the seismic velocities to pressure ( ∂V/∂P) is a continuous function of pressure for a wide variety of rocks over a pressure range from below 100 kPa to above 600 MPa.