## 4 Clustering and Fault Surface Extraction  
The proposed workflow can be used to effectively detect faults, and it requires the processes of extracting and imaging fault surfaces from 3D cubes. The process of manual extraction of fault surfaces is influenced by the interpreter and requires an enormous amount of time. On the other hand, the automatic error extraction methods are quite complex and require several follow-up tasks with considerable computation time. In this workflow, we used orientation clustering to extract fault surfaces more easily. Figure 6: Second edge enhancement with cross-applying using the ant tracking attributes. In the (**a**) aggressive–passive–aggressive sequence, the edges of the small faults are more enhanced, and, in the (**b**) passive–aggressive–passive sequence, the edges of the major faults are enhanced. Figure 7: Fault detection using the (**a**) proposed and (**b**) conventional workflow. The proposed workflow generates clearer and simpler fault edges than conventional results. To perform clustering, the fault surfaces were first converted to points, as shown in Figure 8a. At this point, it is important to transform the information of the direction of the surface using a sufficient number of points for effective description. In addition, information of the azimuth and dip at each point position was extracted at the time of conversion, as shown in Figure 8b,c, respectively. Figure 8: Extracted fault surfaces as (**a**) point type. To perform orientation clustering, (**b**) azimuth and (**c**) dip information for each point position was also extracted. Clustering is an effective method to distinguish and extract similar groups by considering the characteristics of the data. The azimuth and dip information stored at each point was clustered using the density-based spatial clustering of applications with noise (DBSCAN) method [37; 38]; subsequently, the fault was extracted separately. The DBSCAN algorithm expands clusters by finding data that are close to the initial data. The input parameters were the number of neighbors required to define the dense region (MinPts) and the distance representing the neighborhood (\(\epsilon\)). Using these parameters, the data were classified into three types. If the number of points within a neighborhood with distance \(\epsilon\) exceeded the minimum, then such a point was designated as a core point. After a core point was located, data within its neighborhood were defined as connected points or as other core points. If the data point was not connected to a neighbor, it was designated as a border point. Lastly, data in clusters that were neither core nor border points were designated as noise. Therefore, DBSCAN performs density-based clustering, and, unlike K-means, the number of final clusters is not required as an input parameter, which is an advantage. Figure 9 shows clustered fault point sets. Since DBSCAN was used, complexly intertwined faults could be identified individually according to the orientation, and the density-based attributes allowed the extraction of the connectivity of the fault surface. Furthermore, parts that lacked the number of points to be defined as a fault were considered outliers and removed. Figure 10 shows the results of extracting the fault model from the original fault cube using the conventional automatic method and the proposed clustering method. The automated method showed significantly lower connectivity of the fault, and it seemed difficult to implement an accurate model because individual separation of the fault was not well generated at the intersection site of several intersections. On the other hand, using the proposed method, the generated model extracted individual fault surfaces with high connectivity. In addition, unnecessary outliers could be eliminated to obtain simpler and more visible images. Comparing the time spent on the extracting method, it took at least two days to combine the calculation and editing processes when modeling faults using the automatic extraction method.