# Acoustic Shooting and Bounce Ray Method for Calculating Echoes of Complex Underwater Targets
## 5 Acoustic Shooting and Bounce Ray Method
### Acoustic Beam Pipeline Splitting Processing  
When the vertex method is used to track the acoustic beam pipeline in space, the special case of intersecting with discontinuous target surface elements is excluded, and the acoustic beam pipeline incident on different target surface elements needs to be split. In the case of the plane wave incident, the results of the acoustic field integration of a plane element is only related to the integrated area and has nothing to do with the particle size of the plane element. Therefore, a local analysis of the acoustic beam pipeline to be split is shown in Figure 6.  
According to the intersection of the acoustic beam pipeline and target surface element in Figure 6, various splitting definitions are given as follows:  
1. If three of the four vertices of the acoustic beam pipeline fall on the same target surface element and the remaining one falls on the other target surface element, it is called type I splitting, as shown in Figure 6 for pipeline No. 1;
2. If the four vertices of the acoustic beam pipeline fall on two target surface elements in pairs, it is called type II splitting, as shown in Figure 6 for pipeline No. 2;
3. If the four vertices of the acoustic beam pipeline fall in more than three different target surface elements, it is called type III splitting, as shown in Figure 6 for pipeline No. 3.  
The serial number of the target surface element intersecting the four corner tops of the pipeline is recorded, respectively, during the line and surface  
Figure 6: Local and special cases of the intersection between the plane element and acoustic beam.  
pipeline splitting type can be obtained and processed through the above judgment. The process is as follows:  
1. If a pipeline has type I splitting, the pipeline must only intersect with two target surface elements. The intersection points E1 and F1 can be further solved by corner coordinates. The sound field integration is directly carried out on the pentagon plane (A1B1C1F1E1 in Figure 6) and the triangle plane (D1E1F1 in Figure 6).
2. If type II splitting occurs in a pipeline, the intersection point between the pipeline and the target surface element can be further solved by corner coordinates. If there are only two intersection points of E2 and F2 in Figure 6, then the pipeline must only intersect with two target surface elements, which is defined as type II-1 splitting. The sound field integration is directly carried out on two quadrilateral planes (A2B2F2E2 and C2D2E2F2 in Figure 6. If there are more than two intersections, it is defined as a type II-2 split and is treated in the same way as a type III split
3. If a line of four horns falls in three or more graphics, define it as a type III division, and the actual fellowship with the plane cannot be launched directly from the angle of the point coordinates (in Figure 3, the line is down to the four plane); an evenly divided line will be required before the split type judgment and handling;
4. If a pipeline has been split several times to reach the set aperture accuracy and it still belongs to type II-2 or III split, it will be discarded.  
In the actual calculation, type I and Type II-1 are the most important types of split pipelines, which do not require a uniform subdivision of pipeline aperture except for the distributed calculation of the sound field integration. Type III splitting occurs at the center of each grid and is the main source of uniform splitting pipelines. However, the occurrence probability of type II-2 splitting is very low. In order to improve the computational efficiency, the method of direct discard can be adopted.