Abstract
Dynamic elastic properties of dry and water-saturated Green River shale samples were computed from compressional and shear-wave velocity measurements. P- and S-wave velocity measurements were made in three mutually perpendicular directions with respect to the bedding planes. Measurements were also made in several different directions by varying the angle between the bedding planes and the direction of propagation of the wave for angles of 0, 30, 45, 60 and 90 degrees. The oriented samples were subjected to both confining pressure and axial loads, in excess of the confining stress, in the direction of Propagation.
In general, P- and S-wave velocities increased with increasing stress levels, with a corresponding increase in Young's modulus. Water saturation caused the P-wave velocity to increase and the S-wave velocity to decrease. Elastic moduli decreased upon saturation, except for Poisson's ratio, which increased, indicating some degree of weakening of the material. The samples showed a moderate degree of anisotropy; this was to be expected from the laminated nature and shallow occurence of Green River shale.
Introduction
This paper presents some results of an experimental determination of the elastic coefficients of anisotropic materials (in particular, finely layered rocks and minerals such as Green River shale) from measurements of dilatational and shear-ultrasonic-wave velocities. Ultrasonic techniques have been used extensively in nondestructive testing. Several methods have been proposed by McSkimmin, and some of these have been used successfully to measure ultrasonic velocities in rocks. Hughes and Cross, Wyllie et al., and Birch, developed pulse first-arrival techniques for the measurement of dilatational and shear velocities. Williams and Lamb used the method of cancellation of a traveling wave, which was later modified by Myers et al. and perfected by McSkimmin. Although this method is highly accurate, it has not been used as widely as the pulse-transmission methods recently reported by Jamieson and Hoskins, King, and Mattaboni and Schreiber. It has been common practice to use some form of crystal transducers, either quartz or ceramic, that has been cut or polarized in different directions in order to generate either compressional or shear waves. However, accurate determination of shear wave velocities has been difficult due to problems that arise in obtaining a pure shear wave from cross-polarized crystals, which usually also generate a small amount of compressional energy. As reported by Gregory, this energy can be seen as a long precursor preceding the sharp break of the shear first arrival.
The need for generating pure shear waves led to interest in mode-conversion techniques, which are based upon conversion of the mode of vibration through wave reflection or refraction at a discontinuity. Arenberg showed that for certain materials and for certain angles of incidence it is possible to generate pure shear modes by reflection at a boundary. Jamieson and Hoskins used a pyrex glass-air interface for generating pure shear waves, and King used this method successfully for measuring shear-wave velocities in rocks. Gregory arrived at a similar result by refraction of a wave at an aluminum-oil interface. A plane compressional wave, traveling in the oil phase, is incident on the aluminum at an angle larger than the critical angle for compressional waves, and thereby generates a purely transverse, plane-polarized wave in the aluminum.
During the last few years methods have been developed that allow the simultaneous determination of shear and compressional velocities in solids.
SPEJ
P. 389ˆ
Determination of elastic anisotropy of rocks from P- and S-wave velocities: numerical modelling and lab measurements