Abstract
Energy conservation principles are used to derive anisotropic elastic properties and seismic wave velocities of an otherwise isotropic material containing preferentially oriented microcracks. The energy stored in deforming a cracked elastic material equals the sum of energy stored in deforming the homogeneous, isotropic and intact portion of the material, and in the cracks. Both elastic properties and seismic velocities and attenuation of this material are therefore dependent on average crack length, orientation and density. This work found that P-wave velocities in all principal directions: the direction normal to crack planes, and parallel to the short and the long axis of crack planes, decrease as crack density increases. The shear wave velocities in the crack planes, that is, when both the particle motions and the propagation directions are parallel to the planes, remain unchanged because the shear modulus in those planes is not changed. The shear wave velocities in the other two principal directions are found to decrease with increasing crack length and density. These results show that in a cracked, otherwise isotropic elastic material, shear waves in the direction parallel to the crack planes travel the fastest and any other shear waves that make a non-zero angle with the crack planes travel slower. Measured results in both laboratory and field, as summarized by Crampin et al. (J. Petroleum Tech. 1989; 283–288), have confirmed these findings.
Published Version
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