# Research on a 3D Seismic Horizon Automatic-Tracking Method Based on Corrugated Global Diffusion
## 2 Method
### Stage 2: Ripple-Type Global Spatial Diffusion Method  
After establishing the local connection between the horizon points based on DTW, we need to diffuse this connection throughout the entire field, thus forming the complex horizons in the entire field. The selection scheme for the seed tracks remains unchanged, and the middle track is selected as the seed track. In the first step, the seed track x (timeline \(\times\) 1 \(\times\) 1) is spread outward to a labeled matrix of size timeline \(\times\) 3 \(\times\) 3. The specific method is shown in Figure 4.  
Figure 3: Schematic diagram of DTW extracting the best relevant segment. (a) Correlation coefficient diagram calculated from actual seismic channels; (b) the best correlation segment extracted by the DTW algorithm. Figure 2: Schematic diagram of DTW technology. (a) Compare the similarity of the two time series; (b) DTW algorithm to solve the best “correlation coefficient comb”. Set the central road as X, and transfer the label of X road to [1; 2; 3; 4; 5; 6; 7; 8] for a total of 8 data roads via the DTW algorithm. If there is a mapping horizon position between two adjacent roads, it means that each horizon position point on the surrounding 8 data roads can calculate 3 correlation coefficient values with the surrounding 3 roads. For example, a seed point marked as \(\theta\) on the 6 th road can calculate the correlation coefficient with the seismic roads 4, 7, and X. The specific algorithm works as follows:  
Step1: select point \(\theta\) on X lane and choose 3 points around 8 lanes as the optional connection for this point; then, based on the optimal global correlation coefficient, choose the optimal connection group of the current point \(\theta\), forming a horizon surface. From this, obtain the optimal connection of all points on the X lane set. Step 2: calculate the correlation coefficient value of each optimal connection, and label all groups in order of strongest to weakest correlation. This avoids labeling conflicts between two strata. Step3: when selecting candidate points, according to the actual geological horizon attribute, the spatial positions of the same horizon label between two adjacent timeline traces are generally within \(\pm 2\), i.e., the inclination \(\Omega\leq\arctan 2\). This is the spatial constraint added when performing DTW-based correlation coefficient calculations for actual seismic data. As shown in Figure 5, trace X contains a certain type of subpoint \(\theta\). If the horizon assignment work for \(\theta\) is performed, then the mapping point of trace 1 is within 5 data points with a range of \(\pm 2\) units in the \(\theta\) time axis co-ordinate. The correlation of a data segment containing a \(\theta\) label position and a data segment of the same size containing one of the 5 points is obtained by DTW calculation. Step 4: select 3 points with stronger correlation coefficients as alternative points. These 3 alternative points serve as the basis for the next step--the selection of the optimal  
Figure 4: First diffusion diagram. Figure 5: Space constraints. connection path. Based on the optimal connection path, the optimal horizon position can be obtained, and the label is transferred to the optimal horizon position, thus completing the horizon tracking of a data point. Once the first diffusion is completed, the second round of diffusion is performed. First, the labeling transfer direction is determined. If the first horizon labeling transfer work is mapped from the seed point in seismic road b to seismic road 3, the direction is shown (Figure 6). The transfer relationship confirmed in Figure 7 is the labeling transfer process of a certain label from the b lane of the timeline \(\times\) 3 \(\times\) 3-labeled matrix to lane 3 of the timeline \(\times\) 5 \(\times\) 5 matrix. After the transfer road and mapping road are confirmed, the next step will be the selection of the diffusion window.