Seismic velocities of unconsolidated sands: Part 1 — Pressure trends from 0.1 to 20 MPa Michael A. Zimmer 1 , Manika Prasad 2 , Gary Mavko 3 , and Amos Nur 3 ABSTRACT Knowledge of the pressure dependences of seismic velocities in unconsolidated sands is necessary for the remote prediction of effective pressures and for the projection of velocities to unsam- pled locations within shallow sand layers. We have measured the compressional- and shear-wave velocities and bulk, shear, and P- wave moduli at pressures from 0.1 to 20 MPa in a series of un- consolidated granular samples including dry and water-saturated natural sands and dry synthetic sand and glass-bead samples. The shear-wave velocities in these samples demonstrate an average pressure dependence approximately proportional to the fourth root of the effective pressure  V S  p' 1/4 , as commonly observed at lower pressures. For the compressional-wave velocities, the exponent in the pressure dependence of individual dry samples is consistently less than the exponent for the shear-wave velocity of the same sample, averaging 0.23 for the dry sands and 0.20 for the glass-bead samples. These pressure dependences are general- ly consistent over the entire pressure range measured. A compari- son of the empirical results to theoretical predictions based on Hertz-Mindlin effective-medium models demonstrates that the theoretical models vastly overpredict the shear moduli of the dry granular frame unless the contacts are assumed to have no tan- gential stiffness. The models also predict a lower pressure expo- nent for the moduli and velocities  V  p' 1/6  than is generally ob- served in the data. We attribute this discrepancy in part to the in- ability of the models to account for decreases in the amount of slip or grain rotation occurring at grain-to-grain contacts with in- creasing pressure. INTRODUCTION The pressure dependences of the seismic velocities in unconsoli- dated sediments are important considerations in a number of engi- neering applications. The pressure dependence of the shear-wave velocity is often used to project velocities to depths or locations where in situ measurements have not been made — for example, as a part of site-amplification predictions or liquefaction-susceptibility analyses e.g., Youd and Idriss, 1997. Likewise, the hazards posed to offshore drilling by unrecognized overpressures at shallow depths have prompted the use of the pressure dependence of the compres- sional-wave velocity to predict in situ effective pressures. Knowl- edge of these pressure dependences also allows for the use of veloci- ty changes to monitor pressure changes in shallow, unconsolidated aquifers and reservoirs. Although both theoretical and empirical formulations commonly predict a power-law relationship between the velocity and pressure, the exponents of the pressure in these expressions differ significant- ly. Theoretical formulations based on contact theory predict that the seismic velocities of an assemblage of perfect spheres of equal size will vary with the effective pressure to the one-sixth power Walton, 1987; Santamarina and Cascante, 1996; Mavko et al., 1998. In con- trast, empirical fits to the velocities measured in natural sand sam- ples generally produce pressure exponents clustered about one- fourth, though they vary from one-third to one-sixth e.g., Hardin and Richart, 1963; Pilbeam and Vaisnys, 1973; Hryciw and Th- omann, 1993. This difference between the empirical and theoretical values is generally attributed either to an increase in the average number of contacts per grain as the sample compacts with loading or to the nonspherical shape of real sand grains, factors generally not Manuscript received by the Editor March 4, 2006; revised manuscript received May 24, 2006; published online December 20, 2006. 1 Formerly Stanford University; presently ENSCO, Inc., 5400 Port Royal Road, Springfield,Virginia 22152. E-mail: zimmer.michael@ensco.com. 2 Colorado School of Mines, Department of Geophysics, 1500 Illinois Street, Golden, Colorado 80401. E-mail: mprasad@mines.edu. 3 Stanford University, Rock Physics Laboratory, Department of Geophysics, 397 Panama Mall, Stanford, California 94305. E-mail: mavko@stanford.edu; anur@stanford.edu. © 2007 Society of Exploration Geophysicists. All rights reserved. GEOPHYSICS, VOL. 72, NO. 1 JANUARY-FEBRUARY 2007; P. E1–E13, 9 FIGS., 4 TABLES. 10.1190/1.2399459 E1