Attenuation and dispersion of seismic waves in a cracked-fractured medium

This work studies the attenuation of seismic waves caused by wave-induced fluid flow in a cracked fractural medium. Fractures are regarded as very thin and porous layers in a porous background, and the fractured medium is equivalent to a periodically layered White model. Considering the influence of squirt fluid between different types of cracks and pores, the relation between stiffness and frequency in the periodically layered medium is deduced by a modified version of Biot equation. When saturated with fluid, this model exhibits significant attenuation and velocity dispersion due to the wave-induced fluid flowing between fractures and pores or cracks and pores. Under the low frequency limit, the properties of the cracked fractural medium can be determined by the anisotropic Gassmann equation and squirt fluid model. However at high frequencies, the effect of wave-induced flow can be ignored since the pressure in the cracks has not enough time to reach equilibrium. Analysis shows that wave attenuation is mainly affected by the density of cracks, while the frequency range of significant attenuation and velocity dispersion are mainly controlled by the crack aspect ratio. Owing to different crack attenuation mechanisms, the magnitudes of attenuation and velocity dispersion are different, while their general trends are the same.