Limits to crack density: The state of fractures in crustal rocks (original) (raw)
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The fracture criticality of crustal rocks
Geophysical Journal International, 1994
Preface. It is a pleasure and a honour to be included in this issue commemorating the centenary of Robert Stoneley's birth. I was, I believe, the last of the small number of research students supervised by Stoneley, and it gives me great pleasure that most of my research has been, by chance, in a field he initiated-(azimuthal) seismic anisotropy. Bob Stoneley was one of the first seismologists to consider azimuthally anisotropic seismic waves (specifically surface waves) in cubic and orthorhombic symmetries . Although, he considered these papers 'essentially as a development in the theory of elasticity', they were invaluable references to me when I first began to calculate surface waves in an anisotropic Earth. Bob would have been gently amused that a large part of the Earth is now recognized as having orthorhombic anisotropic symmetry.
A review of shear wave splitting in the crack‐critical crust
Geophysical Journal International, 2003
Over the last 15 years, it has become established that crack-induced stress-aligned shear wave splitting, with azimuthal anisotropy, is an inherent characteristic of almost all rocks in the crust. This means that most in situ rocks are pervaded by fluid-saturated microcracks and consequently are highly compliant. The evolution of such stress-aligned fluid-saturated grainboundary cracks and pore throats in response to changing conditions can be calculated, in some cases with great accuracy, using anisotropic poro-elasticity (APE). APE is tightly constrained with no free parameters, yet dynamic modelling with APE currently matches a wide range of phenomena concerning anisotropy, stress, shear waves and cracks. In particular, APE has allowed the anisotropic response of a reservoir to injection to be calculated (predicted with hindsight), and the time and magnitude of an earthquake to be correctly stress-forecast. The reason for this calculability and predictability is that the microcracks in the crust are so closely spaced that they form critical systems. This crack-critical crust leads to a new style of geophysics that has profound implications for almost all aspects of pre-fracturing deformation of the crust and for solid-earth geophysics and geology.
Keywords: explicit fractures finite-difference full-waveform synthetics scattering seismic anisotropy shear-wave splitting Fractures are pervasive features within the Earth's crust and they have a significant influence on the multi-physical response of the subsurface. The presence of coherent fracture sets often leads to observable seismic anisotropy enabling seismic techniques to remotely locate and characterise fracture systems. In this study, we confirm the general scale-dependence of seismic anisotropy and provide new results specific to shear-wave splitting (SWS). We find that SWS develops under conditions when the ratio of wavelength to fracture size (λ S /d) is greater than 3, where Rayleigh scattering from coherent fractures leads to an effective anisotropy such that effective medium model (EMM) theory is qualitatively valid. When 1 < λ S /d < 3 there is a transition from Rayleigh to Mie scattering, where no effective anisotropy develops and hence the SWS measurements are unstable. When λ S /d < 1 we observe geometric scattering and begin to see behaviour similar to transverse isotropy. We find that seismic anisotropy is more sensitive to fracture density than fracture compliance ratio. More importantly, we observe that the transition from scattering to an effective anisotropic regime occurs over a propagation distance between 1 and 2 wavelengths depending on the fracture density and compliance ratio. The existence of a transition zone means that inversion of seismic anisotropy parameters based on EMM will be fundamentally biased. More importantly, we observe that linear slip EMM commonly used in inverting fracture properties is inconsistent with our results and leads to errors of approximately 400% in fracture spacing (equivalent to fracture density) and 60% in fracture compliance. Although EMM representations can yield reliable estimates of fracture orientation and spatial location, our results show that EMM representations will systematically fail in providing quantitatively accurate estimates of other physical fracture properties, such as fracture density and compliance. Thus more robust and accurate quantitative estimates of in situ fracture properties will require improvements to effective medium models as well as the incorporation of full-waveform inversion techniques.
Petroleum Science - PET SCI, 2008
This paper reviews a new understanding of shear-wave splitting (seismic-birefringence) that is a fundamental revision of conventional fluid-rock deformation. It is a New Geophysics with implications for almost all solid-earth geosciences, including hydrocarbon exploration and production, and earthquake forecasting. Widespread observations of shear-wave splitting show that deformation in in situ rocks is controlled by stress-aligned fluid-saturated grain-boundary cracks and preferentially orientated pores and pore-throats pervasive in almost all igneous, metamorphic, and sedimentary rocks in the Earth’s crust. These fluid-saturated microcracks are the most compliant elements of the rock-mass and control rock deformation. The degree of splitting shows that the microcracks in almost all rocks are so closely spaced that they verge on fracture-criticality and failure by fracturing, and are critical systems with the “butterfly wing’s” sensitivity of all critical systems. As a result of th...
Anisotropy and beyond: Geologic perspectives on geophysical prospecting for natural fractures
The Leading Edge, 2007
Recent geologic research on natural fractures challenges assumptions frequently made by geophysicists. Open fractures are not necessarily oriented parallel to the maximum horizontal stress, and fractures do not necessarily close when the fluid pressure within them is reduced. Even in the most mechanically favorable environment, precipitated cements can prop fractures open or seal fractures of any orientation. Fracture sets typically show dispersion in strike, and multiple sets of open fractures can coexist. More importantly, fractures comprise populations that commonly range over orders of magnitude in aperture and length and that occur in nonuniform clusters. Instead of isolated, regularly spaced, large, equally compliant fractures, the Earth presents complex fractal clustering of fractures having a wide range of sizes and variable compliance dictated by natural cements in the fractures and the rock mass. Going beyond anisotropy to document these essential fracture attributes in the interwell space is a key challenge for geophysicists.
Microcrack-induced seismic anisotropy of sedimentary rocks
Journal of Geophysical Research, 1991
The seismic anisotropy often detected in the Earth's crust has been attributed in large part to the presence of open microcracks showing some degree of alignment. This alignment is believed to result from the anisotropic state of in situ stress, since any cracks remaining open at depth will tend to be oriented normal to the direction of the minimum in situ stress. Previous workers have calculated the change in elastic wave velocities due to either randomly oriented or perfectly aligned cracks. In this paper the P and S wave anisotropy in the long-wavelength limit is calculated for an arbitrary orientation distribution of cracks. For the case of an orthotropic distribution of circular cracks it is found that a simple relation exists between the P and S wave anisotropy. To test this prediction, ultrasonic P and S wave velocities were measured for propagation in three orthogonal directions through three samples of Berea sandstone as a function of maximum compressive stress applied perpendicular to the bedding plane. The samples were 50-mm cubes and were stressed to peak in a true triaxial loading frame, while the principal stress components parallel to the bedding plane were held constant at 4 MPa.
Journal of Geophysical Research, 1992
This study was conducted in order to characterize the frequency, orientation, and aperture of macroscopic fractures in the crust and their effect on physical properties over an appreciable depth interval (1829-3450 m). The following are our major findings: (1) Over the range of apparent apertures measured with confidence, the frequency of fractures with a given aperture decreases as aperture increases. With applied corrections for sampling bias, the observed distribution of fracture aperture has a power law form providing evidence of the self-similar nature of fractures in the crystalline crust. Fractal analysis of the fracture aperture data yields a fractal dimension of 1.4 over the range of reliable aperture measurements in this study from 15 to 100 mm. (2) Fracture frequency does not systematically decrease with depth in the study interval. (3) No significant correlation was found between fracture occurrence and lithology, and both fracture spacing and aperture are uncorrelated with fracture orientation or depth. (4) The majority of fractures encountered in the well strike NNW-SSE and dip steeply to the west. One set of steeply dipping fractures appears to be related to the NW striking San Andreas fault and appears to be related to steeply dipping, NW striking shear fractures observed in nearby outcrops that are characterized by laumontitic alteration. (5) The fractures bear no obvious relation to the current northeast direction of maximum horizontal compression but do correlate with anomalies in physical properties measurements of compressional and shear velocity, porosity, and resistivity. (6) Macroscopic fractures strike in a direction nearly orthogonal to the fast propagation direction of seismic wave anisotropy determined from vertical seismic profiling experiments in the well. These fractures appear to be unrelated to the observed seismic anisotropy. (7) Hydraulically conductive fractures and major faults indicate that fluid-conducting fractures are a subset of the overall statistically significant population and not related to the San Andreas fault or to the orientation of SHmax in an obvious way. Field experimentation has documented the response of seismic velocities to macroscopic fractures. In situ velocities depend on fracture spacing, stress state, fracture roughness, and degree of saturation. In situ velocities are generally lower than velocities measured in the laboratory, and this velocity difference is correlated with fracture frequency [
Geophysical Prospecting, 2011
P-and S-wave velocity and attenuation coefficients (accurate to ±0.3% and ±0.2 dB/cm, respectively) were measured in synthetic porous rocks with aligned, penny-shaped fractures using the laboratory ultrasonic pulse-echo method. Shearwave splitting was observed by rotating the S-wave transducer and noting the maximum and minimum velocities relative to the fracture direction. A block of synthetic porous rock of fracture density 0.0201 ± 0.0068 and fracture size 3.6 ± 0.38 mm (measured from image analysis of X-ray CT scans) was sub-sampled into three 20-30 mm long, 50 mm diameter core plugs oriented at 0 • , 45 • and 90 • to the fracture normal (transversely isotropic symmetry axis). Full waveform data were collected over the frequency range 500-1000 kHz for both water and glycerin saturated cores to observe the effect of pore fluid viscosity at 1 cP and 100 cP, respectively. The shear-wave splitting observed in the 90 • core was 2.15 ± 0.02% for water saturated and 2.39 ± 0.02% for glycerin saturated, in agreement with the theory that suggests that the percentage splitting should be 100 times the fracture density and independent of the saturating fluid. In the 45 • core, by contrast, splitting was 0.00 ± 0.02% for water saturation and −0.77 ± 0.02% for glycerin saturation. This dependence on fracture orientation and pore fluid viscosity is consistent with the poro-visco-elastic theory for aligned, meso-scale fractures in porous rocks. The results suggest the possible use of shear-or converted-wave data to discriminate between fluids on the basis of viscosity variations.
Geophysical Prospecting, 2003
Measurements of seismic anisotropy in fractured rock are used at present to deduce information about the fracture orientation and the spatial distribution of fracture intensity. Analysis of the data is based upon equivalent-medium theories that describe the elastic response of a rock containing cracks or fractures in the long-wavelength limit. Conventional models assume frequency independence and cannot distinguish between microcracks and macrofractures. The latter, however, control the fluid flow in many subsurface reservoirs. Therefore, the fracture size is essential information for reservoir engineers. In this study we apply a new equivalent-medium theory that models frequency-dependent anisotropy and is sensitive to the length scale of fractures. The model considers velocity dispersion and attenuation due to a squirt-flow mechanism at two different scales: the grain scale (microcracks and equant matrix porosity) and formation-scale fractures. The theory is first tested and calibrated against published laboratory data. Then we present the analysis and modelling of frequency-dependent shear-wave splitting in multicomponent VSP data from a tight gas reservoir. We invert for fracture density and fracture size from the frequency dependence of the time delay between split shear waves. The derived fracture length matches independent observations from borehole data.