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Rock physical and mechanical properties 49

2.3.6 Anisotropy of V p and V s
Velocity anisotropy in formations can be caused by the following reasons
in the rocks (Barton, 2007): microcracks, fabric, joints, interbeddings, in-
terfaces, faults, and stress anisotropies. Anisotropy effect is small for sand-
stones and carbonates, but large for shales. Lab tests illustrate that both
compressional and shear velocities and their anisotropies increase as the
applied stresses increase (Nur, 1971). The experiments conducted on rock
samples of gneisses and shales show a clear evidence of anisotropy in
Young’s moduli, P-wave velocities, and thermal conductivities, as shown in
Fig. 2.12 (Kim et al., 2012). Therefore, ignoring anisotropy in rock
properties may lead to erroneous results.
The P- and S-wave anisotropy parameters ε and g (Thomsen, 1986) can
be calculated from the following equations:
c 11 c 33
ε ¼
2c 33
(2.29)
c 66 c 44
g ¼
2c 44

Figure 2.12 Laboratory-measured elastic modulus (E q ), P-wave velocity (V p ), and
thermal conductivity (K) variation with respect to anisotropy angle. In the right axis,
values are normalized with respect to average minimum ones. (A) Asan gneiss, (B)
Boryeong shale (Kim et al., 2012).