## 8 Experimental Results and Analysis
### Experiment with Combined Ray Tracing Method  
The combined ray tracing method automatically judges whether to employ the constant sound speed ray tracing method or the equal gradient ray tracing method based on the variation in sound speed gradient.  
Using the EOF inversion of the sound speed profile, the depth interval between every two layers of the sound speed profile was set to be between 2 m and 3 m; thus, the sound speed profile was divided into 100 layers, and the variation in the sound speed profile gradient \(g_{i}\) was obtained.  
In Figure 11, it can be seen that the gradient \(g_{i}\) of the sound speed profile was stable at the 0 th layer, and the sound speed was kept constant between the 0 th layer and the 10 th layer. Between the 10 th layer and the 50 th layer, \(g_{i}\) significantly floated, and the sound speed changed more frequently. After the 50 th layer the gradient of the sound speed \(g_{i}\) tended to stabilize at zero.  
We selected different speed gradient thresholds to stratify the profile. Choosing a too small or a too large threshold could cause an inadequate division of the sound speed profile, so the threshold was adjusted based on the experience and considering the actual conditions. The thresholds of 0.01, 0.06, and 0.1 were respectively used in the experiment to ensure the multiple possibilities of a regional division.  
Figure 11: The sound speed gradient \(g_{i}\).  
Figure 10: Dependence of the MSE of the sound speed profile on the depth.  
In the case of a smaller threshold, such as that of 0.01, when \(g_{i}\geq 0.01\), the sound speed profile was divided into equal-speed-gradient areas, as in Figure 12. So, the areas were interspersed with the equal gradient ray tracing method, which resulted in the unclear distinction between the divisions of the area and increased the iterations.  
When the threshold value was 0.06, the sound speed transform area could be distinguished well from the sound speed stable area, as shown in Figure 13. The entire sound speed profile was divided into three sections. The first section sound speed was stable, and the constant sound speed ray tracing method reduced the amount of iterations and did not produce too much error. In the second section, the equal gradient ray tracing method improved the accuracy of the complex sound speeds. In the last section, the speed of sound tended to be stable, and tracking was performed using the constant sound speed ray tracing method. By increasing the amount of calculation in the local area, the overall tracking accuracy could be improved.  
Figure 12: The experimental results at the threshold of 0.01.  
Figure 13: The experimental results at the threshold of 0.06.  
When the threshold value was too large, such as that of 0.1 presented in Figure 14, in the region where the sound speed changed frequently, \(g_{i}\) was greater than 0.01, and \(G\) was less than or equal to \(A\), which led to the division in too many layers, and the calculation method was switched back and forth, resulting in inaccurate calculation results.  
Hence, it can be concluded that when the threshold was too small or too large, the combined ray tracing method was inaccurate in judgment, and the sound speed profile was layered and disordered, resulting in errors in the sound propagation path correction. In this simulation experiment, at the threshold of 0.06, the level using constant sound speed ray tracing and the level using the equal gradient ray tracing can be better preserved, and enter the calculation of the next slant range correction.