## 1 Introduction  
Ocean reverberation is generated by the scattering mechanism of ocean boundary irregularities and medium inhomogeneities [1] and is one of the dominant environmental factors that have to be considered in the design of active sonar systems [2; 3; 4; 5].  
Since the 1940s, there have been many studies on the prediction of reverberation in the ocean [6; 7; 8; 9]. These studies can be categorized in a variety of ways, e.g., physics of scattering, coherence, scattering modeling, propagation modeling, and geometry of sources and receivers. In terms of propagation modeling, reverberation models are usually classified into energy flux models [10; 11], ray-based models [12; 13; 14; 15], normal mode models [16], and parabolic equation models [17]. Among them, the ray-based model is known to be well-suited for reverberation modeling of the complex ocean environment in the frequency range of 1 to 10 kHz.  
The numerical burdens of reverberation modeling are generally high because the modeling is performed with the repetitive usage of the propagation model and the scattering model along each scattering element of a physical domain [15]. In the case of bistatic sonar, where the source and receiver are separated by a distance, the numerical burden will be even higher, because out-of-plane scattering is included in the calculation [18]. However, such a rigorous approach may be unnecessary for an active towed array where the distance between the source and receiver is not large (\(<\)1 km).  
In this study, we extend the 2D geometrical ray-bundle reverberation model for the fixed mono-static sonar [14] to a 3D environment with the approach and develop a depth-bistatic bottom reverberation model for an active towed array composed of a variable depth source and a triplet line array. This model neglects out-of-plane scattering in the sea floor but allows for bistatic Doppler shift, which is simplified as a straight-line propagation between a moving source, a moving receiver, and fixed scatterers. A major advantage of this depth-bistatic scheme is that it can reduce the computational costs. The fully bistatic scheme basically requires two independent ray-bundle (or ray-beam) tracings for a bottom cell because the source and receiver is located on the out-of-plane, while the depth-bistatic scheme uses one ray-bundle tracing in a plane where the bottom cell, the range, and the receiver are located. When the distance between the source and receiver is small, the latter has the similar accuracy as the former in the long-range reverberation.  
Moreover, we confirm the validity of the proposed model using mid-frequency reverberation data [19] collected in the East Sea of Korea during August 2015 by the Agency for Defense Development of Korea. These data are valuable in two aspects. One aspect is that they were obtained with a variable depth source in the mid-frequency range of 2 to 4 kHz in a deep-water environment. Another aspect is to use the triplet array, which can resolve the left/right ambiguity [20; 21]. This enables a detailed analysis of a coherent reverberation signal in the azimuth. Note that the state-of- the-art reverberation experiments are well described by [PERSON] et al. in [9].  
This paper is organized as follows: Section 2 describes a depth-bistatic bottom reverberation model with a moving source and receiver for a complex bathymetry. In Section 3, an overview of our reverberation experiment and the signal processing method are presented. Some observations for the azimuth and the operation depths from the measured data are described. Section 4 includes the model-data comparisons. Finally, Section 5 contains a summary and conclusions.