Deep borehole log evidence for fractal distribution of fractures in crystalline rock
Deep borehole log evidence for fractal distribution of fractures in crystalline rock
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DOI：
10.1111/j.1365-246x.1991.tb01421.x
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发表时间：
1991-12
影响因子：
2.8
通讯作者：
P. Leary
中科院分区：
文献类型：
--
作者：
P. Leary
在加州南部Cajon Pass的San Andreas断层附近的结晶岩中，声速和电阻率测井在3.5公里的深度进行，在小尺度（亚米）和大尺度（几十到几百米）上都有相关性。对于岩性更敏感的自然伽马强度测井，没有发现这种相关性。声波速度和电阻率测井之间的相关性表明，结晶岩的非岩性控制波动。原位断裂强度是控制岩石性质的合理候选者。利用Hurst重标距参数对1.5m < L <1500m井段的声波速度和电阻率测井曲线的波动进行了研究。对于由标度不变的物理过程引起的对数波动，Hurst重标距标度的数据间隔为LH，0 < H < 1。一个纯随机序列的原位裂缝产生的标度指数H= 0.50。Cajon Pass声波速度和电阻率测井的波动产生H = 0.70的证据，表明原位裂缝组倾向于出现在集群中，而不是在纯粹的随机间隔。在1.5 m < L < 1500 m的测井层段上裂缝成簇的趋势表明，裂缝的形成是一个与长度尺度无关的分形过程，其中较大的裂缝层段是由许多较小的裂缝层段成簇形成的。从井中声速测井得到的地震反射率在1.5m < L <1500m的数据间隔范围内也与尺度无关，赫斯特指数H= 0.21。如果我们将裂缝聚集与地壳断层形成联系起来，Cajon Pass钻孔声速和电阻率测井预测地壳断层具有分形尺度D = 2.30。地震规模分布的等效b值为B 1.15。根据这一假设，观测到的b值< 1.15表明地震在现有（弱？）断层用于结晶岩石裂缝形成的尺度无关力学，其中较大尺度裂缝形成为较小尺度裂缝的簇，提供了小的普遍应力对准的瑕疵、裂缝和微裂缝（其可以赋予结晶岩石各向异性）与有限应变和断层相关的较大尺度裂缝之间的机械联系。因此，在地壳区域的活动，但低应变，裂缝各向异性被观察到与推断的最大主应力，而在活跃的断层地壳，裂缝各向异性被观察到更接近断层平行，如果裂缝对齐的有限应变断层过程。
Summary Sonic velocity and electrical resistivity logs run to a depth of 3.5 km in crystalline rock near the San Andreas fault at Cajon Pass in southern California correlate over scale-lengths both small (sub-metre) and large (tens to hundreds of metres). No such correlations are seen with the more lithologically sensitive natural gamma intensity log. The correlation between the sonic velocity and electrical resistivity logs suggests that a non-lithologic property of the crystalline rock controls fluctuations. In situ fracture intensity is a logical candidate for the controlling rock property. The fluctuations of the individual sonic velocity and electrical resistivity logs are examined with the Hurst rescaled range parameter over borehole log intervals 1.5 m < L < 1500 m. For log fluctuations arising from a scale-invariant physical process the Hurst rescaled range scales with data interval as LH, 0 < H < 1. A purely random sequence of in situ fractures produces a scaling exponent H= 0.50. Fluctuations in the Cajon Pass sonic velocity and electrical resistivity logs yield H˜ 0.70 evidence that in situ fracture sets tend to occur in clusters rather than at purely random intervals. The tendency for fracture clustering over log intervals 1.5 m < L < 1500 m suggests that fracture formation is a fractal process independent of length-scale in which larger fracture intervals form from clustering of numerous smaller fracture intervals. Seismic reflectivity derived from the borehole sonic velocity log is also scale independent over the range of data intervals 1.5m < L < 1500 m with a Hurst exponent H= 0.21. If we associate fracture clustering with crustal fault formation, the Cajon Pass borehole sonic velocity and electrical resistivity logs predict that crustal faults scale fractally with fractal dimension D˜ 2.30. The equivalent b-value for earthquake size distribution is b˜D/2˜ 1.15. On this hypothesis observed b-values < 1.15 indicate a tendency for earthquakes to cluster on existing (weak?) faults. A scale-independent mechanics for crystalline rock fracture formation in which larger scale fractures form as clusters of smaller scale fractures provides a mechanical link between the small pervasive stress aligned flaws, cracks and microfractures which can impart anisotropy to crystalline rock and the larger scale fractures associated with finite strain and faulting. Thus in crustal regions of active but low strain, fracture anisotropy is observed to be aligned with the inferred maximum principal stress, while in actively faulted crust, fracture anisotropy is observed to be more nearly fault parallel as if the fractures are aligned by the finite strain faulting process.