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

Simulation of acoustic wave propagation in a borehole surrounded by cracked media using a finite difference method based on Hudson’s approach