Fractal dimension of fault systems in Japan: Fractal structure in rock fracture geometry at various scales

Based on fault maps, whether or not the fracture geometry of rocks is self-similar, was examined by using a box-counting algorithm. The statistical self-similarity (fractal structure) of the fault fracture systems holds well at the scale of about 2 to 20 km. The fractal dimension in Japan varied from 1.05 to 1.60. The fractal dimension is about 1.5–1.6 at the central part of the Japan Arc, and decreases with distance from the center. At a smaller scale, the fractal structure also holds well in the rock fracture geometry. The fractal dimension of the North Izu Peninsula fault system (branching faults) is 1.49 at the scale of 0.625 to 10 km, the fractal dimension of rock fracture geometry at the scale order of 10^–1 to 10^–2 meters is about 1.49–1.61. The upper limit of the fractal dimension of rock fracture geometry is about 1.6, judging from the estimation of fractal dimension on actual fracture geometry of rocks. This value may impose a restraint on modeling of faulting and the fracture process of rocks.     

Effective migration system of coalbed methane reservoirs in the southern Qinshui Basin

Effective migration system of coalbed methane(CBM)reservoir,which was controlled by development degree and opening-closing degree of fractures,determines the permeability of coal reservoir and can be characterized by the pore-fracture system in the extrinsic form.In this paper,based on coal matrix elastic self-regulating effect theory and coal reservoir combined elastic energy theory,the fracture opening-closing degree parameterΔand the fracture development degree parameterξare suggested for the quantitative study of the effective migration system of CBM reservoir in southern Qinshui Basin.Further,the control functions ofξandΔto CBM enrichment and high production are discussed.The results show that in present stage the area with highξvalue is located in Anze and Qinyuan,and then Zhengzhuang and Fangzhuang,where fracture development degree is high.The area with highΔvalue is located in Zhengzhuang and Fanzhuang,and then Anze and Qinyuan,indicating where coal matrix elastic self-regulating positive effect dominates and fractures tend to be open.Through the comprehensive analysis onξandΔ,it can be found that their best match area is located in Zhengzhuang and Fanzhuang,with high values for fracture development degree and opening-closing degree probably bringing about high fluid pressure and good permeability of reservoirs,which are advantageous to an abundant CBM production.     

Changes in magnetic and fractal properties of fractured granites near the Nojima Fault, Japan

Abstract Anisotropy of magnetic susceptibility (AMS) has been used to infer finite strain fabrics in plastically deformed rocks, but there are few studies of magnetic properties in fractured fault rocks. Changes in magnetic and fractal properties of fractured granites from the Disaster Prevention Research Institute, Kyoto University (DPRI) 500 m drilling core towards the Nojima Fault and of the well-foliated fault gouge are described. Fractal analysis of fractured granites shows that the fractal dimension ( D ) increases linearly toward the gouge zone of the fault. In weakly fractured granites ( D = 1.05–1.24), it was found that the degree of AMS correlates positively with the fractal dimension, suggesting a fracture-related magnetic fabric due to fracturing. In strongly fractured granites ( D = 1.25–1.50), weaker, nearly isotropic AMS is found, suggesting erasure by the fragmentation of the magnetic minerals. Within the fault gouge zone, an isotropic AMS fabric was found, as well as twofold increases in magnetic intensity and susceptibility. These changes reflect the production of new magnetite grains, subsequently confirmed by hysteresis studies, which suggests that fault gouge might be regarded as the source of the regional geomagnetic field contrast along active faults. Thus, AMS is clearly a potentially useful tool for inferring the fracturing texture of magnetic minerals in fractured rocks and detecting active faults from the high susceptibility contrast of fault gouge.     

Fractal dimensions of suspended solids in streams: comparison of sampling and analysis techniques

Fluvial suspended sediment typically consists of a variety of complex, composite particles referred to as flocs. Floc characteristics are determined by factors such as the source, size and geochemical properties of the primary particles, chemical and biological coagulation processes in the water column and shear stress and turbulence levels in the stream. Studies of floc morphology have used two contrasting methods of sampling and analysis. In the first method, particles settle on a microscope slide and are observed from below using an inverted microscope. The second method uses filtration at no or low vacuum and particles deposited on the filter are observed with a microscope. Floc morphology can be quantified using fractal dimensions. The aims of the present study were to examine the effect of the two sampling methods on the fractal dimensions of particle populations, and to evaluate for each method how well the fractal dimensions at the various sampling sites reflect basin conditions. Suspended solids were collected in triplicate on inverted microscope slides and on 0·45 μm Millipore HA filters in two southern Ontario streams with contrasting riparian zones during a minor runoff event resulting from the melt of a freshly fallen snowpack. An image analysis system was used to determine area, longest axis and perimeter of particles. The morphology of the particle population of each sample was characterized using four fractal dimensions (D, D₁, D₂ and D_K). Systematic differences in fractal dimensions obtained with the two methods were observed. For the settling method, outlines of larger particles were frequently blurred because of the distance between the focal plane (the top of the inverted microscope slides) and the plane of the particle outline. In this method, the blurring of large particles can cause an increase in the projected area and length of the particle. The effect on the particle perimeter is unpredictable because it depends on the amount of detail lost through blurring and its effect on the apparent increase in particle size. Because of blurring, D and D₁ tend to be systematically lower for the settling method, whereas the net effect on D₂ is unpredictable. Particle size distributions derived from settling are typically coarser because small, low density particles may remain in the water column and all particles may not deposit on the slides. This loss of fines results in systematically lower D_K values for the settling method compared with the filtration method. Fractal dimensions and particle size distributions obtained with the filtration method were sensitive to and clearly indicated differences between drainage basins and between sites within each basin. These differences were explained by basin characteristics and conditions. Fractal dimensions and particle size distributions obtained with the settling method were less sensitive to drainage basin characteristics and conditions, which limits their usefulness as process indicators. Copyright © 1999 John Wiley & Sons, Ltd.     

横波各向异性在裂缝和应力分析中的应用

针对裂缝性和低孔低渗地层的横波各向异性特征,反演得到横波各向异性参数,研究了裂缝的发育程度、方位和有效性,并对低孔低渗地层的应力场分布状态和方位进行了综合评价;通过对反演得到的快、慢弯曲波形进行频散分析以及计算单极横波各向异性大小,确定了引起横波各向异性的原因,并结合常规测井资料、岩心及FMI成像资料对分析结果进行了验证和对比,最后对研究区8口典型井的横波各向异性进行了综合处理和评价,得到了该区的横波各向异性特征以及和总的应力场走向.结果表明,利用横波的各向异性参数可以有效的评价裂缝的发育程度、走向及有效性,并能准确的确定地应力分布状态和最大水平应力方位.