First-order perturbation approximation for rock elastic moduli in transversely isotropic media
2017
Seismic anisotropy is a relatively common seismic wave phenomenon
in laminated sedimentary rocks such as shale and it can be used to
investigate mechanical properties of such rocks and other geological
materials. Young’s modulus and Poisson’s ratio are the most common
mechanical properties determined in various rock engineering practices.
Approximate and explicit equations are proposed for determining Young’s
modulus and Poisson’s ratio in anisotropic rocks, in which the symmetry
plane and symmetry axis of the anisotropy are derived from the constitutive
equation of transversely isotropic rock. These equations are based
on the media decomposition principle and seismic wave perturbation
theory and their accuracy is tested on two sets of laboratory data.
A strong correlation is found for Young’s modulus in two principal
directions and for Poisson’s ratio along the symmetry plane. Further,
there is an underprediction of Poisson’s ratio along the symmetry
axis, although the overall behavior follows the trend of the measured
data. Tests on a real dataset show that it is necessary to account
for anisotropy when characterizing rock mechanical properties of shale.
The approximate equations can effectively estimate anisotropic Young’s
modulus and Poisson’s ratio, both of which are critical rock mechanical
data input for hydraulic fracturing engineering.
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