Abstract
Several physical parameters and anisotropy related to rock textural arrangements, schistosity and weakness planes such as cracks and joints affect the P-wave velocity (VP). First, VP anisotropy of quartz-mica schist as a common type of widespread metamorphic rock was compared with VP anisotropy of jointed homogeneous limestone specimens to clarify effect of these two different types of anisotropies. The results showed that the VP anisotropy of quartz-mica schist texture is stronger than the VP anisotropy of jointed limestone, because all body of quartz-mica schist specimens have VP anisotropy behavior. Many rocks are anisotropic and degree of anisotropy varies from one to another. Various investigations have been carried out on VP anisotropy but there is not a unique comprehensive relation to represent the influence of different degrees of anisotropy on the VP for different rocks. The relation between VP and angle (θ) between the axis of symmetry (perpendicular to weakness planes) with the wave propagation direction was analyzed for a wide range of anisotropy degrees using the results of nine different types of rocks including: Angouran quartz-mica schist, Golgohar mica schist, amphibole schist, mica-quart schist, Marcellus shale, Withby shale WUK47B, WUK70 and WUK2, and Veroia-Polymylos gneiss. A new simple empirical relation fitted to all groups of results was obtained to assess VP for different degrees of anisotropies with a good correlation of determination (R2 = 0.937), low RMSE (RMSE = 320 m/s) and low CV (CV = 7.0%). P wave velocity anisotropy can simply be predicted by the developed relation using only two parameters of VP0 and VP90 or ε that is the percentage change of VP0 with respect to VP90. A VP anisotropy classification diagram was also developed based on the different values of ε.
Highlights
Wave velocity in anisotropic rock mediaThe relationship between stress and strain in x, y and z directions for vertical transverse isotropic symmetry (VTI) in rock media can be written as in the matrix form follows: xyz CVTI xyz (1)The transverse anisotropic matrix has five non-zero values distributed among 12 non-zero elements
P-wave velocity anisotropy can be affected by orientations of rock forming crystals and their textural arrangements and parameters such as rock fractures, cracks and joints as dominant weakness planes
The results showed that the VP anisotropy of rock texture in quartz-mica schist is stronger than the VP anisotropy of jointed rock (Figs. 7 and 8)
Summary
The relationship between stress ( xyz) and strain ( xyz) in x, y and z directions for vertical transverse isotropic symmetry (VTI) in rock media can be written as in the matrix form follows: xyz CVTI xyz (1). C11, C33, C44, C66 and C13 are the five elastic stiffness needed to describe a VTI media. The stiffness matrix is explained using P wave velocity along the foliation direction ( VP90o ), P wave velocity perpendicular to the foliation ( VP0o ), S wave velocity along the foliation direction. V S0 o as follows (Winterstein 1990):
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