# DSCope: Development of Automatic Program for Detecting Fractures and Measuring Dip Angles
## 3 Application to the Field Drilling Cores
### Distribution of Fracture Dip Angles  
Based on the above results, analysis was conducted to statistically set values such as the thresholds. To achieve this, the background noise of the rock needed to be set. The results of analyzing 4.5\(\sigma\) and 5.0\(\sigma\) showed that at a difference of 0.5\(\sigma\), the standard deviation of the B-threshold for detecting fractures increased by 0.001. Hence, the noise distribution of the rock background was assumed to have a normal distribution with an average of 0 and a standard deviation of 0.011. Figure 10 presents this as a graph. The black line indicates the background noise, and the red dashed line and blue dotted line indicate the settings for 4.5\(\sigma\) and 5.0\(\sigma\), respectively. According to these settings, the ranges with higher detection rates than noise are indicated by arrows of different colors. In the setting for 4.5\(\sigma\), using a threshold value between 1.6\(\%\) and 14.4\(\%\) could detect fractures well. The point with the maximum difference of 7.3\(\%\) is the red vertical line. In the setting for 5.0\(\sigma\), the threshold value needed to be set to 1.4\(\%\) or higher or 11.8\(\%\) or lower. The threshold value showing the largest difference with the background noise was 6.2\(\%\) (blue vertical line).  
Reliability was verified by comparing the results from the visual analysis with the results obtained from the DSCope program. The data used for verifying reliability were the same as the data used to verify the differences according to the settings. Around 50 cores down to 50 m in depth were used for comparison with the results from the visual analysis. The settings used in this analysis were \(\sigma=4.7\) and threshold = 7\(\%\). In addition, only the middle parts of the core photographs were used after cutting off approximately 30\(\%\) from both sides.  
The DSCope program recognized 366 fractures in total. However, 87 of them were in the fracture zone and thus excluded, because it was impossible to measure the dip angles using linear fitting. Furthermore, 173 wood chips inserted in the middle to mark the depth of the drilling cores and parts of the tops and bottoms of the drilling cores were excluded from the results because they were not fractures. In other words, 106 fractures were automatically measured by DSCope. Among the 138 fractures whose dip angles could be measured, 106 fractures (77\(\%\)) were automatically measured by DSCope, and 32 fractures were manually detected and added. Of the 32 fractures, 6 parts were detected and measured manually because they could not be detected by DSCope. When two or more fractures were detected in one scanbox, the fractures were measured after changing the  
Figure 9: Scatter plot of the bottom thresholds at two different sigma values.  
scanbox to a smaller size (i.e., 14 parts). However, two of them were excluded because they could not be automatically measured by the program. When the dip angle measurement was inaccurate due to noise, the angle was measured again. A total of 16 fractures were measured again, but 2 of them could not be measured due to noise hindering the marking of the edges. We present the results in Figure 11.  
The results of the visual analysis and DSCope analysis are summarized in Table 1. The DSCope code detected 86% of the fractures at low angles (0-30\({}^{\circ}\)) and reproduced 64% of the fractures at medium angles (30-60\({}^{\circ}\)). However, it could measure only 8% of the fractures at high angles (60-90\({}^{\circ}\)), which were believed to be influenced by the fracture zones. The reason this problem happened was that most fractures with high angles were located in the fracture zones, which excluded them from the DSCope results.  
Figure 11: Distribution of the measured angles of the cores up to 50 m in depth through DSCope.  
Figure 10: Probability of detection as a function of the threshold.