甘肃北山花岗岩裂隙几何学特征研究及岩石质量初探

文中以甘肃北山花岗岩中发育的构造裂隙(主要指节理)为研究对象,通过野外裂隙调查,应用传统的概率统计方法与分形几何学理论,利用Mapinfo,ArcGIS平台进行裂隙几何学参数(方位、长度、密度等)的统计、计算和裂隙网络的空间结构分析,研究花岗岩岩体中裂隙的几何学特征。并以此为基础,对甘肃北山花岗岩岩体质量优劣进行初步评价。结果表明:在10～200cm范围内,裂隙网络是分形的;5个测点裂隙网络的分维值分别是1.636,1.548,1.596,1.724,1.604。分维数D不仅能刻画岩体中结构面发育的数量,而且能反映结构面在岩体中分布的均匀程度和交切方式。因此,可以表征岩体的质量优劣,对岩体质量进行分级。按照分维所划分的岩体质量分级,北山花岗岩属于裂隙较发育、岩体质量等级一般的岩体     

Fractal analysis of 2-D fracture networks of geothermal reservoirs in south-western Turkey

Natural fracture patterns of producing geothermal formations in south-western Turkey are mapped at different scales. The fractal dimensions of different fracture network properties, such as spatial distribution, density, connectivity, orientation, and length are measured by different methods. Analysis of the natural fracture patterns from giga to microscales identifies the descending behavior of box-counting fractal dimension with respect to the scale. It is observed that the fracture networks represent scale-invariant properties, but fractal dimensions might notably differ when the mass dimension is measured applying different methods. Anisotropic nature of fracture networks is also included in the fractal analysis.     

Fractals,fault-gouge,and friction

The particle-size distribution of a natural fault-gouge has been determined over the range from 5 m to 40 cm. The gouge is self-similar over the range from 5 m to 1 cm having a fractal dimension of 2.60±0.11. The lower and upper fractal limits were also determined. The lower fractal limit occurs at a dimension of about 1–10 m where mineral cleavage and intergranular porosity dominate the cataclasis. The upper fractal limit occurs at particle sizes on the order of 1 cm where the scaled particle density decreases abruptly by a factor of about three. By analogy to soil-mechanics shear box tests and laboratory rock friction experiments, it is argued that the upper fractal limit of the gouge determines the characteristic displacement parameter in stick-slip friction models. A characteristic displacement on the order of 1 cm is consistent with estimates based on numerical simulations of faulting.     

The fractal geometry of flow paths in natural fractures in rock and the approach to percolation

The distributions of contact areas in single, natural fractures in quartz monzonite (Stripa granite) are found to have fractal dimensions which decrease fromD=2.00 to values nearD=1.96 as stress normal to the fractures is increased from 3 MPa up to 85 MPa. The effect of stress on fluid flow is studied in the same samples. Fluid transport through a fracture depends on two properties of the fracture void space geometry. the void aperture; and the tortuosity of the flow paths, determined through the distribution of contact area. Each of these quantities change under stress and contribute to changes observed in the flow rate. A general flow law is presented which separates these different effects. The effects of tortuosity on flow are largely governed by the proximity of the flow path distribution to a percolation threshold. A fractal model of correlated continuum percolation is presented which quantitatively reproduces the flow path geometries. The fractal dimension in this model is fit to the measured fractal dimensions of the flow systems to determine how far the flow systems are above the percolation threshold.     

Modelling frequency-dependent seismic anisotropy in fluid-saturated rock with aligned fractures: implication of fracture size estimation from anisotropic measurements

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.     

Scale Effects Related to Flow in Rough Fractures

— A numerical fracture flow simulation based on the lubrication approximation is used to investigate the influence of roughness on the flow inside a rough fracture, at low Reynolds number. Facing surfaces are described as self-affine topographies with identical roughness magnitude. Resolution of the Reynolds equation is achieved using two distinct numerical schemes, with consistency. Fracture closure is studied assuming perfect plastic contact between facing surfaces. Long-range correlations are shown to exist in the local aperture field due to the fracture geometry and subsequently in the local fluxes inside the fracture. Flow channeling is the result of these correlations in terms of spatial distribution of the flow, and is responsible for either flow-enhancing or flow-inhibiting behavior of the fracture. Matching between the two surfaces at scales larger than a mismatch scale is studied. The mismatch scale is the upper limit scale for the local apertures scale invariance. It appears to control flow channeling and the related dispersion of the possible behaviors over a large statistics of fractures with identical statistical features. Hydraulic anisotropy of a given fracture is investigated: the dependence of the fracture transmittivity on the pressure drop orientation is proved to be sinusoidal, with an amplitude that is controlled by the mismatch scale.     

Seismic prediction method of multiscale fractured reservoir

Common prestack fracture prediction methods cannot clearly distinguish multiplescale fractures. In this study, we propose a prediction method for macro- and mesoscale fractures based on fracture density distribution in reservoirs. First, we detect the macroscale fractures (larger than 1/4 wavelength) using the multidirectional coherence technique that is based on the curvelet transform and the mesoscale fractures (1/4–1/100 wavelength) using the seismic azimuthal anisotropy technique and prestack attenuation attributes, e.g., frequency attenuation gradient. Then, we combine the obtained fracture density distributions into a map and evaluate the variably scaled fractures. Application of the method to a seismic physical model of a fractured reservoir shows that the method overcomes the problem of discontinuous fracture density distribution generated by the prestack seismic azimuthal anisotropy method, distinguishes the fracture scales, and identifies the fractured zones accurately.     

断层滑动速率,地震重复时间和平均应力降

本文综述了国内外大地震复发间隔研究的现状，系统整理了中国大陆活断层滑运速率，已发现的古地震遗迹及古地震复发间隔，结果表明，在滑动速率较在的活断层发现的古地震复发间隔较短，Ｋａｎａｍｏｒｉ和Ａｌｌｅ（１９８５）研究了具有大范围重复时间（２０年到几千年）的板内大地震的震源参数，发现复发间隔较长的大地震具有较高的平均应力降，我们在实验室内研究了应变速率不同时固体围压三轴压缩下完整花岗岩破裂后的粘滑现象。     

A seismic reflection from isotropic‐fractured fluid‐saturated layer

Average elastic properties of a fluid‐saturated fractured rock are discussed in association with the extremely slow and dispersive Krauklis wave propagation within individual fractures. The presence of the Krauklis wave increases P‐wave velocity dispersion and attenuation with decreasing frequency. Different laws (exponential, power, fractal, and gamma laws) of distribution of the fracture length within the rock show more velocity dispersion and attenuation of the P‐wave for greater fracture density, particularly at low seismic frequencies. The results exhibit a remarkable difference in the P‐wave reflection coefficient for frequency and angular dependency from the fractured layer in comparison with the homogeneous layer. The biggest variation in behaviour of the reflection coefficient versus incident angle is observed at low seismic frequencies. The proposed approach and results of calculations allow an interpretation of abnormal velocity dispersion, high attenuation, and special behaviour of reflection coefficients versus frequency and angle of incidence as the indicators of fractures.     

Low-frequency anisotropy in fractured and layered media

Computing effective medium properties is very important when upscaling data measured at small scale. In the presence of stratigraphic layering, seismic velocities and anisotropy parameters are scale and frequency dependent. For a porous layer permeated by aligned fractures, wave-induced fluid flow between pores and fractures can also cause significant dispersion in velocities and anisotropy parameters. In this study, we compare the dispersion of anisotropy parameters due to fracturing and layering at low frequencies. We consider a two-layer model consisting of an elastic shale layer and an anelastic sand layer. Using Chapman's theory, we introduce anisotropy parameters dispersion due to fractures (meso-scale) in the sand layer. This intrinsic dispersion is added to anisotropy parameters dispersion induced by layering (macro-scale) at low frequencies. We derive the series coefficients that control the behaviour of anisotropy parameters at low frequencies. We investigate the influences of fracture length and fracture density on fracturing effect, layering effect and combined effect versus frequency and volume fraction of sand layer. Numerical modelling results indicate that the frequency dependence due to layering is not always the dominant effect of the effective properties of the medium. The intrinsic dispersion is not negligible compared with the layering effect while evaluating the frequency-dependent properties of the layered medium.     

Statistical distribution of natural fractures and the possible physical generating mechanism

We have fitted field measurements of fracture spacings (from the vicinity of Lake Strom Thurmond, Georgia, U.S.A.) to the Weibull, Schuhmann and fractal distributions. The fracture spacings follow a fractal and Weibull distribution which implies that they were formed as a result of a repetitive fragmentation process. The limited variation of the fracture density with orientation in the study area suggests that the stress distribution generating these fractures may be uniform.     

Resolving the Geometry of Hydraulic Fractures from Tilt Measurements

This paper discusses the resolution of geometrical characteristics of pressurized fractures from tiltmeter data. The quasi-static deformation and tilt field induced by such fractures can be modeled by superposition of displacement discontinuity (DD) singularities. Despite the relatively common use of such measurements to infer fracture characteristics, there is a widespread misunderstanding of what can be accurately determined, depending on the relative distance between the tiltmeter array and the fracture. We investigate in detail the resolution of the dimensions and orientation of hydraulic fractures or faults from tilt measurements. In particular, we formally prove that at a distance larger than about twice the characteristic length of the fracture, elastostatic measurements such as those measured by tiltmeters are not able to resolve independently all the dimensions of the fracture, although the fracture volume can be robustly inverted from the data. The resolution of fracture orientation is also discussed using an analysis based on a spatial Fourier Transform of the tilt field. The relative angle between the plane where the measurements are located and the fracture plane plays a major role in the accuracy of this estimation. In an illustrative field example, where the measurements are located in the far-field of the fracture deformation field, we show how a single DD singularity can be used to model tiltmeter data and efficiently obtain the fracture orientation and volume.     

裂缝性地层方位侧向测井响应数值模拟

为研究井周裂缝发育特征,本文提出一种新型方位侧向测井方法,利用三维有限元法,模拟裂缝的方位侧向测井响应.结果显示,深浅侧向电阻率幅度差异受裂缝倾角的控制,低角度缝为负差异,高角度缝为正差异;倾斜裂缝张开度的增大使测井响应值减小,方位电阻率差异增大;井周方位电阻率可反映裂缝方位产状,单一缝或裂缝密度较小时,沿裂缝走向的方位电阻率小,沿裂缝倾向的方位电阻率大;裂缝发育地层的测井响应显示宏观各向异性特征,但方位电阻率的差异显示发生反转现象,即沿裂缝走向/层理方向的方位电阻率大,沿裂缝倾向/垂直层理方向的方位电阻率小;对方位电阻率测井响应进行井周成像,直观显示了裂缝的产状和发育特征.     

岩石分形断裂的统计理论

本文研究了岩石分形断裂的统计理论.认为岩石断裂是岩石内部微裂缝成核、形成和传播的非平衡过程,导出了描述这个过程的微分方程.运用位错塞积成核机理,得到了岩石发生分形断裂的微裂缝大小的统计分布函数和平均长大速率.从理论上得出了岩石非弹性体积应变与微裂缝数目成正比,从而解释了实验室研究的结果.另外发现岩石的分维是决定岩石脆性的一个重要因素,分维值愈小,岩石愈脆.但岩石的分维值与岩石强度无明显关系.最后,从微裂缝大小的统计分布函数出发,导出了b值与岩石分维值的关系.     

Numerical investigation of alternative fracture stiffness measures and their respective scaling behaviours

We study the mechanical deformation of fractures under normal stress, via tangent and specific fracture stiffnesses, for different length scales using numerical simulations and analytical insights. First, we revisit an equivalent elastic layer model that leads to two expressions: the tangent stiffness is the sum of an “intrinsic” stiffness and the normal stress, and the specific stiffness is the tangent stiffness divided by the fracture aperture at current stress. Second, we simulate the deformation of rough fractures using a boundary element method where fracture surfaces represented by elastic asperities on an elastic half‐space follow a self‐affine distribution. A large number of statistically identical “parent” fractures are generated, from which sub‐fractures of smaller dimensions are extracted. The self‐affine distribution implies that the stress‐free fracture aperture increases with fracture length with a power law in agreement with the chosen Hurst exponent. All simulated fractures exhibit an increase in the specific stiffness with stress and an average decrease with increase in length consistent with field observations. The simulated specific and tangent stiffnesses are well described by the equivalent layer model provided the “intrinsic” stiffness slightly decreases with fracture length following a power law. By combining numerical simulations and the analytical model, the effect of scale and stress on fracture stiffness measures can be easily separated using the concept of “intrinsic” stiffness. We learn that the primary reason for the variability in specific stiffness with length comes from the fact that the typical aperture of the self‐affine fractures itself scales with the length of the fractures.     

Anisotropic stress accumulation in cooling lava flows and resulting fracture patterns: Insights from starch-water desiccation experiments

Desiccation of starch-water slurries is a useful analog for the production of polygonal fractures/columnar joints in cooling lava flows. When left to dry completely, a simple mixture of 1:1 starch and water will produce columns that appear remarkably similar to natural columnar joints formed in cooled lava flows. Columns form when the accumulation of isotropic stress exceeds the tensile strength of a material, at which point a fracture forms and advances through the material perpendicular to the desiccating surface. Individual fractures will initially form orthogonal to the desiccation surface but will quickly evolve into a hexagonal fracture network that advances incrementally through the material. However, some fracture patterns found within natural lava flows are not hexagonal (Lodge and Lescinsky, 2009-this issue), but rather have fracture lengths that are much longer than the distance to adjacent fractures. These fractures are commonly found at lava flows that have interacted with glacial ice during emplacement. The purpose of this study is to utilize starch analog experiments to better understand the formation of these fractures and the stress regimes responsible for their non-hexagonal patterns.To simulate anisotropic conditions during cooling, the starch slurry was poured into a container with a movable wall that was attached to a screw-type jack. The jack was then set to slowly extend or retract while the slurry desiccated. This resulted in either a decrease or increase in the chamber cross-sectional area thus creating compressional or extensional regimes. Decreasing chamber area (DCA) experiments resulted in fractures with larger lengths parallel to the direction of wall movement (also direction of compression). It also caused localized thrust faulting and curved column development. Increasing chamber area (ICA) experiments produced a zone of horizontal column development along the expanding margin (produced when the wall detached from the sample). Within this zone vertical fracture traces were observed that extended beyond individual columns.The viscoelastic rheology of both starch-water slurries and cooling lava flows aid in the production of these long and continuous fractures. During desiccation/cooling, the total strain in the material is divided into elastic strain (stress accumulating) and viscous strain (stress relaxing). During isotropic conditions, the viscous component is also isotropic therefore stress is relaxed equally in all directions. However, if there is an existing viscous strain, such as in the DCA and ICA experiments, stress can be preferentially relaxed in a single direction resulting in fracture development with preferred orientations.     

Frequency-dependent PP and PS reflection coefficients in fractured media

When a porous layer is permeated by mesoscale fractures, wave-induced fluid flow between pores and fractures can cause significant attenuation and dispersion of velocities and anisotropy parameters in the seismic frequency band. This intrinsic dispersion due to fracturing can create frequency-dependent reflection coefficients in the layered medium. In this study, we derive the frequency-dependent PP and PS reflection coefficients versus incidence angle in the fractured medium. We consider a two-layer vertical transverse isotropy model constituted by an elastic shale layer and an anelastic sand layer. Using Chapman's theory, we introduce the intrinsic dispersion due to fracturing in the sand layer. Based on the series coefficients that control the behaviour of velocity and anisotropy parameters in the fractured medium at low frequencies, we extend the conventional amplitude-versus-offset equations into frequency domain and derive frequency-dependent amplitude-versus-offset equations at the elastic–anelastic surface. Increase in fracture length or fracture density can enlarge the frequency dependence of amplitude-versus-offset attributes of PP and PS waves. Also, the frequency dependence of magnitude and phase angle of PP and PS reflection coefficients increases as fracture length or fracture density increases. Amplitude-versus-offset type of PP and PS reflection varies with fracture parameters and frequency. What is more, fracture length shows little impact on the frequency-dependent critical phase angle, while the frequency dependence of the critical phase angle increases with fracture density.     

Fractal characterization and frequency properties of near-fault ground motions

This study explores the irregularity and complexity of strong earthquake ground motions from the perspective of fractal geometry, and constructs a relation with the frequency content of the ground motions. The box-counting fractal dimensions and five representative period parameters of near-fault ground motions from the Chi-Chi and Northridge earthquakes are calculated and compared. Numerical results indicate that the acceleration and velocity time histories of ground motions present the statistical fractal property, and the dominant pulses of near-fault ground motions have a significant influence on their box dimensions and periods. Further, the average box dimension of near-fault impulsive ground motions is smaller, and their irregular degree of wave forms is lower. Moreover, the box dimensions of ground motions reflect their frequency properties to a large extent, and can be regarded as an alternative indicator to represent their frequency content. Finally, the box dimension D of the acceleration histories shows a considerably negative correlation with the mean period T. Meanwhile, the box dimension of the velocity histories Dye is negatively correlated with the characteristic period T and improved characteristic period Tgi.     

Fractures: Finite-size scaling and multifractals

The distributions of contact area and void space in single fractures in granite rock have been determined experimentally by making metal casts of the void spaces between the fracture surfaces under normal loads. The resulting metal casts on 52 cm diameter core samples show a complex geometry for the flow paths through the fracture. This geometry is analyzed using finite-size scaling. The spanning probabilities and percolation probabilities of the metal casts are calculted as functions of observation scale. Under the highest stresses of 33 MPa and 85 MPa there is a significant size-dependence of the geometric flow properties for observation scales smaller than 2 mm. Based on this data, the macroscopic percolation properties of the extended fracture can be well represented by relatively small core samples, even under normal stresses larger than 33 MPa. The metal casts also have rich multifractal structure that changes with changing stress.     

地震资料中的多尺度断裂与流体响应特征：数值模拟分析

流体在断裂和岩石骨架间的交换被认为是影响岩石弹性参数各向异性的主要原因,理论研究表明断裂尺度同样对弹性参数的各向异性也有影响.为了说明两者对各向异性影响以实现多尺度断裂裂隙的识别,本文在等效介质模型的基础上,应用数值分析的方法研究速度和衰减(1/Q)随多尺度断裂、频率和流体因子变化规律.结果表明介质弹性参数是频率依赖的,并且参数中存在衰减项,而这种频率依赖性与介质物性参数中的断裂尺度及流体性质存在一定的联系;当断裂定向分布时,参数结果显示为各向异性;不同断裂尺度具有不同的波速频散特性,剪切波分裂程度依赖于频率,断裂尺度起着控制作用,高频时对小尺度的敏感,低频段对大尺度敏感.在地震频段Thomsen参数随着频率的增大而减小,随着断裂尺寸的增大而减小.因此地震数据可能区分断裂和微裂隙引起各向异性,从而可测量断裂尺度.