The elastic nonlinear behavior of rocks as evidenced by deviations fro
m Hooke's law in stress-strain measurements, and attributable to the p
resence of mechanical defects (compliant features such as cracks, micr
ofractures, grain joints), is a well-established observation. The purp
ose of this paper is to make the connection between the elastic nonlin
earity and stress-induced effects on waves, in this case uniaxial-stre
ss-induced transverse isotropy. The linear and nonlinear elastic coeff
icients constitute the most condensed manner in which to characterize
the elastic behavior of the rock. We present both the second- and the
third-order nonlinear elastic constants obtained from experimental dat
a on rock samples assumed homogeneous and isotropic when unstressed. A
s is normally the case, the third-order (nonlinear) constants are foun
d to be much larger than the second-order (linear) elastic constants.
Contrary to results from intact homogeneous solids (materials without
mechanical defects), rocks exhibit weak to strong nonlinearity and alw
ays in the same manner (i.e., an increase of the moduli with pressure)
. As a consequence the stress-induced P wave anisotropy and S wave bir
efringence can be large. The stress-induced P wave anisotropy appears
to be much larger than the S wave birefringence. The fast direction is
parallel to the stress direction, and the anisotropy goes as sin(2) t
heta, theta being the angle between the propagation direction and the
stress direction. Experiments on rocks indicate that at low applied st
resses, the proportionality of the stress and the induced S birefringe
nce and P anisotropy predicted by theory is well corroborated.