Attenuation and Dispersion in Fluid-Saturated Rocks Due to Circular Cracks

We consider interaction of a normally incident time-harmonic longitudinal plane wave with a circular crack imbedded in a porous medium governed by Biot’s equations of dynamic poroelasticity. The problem is formulated in cylindrical coordinates as a system of dual integral equations for the Hankel transform of the wave field, which is then reduced to a single Fredholm integral equation of the second kind. The solution of this equation yields elastic wave dispersion and attenuation in a medium containing a random distribution of aligned cracks. These dissipation effects are caused by wave induced fluid flow between pores and cracks.