## 4 Conclusions  
This study has carried out an acoustic stability pre-clustering analysis of EOF projection coefficients, classified the main disturbance types of SSPs in the South China Sea, and used different categories of background profiles according to the clustering results during inversion to improve inversion accuracy. We have shown that Equation (4) confirms that sea surface parameters can be used for SSP inversion, where the EOF projection coefficients play a key role in the inversion process.  
An SSP inversion experiment was carried out using data obtained for the South China Sea area, and the results after acoustic stability pre-clustering were compared with the inversion effect of the non-clustering method to verify the improvement of the acoustic stability analysis method on the inversion accuracy of SSPs. The inversion accuracy shows seasonal fluctuations. Compared with the direct inversion method, although the acoustic stability analysis also has seasonal errors, it can effectively reduce this error compared with the direct inversion method. Therefore, introducing the acoustic stability clustering method in the preprocessing of SSPs can significantly improve the efficiency of SSP inversion. Some samples within the study range have strongly random disturbances, which are the main reasons for the SSP inversion errors. While the method of directly using EOF inversion cannot clearly express these random disturbances, the pre-clustering method is able to account for them. After carrying out an acoustic stability pre-clustering analysis of  
Figure 5: Comparing simulated losses from the clustered (red) and unclustered (green) simulations with measured losses (grey).  
the disturbances, the inversion errors were reduced by about 20% compared with direct inversion, producing profiles that are basically consistent with the true SSPs. Although both the acoustic stability analysis method and the direct inversion method have obvious errors near the sea surface, the lower inversion errors of the acoustic stability analysis method provide the possibility for obtaining SSPs worldwide. The highly accurate inversion results mean that high-resolution and high-precision SSPs can be obtained for areas all across the globe directly through remote sensing data without field measurements.  
Finally, through the transmission loss simulation experiment, it was concluded that the inversed SSPs can be used for a wide range of experiments, such as sound field calculation. Sound field simulation is the basis for applications such as sonar performance evaluation and matched field inversion. By using the acoustic stability analysis method to coordinate remote sensing parameters, the results can be extended to various marine parameters. However, in the subsurface depth of seawater, the performance of the pre-clustering method is affected by the sudden changes in acoustic stability. This issue needs to be addressed by further constraining the stability conditions in future work.  
Conceptualization, Z.Z. and K.Q.; Data curation, Z.L.; Funding acquisition, K.Q.; Investigation, K.Q.; Methodology, Z.Z. and K.Q.; Project administration, K.Q.; Resources, Z.L.; Supervision, K.Q.; Validation, Z.L.; Writing--original draft, Z.Z. and K.Q.; Writing--review & editing, Z.Z. and K.Q. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the open fund of the National Key Laboratory of Science and Technology on Underwater Acoustic Antagonizing, grant number JCKY2024207 CH07.  
The data presented in this study are available on request from the corresponding author due to their use in an ongoing study by the authors.  
The authors declare no conflicts of interest.