## 1 Introduction  
As an important phenomenon in marine dynamics, the ocean front represents a narrow transition zone between two different water masses [1]. The frontal zone is located in the convergence area, where there is a strong vertical movement, and the exchange of momentum, heat, and water vapor is very active [2]. Therefore, the ocean front has become an important research field of physical oceanography. The position and strength of the ocean front change with time [3]. For the detection of the ocean front, the dynamic method or the gradient judgment method of hydrological elements including temperature can be used [4, 5], in which a critical value should be given first. If the calculated horizontal temperature gradient is greater than this critical value, it is considered that there is an ocean front [6]. The influence of the ocean front on acoustic propagation is also of great concern to hydroacoustic scholars [7]. When the horizontal gradients of temperature and salinity change, the ocean front appears in this area, which affects the structure of sound speed profile (SSP) [8], then the acoustic propagation characteristics of the sea area [9], and finally, the underwater detection [10]. From the perspective of the acoustic effect of the ocean front, the traditional dynamic methods or gradient methods can no longer meet the needs of research since the acoustic effect of the ocean front is based on SSP, rather than a single hydrological element. In recent years, there has been a new research method of using the fuzzy cluster analysis of SSP for detecting the ocean front. Fuzzy cluster analysis refers to constructing a fuzzy matrix according to the properties of the research object itself and determining the cluster relationship according to certain membership, aiming to perform clustering objectively and accurately [11]. Common fuzzy clustering algorithms include the k-means algorithm, fuzzy C-means (FCM) algorithm, and so on. The classification research of the SSP by cluster analysis was first used in the 21 st century. [PERSON] [12] used the hierarchical clustering method to classify the SSP of the North Atlantic and the Northeast Pacific. [PERSON] et al. [13] used principal component analysis (PCA) and self-organizing map (SOM) to automatically cluster the SSP, which was applicable in terms of the sea area of the Strait of Gibraltar. In addition, [PERSON] and [PERSON] [14] applied fuzzy clustering to oceanographic parameters related to acoustics and divided them into multiple categories, which proved the practicability of the method. Although the use of various cluster analysis methods to study the SSP has achieved some gratifying results, the necessity of using the high spatial resolution data of the whole sea depth may lead to some inconveniences in the actual ocean exploration [15]. Although many works have been carried out on the modeling of the ocean front [16; 17; 18], there is still little research conducted on the combination of theoretical model and actual ocean front. Since the previous models are still based on single parameters such as temperature or current speed [19], it is believed by some hydroacoustic scholars that they are no longer suitable for the research of the ocean front model of the sound speed field. [PERSON] et al. [20] by comparing the ocean front temperature model with the measured data, the effectiveness of the model in the sound field prediction was basically verified, and the root means square error (RMSE) calculated by the model was within 7 dB compared with the measured one. In this paper, in order to reduce the dependence of ocean front modeling on the data of the whole sea area and the whole sea depth, we only cluster the surface sound speed of the sea with the fuzzy C-means (FCM) algorithm, to obtain the position and range of the frontal zone.