Effect of fracture compliance on wave propagation within a fluid-filled fracture

Open and partially closed fractures can trap seismic waves. Waves propagating primarily within fluid in a fracture are sometimes called Krauklis waves, which are strongly dispersive at low frequencies. The behavior of Krauklis waves has previously been examined for an open, fluid-filled channel (fracture), but the impact of finite fracture compliance resulting from contacting asperities and porous fillings in the fracture (e.g., debris, proppants) has not been fully investigated. In this paper, a dispersion equation is derived for Krauklis wave propagation in a fracture with finite fracture compliance, using a modified linear-slip-interface model (seismic displacement-discontinuity model). The resulting equation is formally identical to the dispersion equation for the symmetric fracture interface wave, another type of guided wave along a fracture. The low-frequency solutions of the newly derived dispersion equations are in good agreement with the exact solutions available for an open fracture. The primary effect of finite fracture compliance on Krauklis wave propagation is to increase wave velocity and attenuation at low frequencies. These effects can be used to monitor changes in the mechanical properties of a fracture.