Seismic properties of unconsolidated sands: Tangential stiffness, Vp/Vs ratios and diagenesis

Abstract

Ultrasonic and well log measurements of unconsolidated sands indicate that observed velocities are lower than predicted from Hertz‐Mindlin contact theory for random packing of identical grain sizes. In particular, the Vp/Vs ratios are significantly higher than predicted from models. This discrepancy is important to understand prior to AVO analysis of unconsolidated sands. We perform a sensitivity study of the contact model and find that the model most likely to fit observed Vp, Vs and Vp/Vs is the model where the effective elastic constants are calculated by assuming some of the grains to have no tangential stiffness. In general, contact theories relate effective bulk and shear moduli to tangential and normal stiffness, and the choice of tangential contact stiffness model changes the effective moduli of the grain pack. Bachrach et al. (2000) showed that Vp/Vs ratio in unconsolidated sands is related to the percent of grains that have no tangential contact stiffness, while grain angularity (i.e., accounting for non‐uniform contact radius) may reduce both the bulk and shear moduli. In this paper we analyze the elasticity and AVO response of specific deep water reservoir sands and find that their Poisson's ratio is consistent with that of sands at low effective stress. This may be supported by laboratory measurements of stress distribution in granular media. We also note that at higher pressures, the effect of angularity is of second order compared to the effect of zero tangential contact stiffness.