# A Method for Predicting Radiated Acoustic Field in Shallow Sea Based on Wave Superposition and Ray
## 1 Introduction  
The accurate prediction of acoustic radiation of underwater vehicles is an important engineering application. The accurate simulation of radiated noise is also important for acoustic field characteristics analysis and acoustic measurement research. The oceans surrounding China mostly consist of shallow water and have a typical shallow water waveguide environment. In the shallow sea, the traditional free-space analysis method is limited due to the acoustic reflection phenomenon of the upper and lower boundary surfaces, and the acoustic radiation prediction in the shallow sea becomes very complicated.  
The acoustic propagation model used in sea includes ray theory [1], normal model theory [2; 3], wavenumber integration method [4], and parabolic equation method [5]. The advantage of the ray theory is that the physical meaning is intuitive and has good adaptability to high frequency problems. The normal wave theory is suitable for low frequency problems and provides accurate calculation in the far field. The wave number integration method is an integral transformation method of a horizontal layered medium and provides fast calculation speed. The parabolic equation method performs better in dealing with the problem of sound propagation in the environment related to distance. This kind of research method that uses a point source, ignores the vibration distribution of the structure surface and the directivity of the acoustic radiation. Hence, it is not appropriate to regard the elastic structure as a point source with the same source strength and directivity. The Finite Element Method (FEM) is only applicable to the near field region. However, for the far acoustic field, and with the high frequency condition, the number of grid elements in the FEM is too large to calculate, and the FEM is inapplicable in this scenario. The wave superposition method [6; 7] has excellent structural adaptability. Most of the current research focuses on free space and half-free space, but there are few researchers who concentrate on the sea waveguide [8; 9; 10; 11].  
For the acoustic radiation problem of the elastic structure in the shallow sea, some combined models are developed under the condition that it is difficult to meet the calculation requirements by asingle method. [PERSON] proposed a method that combines the wave superposition method and normal mode Green's function method, which effectively predicted the acoustic radiation of large elastic structures under shallow sea [12]. This method uses the normal mode Green's function to calculate the far field pressure, while the normal mode green function has a large order at high frequencies, which has a greater impact on the computational efficiency. Hence, this method is not appropriate for calculation speed at high frequencies. [PERSON] proposed a method that combines the finite element method with the parabolic equation method to obtain cylindrical field data in the near field active region, and a complete far field solution in the far-field passive region, using the parabolic equation method [13]. The parabolic equation method is a recursive method, and far field calculation leads to error accumulation. In addition, it is difficult to directly obtain the data of a near field cylindrical field.  
In this paper, a new method is proposed for the prediction of an acoustic field radiated from the structure excited at a frequency. Based on the combination of wave superposition and ray theory, the structure source is equivalent to a set of virtual sources that are reconstructed by matching the surface normal velocity of the structure source. Finally, the complete acoustic field is obtained by superimposing sound radiation fields from all virtual sources using ray theory.