# A Shallow Seafloor Reverberation Simulation Method Based on Generative Adversarial Networks
###### Abstract  
Reverberation characteristics must be considered in the design of sonar. The research on reverberation characteristics is based on a large number of actual reverberation data. Due to the cost of trials, it is not easy to obtain actual lake and sea trial reverberation data, which leads to a lack of actual reverberation data. Traditionally, reverberation data are obtained by modeling the generation mechanism of seafloor reverberation. The usability of the models requires a large amount of actual seafloor reverberation data to verify. In terms of the reverberation modeling theory, scattering models are mostly empirical, computationally intensive and inefficient. In order to solve the above obstacles, we propose a shallow seafloor reverberation data simulation method based on the generative adversarial network (GAN), which uses a small amount of actual reverberation data as reference samples to train the GAN to generate more reverberation data. The reverberation data generated by the GAN are compared with that simulated by traditional methods, and it is found that the reverberation data generated by the GAN meet the reverberation characteristics. Once the network is trained, the reverberation data are generated with very little computation. In addition, the method is universal and can be applied to any sea area. Compared with the traditional method, this method has a simple modeling idea, less computation and strong universality. It can be used as an alternative method for sea trials to provide data support for the study of seafloor reverberation characteristics, and it has broad application prospects in antireverberation technology research and active sonar design. shallow seafloor; reverberation; reverberation simulation; generative adversarial network 202320013595100233  
factors [5; 6]. Ray acoustic theory is widely used for modeling short-range reverberations in the deep sea [7]. However, for shallow-sea long-range reverberations, the model based on ray theory becomes too complicated due to the need to consider the multipath phenomenon, and the reverberation calculation error based on the ray reverberation model will be large. In the 1960s, [PERSON] and [PERSON] proposed a theoretical model for calculating the reverberation intensity with a normal-mode wave method [8]. The normal-mode wave theory gives a strict analytical solution to the sound field, with available fast algorithms and numerical models [9; 10; 11]. The normal-mode wave reverberation model makes up for the deficiency of the ray reverberation model [12]. The long-range seafloor reverberation model based on the normal-mode wave theory is widely used [13; 14]. The normal-mode reverberation model uses the empirical Lambert scattering function to express the scattering process. [PERSON]'s theorem was originally used in optics to describe the reradiation of light energy from irregular surfaces. The Lambert model is accurate in calculating the scattering intensity of rough surfaces, but it is only applicable in the case of small grazing angles [15]. It is necessary to verify the accuracy of the reverberation model based on [PERSON]'s theorem with experimental data [16]. The seafloor reverberation is generally thought to result from the scattering caused by the rough undulating interfaces and the uneven media on the seafloor [17]. Many researchers have built reverberation models based on the physical mechanism of seafloor scattering [18; 19; 20]. For scattering problems, the Kirchhoff-Helmholtz integral formula can be used to strictly obtain the integral equation of a scattered wave [21]. The reverberation model based on the Kirchhoff-Helmholtz integral equation is used to calculate the scattering field of rigid spheres in horizontal layered waveguides. The scattering field of the target is expressed as the superposition of the product of the normal modes and the plane wave scattering function.