Abstract

Because of the viscous properties of rock, a viscoelastic model is closer to the real situation of rock media than an elastic model is. Cracks in the media are common geophysical phenomena. In particular, horizontal cracks are widely developed in the thin interbeds of sedimentary rock. Taking a Cole—Cole viscoelastic medium as the background medium, we compute the frequency-dependent velocities, quality factors, anisotropy coefficients, crack densities, and crack aspect ratios of P- and S-waves based on Hudson’s theory.

We give the velocity-stress staggered finite-difference equations of the elastic wave propagation in a cylindrical coordinate system for a viscoelastic medium with horizontal cracks and numerically simulate acoustic propagation in the cracked medium with different crack densities and aspect ratios.

The simulation results indicate that as the crack density increases outside a borehole the P- and S-wave velocities decrease and their amplitudes increase, in a borehole the P- and S—wave velocities and amplitudes decrease; as the crack aspect ratios increases outside a borehole the P-wave velocities decrease, its amplitudes change little and the S-wave amplitudes and velocities change little, in a borehole the P-wave velocities and amplitudes decrease and the S-wave velocities in a borehole change little, and the S-wave amplitudes decrease.