Cracked media are a common geophysical phenomena. It is important to study the propagation\ncharacteristics in boreholes for sonic logging theory, as this can provide the basis for the sonic\nlog interpretation. This paper derives velocityââ?¬â??stress staggered finite difference equations of\nelastic wave propagation in cylindrical coordinates for cracked media. The sound field in the\nborehole is numerically simulated using the finite-difference technique with second order in time\nand tenth order in space. It gives the relationship curves between the P-wave, S-wave velocity,\nanisotropy factor and crack density, and aspect ratio. Furthermore, it gives snapshots of the\nborehole acoustic wave field in cracked media with different crack densities and aspect ratios.\nThe calculated results show that in dry conditions the P-wave velocity in both the axial and radial\ndirections decreases, and more rapidly in the axial direction while the crack density increases.\nThe S-wave velocity decreases slowlyïâ?? with increasing crack density. The attenuation of the wave\nenergy increases with the increase in crack density. In fluid-saturated cracked media, both the\nP-wave and S-wave velocity increases with the aspect ratio of the cracks. The anisotropy of the\nP-wave decreases with the aspect ratio of the cracks. The aspect ratio of the crack does not\nobviously affect the energy attenuation.
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