Elastic waves through a simulated fractured medium

Abstract

Ultrasonic velocities were measured on a block composed of lucite plates with roughened surfaces pressed together with a static normal stress to simulate a fractured medium. The measurements, normal, parallel, and oblique to the fractures, show that for wavelengths much larger than the thickness of an individual plate, the block can be modeled as a particular type of transversely isotropic (TI) medium that depends on four parameters. This TI medium behavior is the same as that of an isotropic solid in which are embedded a set of parallel linear slip interfaces, specified by (1) the excess compliance tangential to the interfaces and (2) the excess compliance normal to the interfaces. At all static stress levels, we inverted the data for the background isotropic medium parameters and the excess compliances. The background parameters obtained were basically independent of stress level and agreed well with the bulk properties of the lucite. The excess compliances decreased with increasing static closing stress, implying that increasing static stress forces asperities on either side of a fracture into greater contact, gradually eliminating the excess compliance that gives rise to the anisotropy. A medium with such planes of excess compliance has been shown, theoretically, to describe the behavior of a medium with long parallel joints, as well as a medium with embedded parallel microcracks.

Modelling Orthorhombic Anisotropic Effects for Reservoir Fracture Characterization of a Naturally Fractured Tight Carbonate Reservoir, Onshore Texas, USA

“…Another very visible effect in the polar plots is that the velocity ellipse is aligned along the crack orientation where the maximum velocity is observed parallel to the crack axis. This agrees with the observation recorded by Hsu and Schoenberg (1993) and Hudson (1981) that during polarization in an anisotropic medium, the fastest P-wave velocity travels in a direction parallel to the orientation of the aligned fractures. Figure 9 expresses the effect of fracture-induced anisotropy (azimuthal anisotropy) in the form of variation in P-and S-waves' velocity with angle and S waves birefringence.…”

When do fractured media become seismically anisotropic? Some implications on quantifying fracture properties

“…Thus, even for the scalar crack case, our results indicate that the LS model is inconsistent with the vast majority of real fracture behaviour. This brings us to another important limitation of the LS model, the assumption that the lateral dimension of linear slip interface be greater than the dominant seismic wavelength (Hsu & Schoenberg, 1993) or the assumption of a smooth stress field (Kachanov, 1992) thus limiting scattering within the fracture normal direction. For our models, the wavelength of the S-waves range on the order of the fracture size (i.e., the fracture size is not significantly greater than the wavelength) and so the LS model does not model the scattering from fracture edges and tips It should be noted that the general assumption involved with the LS model is the LWA, such that λ S /d ≫ 1 (Sayers & Kachanov, 1991;Schoenberg & Sayers, 1995).…”

Wave Propagation in the Effective Model of Alternating Porous and Impermeable Solid Layers

“…De tels mod•les, Žlastiques, ont ŽtŽ largement utilisŽs ces quarante derni•res annŽes. Ils ont ŽtŽ rŽcemment remis ˆ jour pour la description des roches fracturŽes (Hsu et Schoenberg, 1993). Dans ce cas, il sÕagit de mod•les stratifiŽs Žlastiques ˆ fractures.…”