## 1 Introduction  
In the field of marine acoustics, the sound speed profile (SSP) is an important waveguide parameter for various underwater acoustic problems, especially in underwater acoustic target recognition, positioning, tracking, and sound field modeling [1]. The general method of obtaining SSPs is on-site real-time measurements, such as direct acquisition through a sound velocity profiler [2], or indirect acquisition through a conductivity-temperature-depth profiler combined with sound speed empirical formulas [3]. The main drawbacks of this method are the huge consumption of human and material resources and the low efficiency caused by point-by-point measurements, which cannot meet the large data needs of marine research. In recent years, to obtain SSPs more conveniently, the method of inverting SSPs based on environmental parameters has developed rapidly. In 1995, [PERSON] used the matched field processing framework to invert SSPs and achieved good results [4]. Later, [PERSON] et al. introduced a genetic algorithm into the matched field processing framework to improve the accuracy of SSP inversion further [5]. In 1997, [PERSON] et al. inversed SSPs using matched field processing and a hybrid scheme for vertical slice tomography, achieving high-precision inversion [6]. Although the matched field processing method can effectively solve the problem of data volume demand, it takes a long time to run the method, and the solution to the inverse problem has obvious nonuniqueness. With the development of machine learning algorithms, neural network models have gradually been introduced into the field of SSP inversion [7]. [PERSON] et al. proposed an SSP inversion model combining an artificial neural network and pre-ray theory, realizing real-time monitoring of shallow sea SSPs [8]. [PERSON] et al. used a hierarchical long short-term memory neural network to construct a prediction model for full ocean depth SSPs, but it depends highly on sonar observation data and focuses on constructing a spatial sound speed field [9]. Machine learning algorithms require a large amount of data, and with the continuous accumulation of data over recent years, data-driven machine learning inversion methods have gradually emerged. [PERSON] proposed a subsurface SSP inversion method based on self-organizing maps [10]. [PERSON] et al. used the extreme gradient boosting algorithm to estimate global subsurface temperature anomalies and salinity anomalies based on satellite observations and Argo data [11]. [PERSON] et al. used a neural network to combine multiple sea surface parameters to enhance the accuracy of SSP inversion [12], providing a more efficient method for SSP inversion. However, although machine learning-based SSP estimation methods have shown good performance in most cases, the estimation accuracy of such data-intensive statistical methods still faces challenges when applied to areas with local disturbances. The sound speed in seawater can be calculated from the temperature and salinity of seawater. Sea level (SL) data and sea surface temperature (SST) data can be obtained by satellite remote sensing, from which temperature and salinity profiles can be estimated and the SSP of the target sea area can be calculated using empirical formulas. Generally, when estimating SSPs, the empirical orthogonal function (EOF) can be used to reduce the dimensions of unknown parameters. [PERSON] proved that there is a certain relationship between SL, SST, and EOF [13], and used this relationship to estimate SSPs in the northwest Atlantic Ocean and northwest Pacific Ocean [14]. Later, [PERSON] et al. applied this method to global SSP inversion, effectively confirming the effectiveness of the single empirical orthogonal function regression [15]. The above methods estimate the sound speed profile using linear relationships.