Frequency Dependence of Fracture Specific Stiffness L. J. Pyrak-Nolte and D. D. Nolte Geophysical Research Letters, vol. The frequency dependence of fracture specific stiffness, for seismic or ultrasonic wave transmission, is shown to be a simple scaling property of fractures with spatially inhomogeneous distributions of stiffness.
Different frequencies sample different subsets of the fracture geometry.
Therefore the frequency dependence may be a simple consequence of fracture geometry and may require no additional dynamical mechanism. In this letter, the dynamic fracture stiffness is determined based on the displacement discontinuity model for wave transmission across a fracture. Local transmission coefficients are assumed to depend on the local static stiffness, the dynamic stiffness is frequency independent. A strongly inhomogeneous distribution of fracture stiffnesses produces a strong frequency dependence for the dynamic stiffness. Frequency dependent specific stiffness as functions of frequency.