Frequency-dependent acoustic anisotropy in fractured rock

Frequency-dependent acoustic wave propagation in fractured rock is examined for a set of equally-spaced, parallel fractures. Exact solutions for the velocity of the waves are obtained as a function of wave frequency and fracture stiffness and spacing. Waves propagating obliquely to the fractures show strongly anisotropic velocities for low fracture stiffnesses and high frequencies. For high frequencies, propagation of the waves is sometimes prohibited due to the interference of multiply scattered waves (stop-pass behavior). For the waves propagating parallel to the fractures, multiple guided modes are shown to exist with velocities and particle motions that are dependent on fracture stiffness and frequency.