Elastic wave velocity changes due to the fracture aperture and density,
and direct correlation with permeability: an energetic approach to mated
rock fractures
Abstract
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.