# Research on a 3D Seismic Horizon Automatic-Tracking Method Based on Corrugated Global Diffusion
## 2 Method
### Stage 2: Ripple-Type Global Spatial Diffusion Method
As shown in Figure 7, select the two lanes on the left and right of the diffusion road (b road) as the diffusion window ([a, b, c]) and the two lanes on the left and right of the diffused road (3 roads) ([1, 2, 3, 4, 5]) as the diffused window. These two data windows are the dataset for the next step of DTW relevance calculation. The next step is to select backup points. Once the diffusion window is confirmed, 3 backup points regarding the labeled horizon \(\theta\) can be selected through the diffusion relationship. The diffusion relationship is shown in Figure 8.  
Figure 6: Label transfer direction. Figure 7: Selection of diffusion window. The calculation of \(\theta\) horizon is carried out by selecting the candidate points of the horizon according to the guiding relationship shown by the arrow in the Figure 5, with the [1, 2, 3, 4, 5] as the spreading window. The selection method is not much different from other DTW horizon-tracking algorithms. By calculating the partial dataset between road a and road 1 with respect to the \(\theta\) horizon, 3 candidate points can be selected from among the 5 candidate points (as shown in Figure 5), and 15 candidate points can be obtained for the 5 datasets in the spreading window. Then, the next step is to calculate the correlation coefficient. This step is also where the algorithm differs from other DTW-based horizon-tracking algorithms. To strengthen the association between the horizon points within the same horizon plane, this paper abandons the horizon propagation method (from single horizon to single horizon) and, instead, chooses to use it as a basis for the next processing step, which is the calculation of the correlation between the same horizon label within the expanding window between different data horizons. The calculation relationship is shown in Figure 9.  
According to the arrow direction shown in the above graph, after the inner and outer diffusion windows are determined, the correlation between horizons can be calculated according to Figure 9. In order to strengthen the correlation between horizon points during  
Figure 3:0 Diffusion relation. Figure 3:1 Correlation coefficient calculation. As shown in Figure 11, this is a set of optimal solutions, selecting these 5 optimal points from among 15 candidate points as the diffused horizon points. Only the middle horizon points (i.e., the red points in channel 3) are needed, as shown in Figure 3:2  
Thus, the horizon label \(\theta\) that is passed is determined at the 3-dimensional spatial position, and the matrix label values of the points shown in Figure 12 are marked as \(\theta\), where the labeling is successfully passed. The other labeling information transmission process is the same. The next step is to pass the horizon label \(\theta\) from seismic channel c to seismic channel 4 (as shown in Figure 8, the arrow direction is the horizon transmission direction), the selection of the window and calculation process remains unchanged, and this process is repeated until it is finished. To ensure that there is no labeling or horizon mixing when adjacent horizons diffuse, we also need to impose certain diffusion restrictions on the two adjacent horizons. As shown in Figure 13, the horizon label \(\omega\) and \(\lambda\) on channel a have the same spatial constraints (\(+/-2\)) during the horizon label transfer process from channel a to the outer ring channel 1. After the transfer of the \(\omega\) level on track a is completed, during the transfer of the \(\lambda\) level, we detect the points set below the candidate point of the \(\lambda\) level on track 1, and see if it has already been occupied by the \(\omega\) level or higher-level labels. If this is the case,  
Figure 3:3 Optimal path. Figure 3:4 Diffusion point. Figure 3:5 Adjacent horizon diffusion limit. the optimal candidate point for this \(\lambda\) level is denied, and the second best among the 3 alternative level points is selected.