Summary
Laboratory wavefront imaging experiments were performed on isotropic samples containing orthogonal fractures to determine the effect of fracture networks on elastic wave propagation. The arriving acoustic wavefront was recorded over a two-dimensional area as a function of time while the samples were subjected to bi-axial loading conditions for a range of stresses (0.4 to 8 MPa). The orthogonal fracture network formed rectangular wave guides that strongly confined the wavefront at low stresses. As the stress increased, the energy transmitted across the fractures increased because of the increase in fracture specific stiffness. Analysis of the arrival times and amplitudes determined that: (1) the stiffness of the fractures was non-uniform and (2) fracture intersections can significantly delay the propagating wavefront.
Introduction
Research on elastic wave propagation in fractured media has mostly focused on single fractures and sets of parallel fractures. From these studies, single fractures are known to delay and attenuate waves [Schoenberg, 1980; Angel & Achenback, 1985; Pyrak-Nolte et al., 1990a; Gu et al., 1996; Nakagawa et al., 2000 & 2004] as well as support fracture interface waves that are guided by the fracture plane [Pyrak-Nolte & Cook, 1987; Pyrak-Nolte et al., 1992; Gu et al., 1996; Shao & Pyrak-Nolte, 2013]. The ability to guide waves along a fracture, the amount of delay and attenuation of transmitted and reflected modes, all depend on the frequency of the signal and the coupling between the two fracture surfaces. The compliance or specific stiffness of a fracture captures the coupling between the surfaces which depends on the amount contact between the two surfaces and the aperture distribution [Hopkins et al. 1990]. As the stiffness of a fracture increases, guided mode time delay and energy of internally reflected waves decrease.
For a set of parallel fractures, each individual fracture exhibits the behavior just described as well as wave interference effects (e.g. stop-band behavior) related to the spacing of the fracture, signal wavelength and stiffness of the fractures [Nakagawa et al, 2000]. In addition, wave guiding can occur between two fractures [Nihei et al., 1999; Nakagawa et al., 2002; Xian et al. 2001, Shao et al. 2015]. While wave guiding is known to arise from impedance (density × phase velocity) contrasts in layered media, parallel fractures in isotropic media have also been shown to produce guided modes [Xian et al. 2001]. Parallel fractures can form planar wave guides: when fractures are weakly coupled (low specific stiffness), waves are internally reflected between the parallel fractures leading to constructive and destructive interference. The existence and strength of such guided-modes also depend on the wavelength of the signal, fracture specific stiffness and the spacing between two consecutive fractures.
