Intersection Waves

Abstract

Intersections in a fracture network control the connectivity of the flow paths through rock. The long near‐linear geometric nature of fractures makes them difficult to identify and characterize. We present a new type of elastic wave, an intersection wave, which travels along an intersection and is sensitive to the coupling between two orthogonal fractures that define the intersection. Group theory for C2v and C4v point groups predicts sets of propagating elastic waves confined to the fracture intersection. Along with the use of the wave equation and displacement discontinuity boundary conditions, the dispersion relationships for intersection waves are predicted. Experimental ultrasonic measurements on a nonwelded linear intersection between two orthogonal, synthetic fractures in aluminum confirm the existence of multiple modes that travel between the speed of wedge waves (sub‐Rayleigh waves) when the intersection is completely, and bulk shear waves, when the intersection is closed, as predicted by theory. Between these two limits, the intersection behaves as a nonwelded contact and yields these new intersection waves that are dispersive and sensitive to the coupling along the intersection. Intersection waves provide the foundation for new geophysical approaches for characterizing the hydraulic connectivity of fracture networks.

Long‐Wavelength Propagation in Fractured Rock Masses (3D Stress Field)

“…Within this framework, we can group previous research into short wavelength ( λ / a < 10) and long wavelength ( λ / a > 10) propagation studies. Short‐wavelength propagation studies have explored the angle of incidence (Gu et al., 1996), multiple parallel fractures (Pyrak‐Nolte et al., 1990a; Schoenberg, 1983; Shao & Pyrak‐Nolte, 2016), fracture intersection waves (Abell et al., 2017; Pupyrev et al., 2019), and fluid‐filled fractures (Barbosa et al., 2016; Pyrak‐Nolte et al., 1990b). Associated analyses often assume continuous stress but discontinuous displacements across the fracture (Schoenberg, 1980).…”