Many carbonate rocks are composed of layers and contain fracture sets that cause the hydraulic, mechanical and seismic properties to be anisotropic. Co-located fractures and layers in carbonate rock lead to competing wave-scattering mechanisms: both layers and parallel fractures generate compressional-wave (P-wave) guided modes. The guided modes generated by the fractures may obscure the presence of the layers. In this study, we examine compressional-wave guided modes for two cases: wave guiding by fractures in a layered medium with sub-wavelength layer thickness; and wave guiding in media with competing scattering mechanisms, namely layering (where the thickness is greater than a wavelength) and parallel sets of fractures. In both cases, the fracture spacing is greater than a wavelength. When the layer thickness is smaller than a wavelength, P-wave guiding is controlled by the spacing of the fractures, fracture specific stiffness, the frequency of the signal and the orientation of the layering relative to the fracture set. The orientation of the layering determines the directionally dependent P-wave velocity in the anisotropic matrix. When the layer thickness is greater than a wavelength and an explosive point source of a signal is located in the layer containing a fracture, the fracture either enhanced or suppressed compressional-mode wave guiding caused by the layering in the matrix.Carbonate reservoirs pose a scientific and engineering challenge to geophysical prediction and monitoring of fluid flow in the subsurface. This is particularly true for carbonate rocks, many of which form in spatially and temporally variable depositional environments, and are modified further by diagenesis and deformation during the subsequent rock history. Variations in primary depositional geometries (metre to kilometre scale), as influenced by factors such as their depositional environments, sealevel fluctuations and climate, are reflected by distinct stacking patterns of rock layers or bodies, and variations in their thickness and lateral continuity. Depositional and/or construction processes influence finer-scale (micron to centimetre scale) textural variations and the formation of sedimentary structures. The resulting pore systems in the rock matrix comprise pores that vary in scale from submicron to centimetres. Fossil and primary mineral content, as well as spatial and compositional variations in cements, introduce further heterogeneities to the rock texture. Both cements and pore structure can be modified multiple times by temporal variations in the compositions, temperatures and flow rates of fluids migrating through the rocks. Carbonate rocks that have been subjected to deformation in response to burial, tectonic and induced (e.g. during hydrocarbon production) stresses commonly develop arrays of fractures as well as stylolites. While the orientations of these features vary with the burial and deformation history, fracture arrays are commonly steeply dipping, while stylolites tend to be oriented parallel to bedding.Diffi...
The detection of fractures in an anisotropic medium is complicated by discrete modes that are guided or confined by fractures such as fracture interface waves. Fracture interface waves are generalized coupled Rayleigh waves whose existence and velocity in isotropic media depend on the stiffness of the fracture, frequency of the source, and shear-wave polarization. We derived the analytic solution for fracture interface waves in an orthorhombic medium and found that the existence and velocity of interface waves in anisotropic media are also affected by the orientation of a fracture relative to the layering. Laboratory measurements of fracture interface waves using ultrasonic transducers (central frequency ∼1 MHz) on garolite specimens confirmed that the presence of fracture interface waves can mask the textural shear-wave anisotropy of waves propagating parallel to the layering. At low stresses, a layered medium appears almost isotropic when a fracture is oriented perpendicular to the layering, and conversely, a layered medium exhibits stronger anisotropy than the matrix for a fracture oriented parallel to the layering. The matrix shear-wave anisotropy is recovered when sufficient stress is applied to close a fracture. The theory and experimental results demonstrated that the interpretation of the presence of fractures in anisotropic material can be unambiguously interpreted if measurements are made as a function of stress, which eliminates many fractured-generated discrete modes such as fracture interface waves.
Simulation of elastic-wave propagation in rock requires knowledge of the elastic constants of the medium. The number of elastic constants required to describe a rock depends on the symmetry class. For example, isotropic symmetry requires only two elastic constants, whereas transversely isotropic symmetry requires five unique elastic constants. The off-diagonal elastic constant depends on a wave velocity measured along a nonsymmetry axis. The most difficult barrier when measuring these elastic constants is the ambiguity between the phase and group velocity in experimental measurements. Several methods to eliminate this difficulty have been previously proposed, but they typically require several samples, difficult machining, or complicated computational analysis. Another approach is to use the surface (Rayleigh) wave velocity to obtain the off-diagonal elastic constant. Rayleigh waves propagated along symmetry axes have phase and group velocities that are equal for materials with no frequency dispersion, thereby eliminating the ambiguity. Using a theoretical secular equation that relates the Rayleigh velocity to the elastic constants enable determination of the offdiagonal elastic constant. Laboratory measurements of the elastic constants in isotropic and anisotropic materials were made using ultrasonic transducers (central frequency of 1 MHz) for the Rayleigh-wave method and a wavefront-imaging method. The two methods indicated agreement within 1% and 3% for isotropic and transversely isotropic samples, respectively, demonstrating the ability of the Rayleigh-wave method to measure the off-diagonal elastic constant. The surface-wave approach eliminates the need for multiple samples, expensive computational calculations, and most importantly, it removes the ambiguity between the phase and group velocity in the measured data for materials with no frequency dispersion because all measurements are made along symmetry axes.
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