Effective antiplane properties in presence of frictional shear cracks

Cracked solids are viewed as equivalent homogenous media that sustain the propagation of coherent shear horizontal waves in the presence of multiple scattering. Strip-like cracks are filled with viscous fluid and are randomly distributed. Their faces undergo viscous friction. The effective wave number and shear stiffness are calculated for parallel cracks in terms of the far-field response of a single crack. Attention is focused on the derivation of this single-scattering property in the general case of oblique incidence. Effect of the crack density and fluid viscosity on the effective properties is investigated. Simple low- and high-frequency analytical approximations allow a direct assessment of the crack density and fluid viscosity from seismic wave measurements. Knowledge of these parameters facilitates more precise estimation of the crack size in the Earth's crust.