Analysis of the spatial variability on a fracture network based on an oriented semivariogram
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摘要:
运用地质统计学中的定向半变异函数，研究了个旧高松矿田莲花山断裂和五指山背斜裂隙网络的空间变异性。首先基于ArcGIS将野外露头裂隙网络进行数字化处理并提取裂隙密度和强度，然后依托GSLIB对裂隙密度和强度图沿着0~175°方位角计算，创建了36个实验性半变异函数并进行克里金插值，最后创建归一化的半变异函数图，量化各个断裂强度和断裂密度的二维空间变异性。研究表明，越是靠近断层裂隙密度和强度的空间变化幅度越大，并且其空间变异性存在显著的各向异性。空间变异性最小的方向平行断层且靠近断层，最大方向垂直断层且靠近断层，在褶皱近端空间变异性最小的方向平行于褶皱轴面方向，最大的方向则垂直于褶皱轴面方向。裂隙网络空间变异性质反映了断层和褶皱对裂隙网络发育的不同影响，为构建矿田三维裂隙网络空间分布模型提供参考。
Abstract:Using an oriented semivariogram in geostatistics, this paper studied the spatial variability of the fissure network of Lianhuashan fault and Wuzhishan anticline in Gejiu Gaosong Ore Field. First, the field outcrop fracture network was digitized based on ArcGIS, and the fracture density and intensity were extracted. Then, based on GSLIB, the fracture density and intensity maps were calculated along the azimuth angle of 0-175°, 36 experimental semivariograms were created and Kriging interpolation was carried out, and finally, normalized semivariogram graphs were created to quantify the two-dimensional spatial variability of individual fracture intensity and density. It was indicated that the closer to the fault, the greater the spatial variation of the fracture density and intensity, and the its spatial variability was featured in significant anisotropy. The direction with the smallest spatial variability was parallel and close to the fault, the largest direction was perpendicular and close to the fault, the direction with the smallest spatial variability at the proximal fold was parallel to the axial direction of the fold, and the largest direction was perpendicular to the axial direction of the fold. The spatial variability of the fracture network reflected the different effects of faults and folds on the development of the fracture network and provided a reference for the establishment of a three-dimensional fracture network spatial distribution model in the ore field.
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Key words:
- geostatistics /
- fracture network /
- spatial variability /
- Gaosong Ore Field /
- Kriging interpolation
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图 3 裂隙网络轨迹数字化图(n代表相应区域的裂隙或交点数量)
Figure 3. Digitized map of the fracture network trajectory
图 4 创建半变异函数数据点含义图
Figure 4. Schematic diagram of creating a data point for a semivariogram
图 5 创建定向半变异函数变量示意图
Figure 5. Schematic diagram of creating a directional semivariogram variable
表 1 使用Gslib程序时所需输入参数及含义
Table 1. Input parameters and meanings required to use the Gslib program
输入参数 取值 含义 Number of lags 10 每个半方差函数的滞后数 Unit lag separation distance/m 10 每个滞后的间隔距离 Lags tolerance/m 5 滞后容许值 Azimuth/(°) 0, 5…, 175 方位角 Az tol/(°) 10 角度容许值 Bandwidth h/m 20 方位角带宽 Ndir 36 需要考虑的方向数 
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表 2 样本属性
Table 2. Sample attribute
断裂强度 区域1 区域2 区域3 n 503 520 514 x 0.548 3 0.551 6 0.689 6 s 0.234 5 0.242 6 0.258 3 s2 0.054 9 0.058 9 0.066 7 CV 0.427 7 0.439 8 0.374 6 断裂密度 区域1 区域2 区域3 n 663 823 593 x 0.067 7 0.069 5 0.096 5 s 0.087 4 0.089 4 0.098 3 s2 0.007 6 0.007 9 0.009 6 CV 1.290 9 1.286 1 1.018 6 注：s为样本标准偏差; x为样本平均值；CV为变异系数
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表 3 相对变异率
Table 3. Relative variation rate
属性 方位角/(°) 变异体积 相对变异率 区域1 断裂强度 10 103.44 1.28 50 80.62 断裂密度 10 92.93 1.18 50 78.80 区域2 断裂强度 10 93.06 0.82 50 113.52 断裂密度 10 81.26 0.82 50 99.45 区域3 断裂强度 10 83.96 0.77 50 108.51 断裂密度 10 81.17 0.64 50 126.24
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