In an effort to reveal the subsurface hydraulic changes in fractures by seismic monitoring, aperture-related velocity changes need to be investigated. We developed a numerical approach for calculating changes in elastic wave velocity with fracture aperture opening by determining the internal energy of a digitized fracture model based on natural rough surfaces. The simulated local elastic energy revealed that the interaction energy converged within 1.5 mm of the mean fracture position, and was insignificant unless the fractures intersected. This energetic approach clarified the aperture–velocity relationship and reproduced the experimental results. Further calculations using digital fractures with various sizes and density demonstrated that the velocity can be accounted for by the superposition of a linear function of fracture density and quadratic function of aperture, and is insensitive to the fracture size. Although the relationship between fracture permeability and elastic wave velocity (i.e., the k-V relationship) depends on the fracture density, the offset-normalized k-V relationship shows clear linearity with the fracture density. The proposed k-V relationship as a function of the aperture and fracture density indicates that laboratory-scale fracture properties of a single fracture can be applied to multiple fractures on a larger scale. Our findings can be used to interpret temporal changes in seismic observations and to monitor fluid flow in fractures.
