Quantifying Rock Fracture Compliance from Elastic Wave Velocities

The purpose of this study is to test the reliability of various methods to quantify fracture compliance with elastic wave measurements. Fracture compliance is the inverse of fracture stiffness and controls many characteristics of fractures that are important for geoengineering, e.g. strength, seismic visibility and hydraulic properties. We present ultrasonic through-transmission laboratory measurements for the compliance of smooth fractures in Westerly Granite samples that were exposed to a range of uniaxial loading pressures. The influence of sample width and source transducer on the measurements are constrained with numerical discrete lattice simulations. The results of this study confirm a recently established unique relationship between phase delay and fracture compliance for fracture systems that obey linear-slip theory. We suggest that this confirmation opens the potential for a wider application of time delay based compliance quantification that was previously limited by a non-unique relationship. In some circumstances precise phase delay measurements can be difficult to achieve. We show that in such cases employing first break arrival time measurements in conjunction with numerical simulations are an effective alternative. The application of the proposed method to multiply fractured media and to larger scales at sonic and seismic frequencies is also considered.