## 4 Model/Data Comparison  
A comparison of the modeled data and the measured data is shown in this section. For the reverberation modeling, the empirical [PERSON]'s law scattering function with kernels [25] was used as given by:  
\[\sigma(\theta_{n},\theta_{m})=\mu(\sin\theta_{n})^{p}(\sin\theta_{m})^{q}, \tag{7}\]  
where \(\mu\) is the empirical [PERSON]'s coefficient and \(p\) and \(q\) are scattering kernels. We set [PERSON]'s coefficient \(\mu\) to be \(-40\) dB for CW and \(-37\) dB for LFM. Two scattering kernels are chosen to be 0.5 through data fitting. The sea-floor bathymetry is created using the General Bathymetric Chart of the Oceans (GEBCO) with a 15 arc-second resolution grid (\(\sim\)450 m) [26]. The properties of the ocean bottom are obtained from the geological database of the co-located sediment coring. The sound speed of the surficial sediment is 1470 m/s, its density is 1200 kg/m\({}^{3}\), and the attenuation coefficient is 0.08 dB/\(\uplambda\), which corresponds to silt-clay sediment. The bottom is regarded as a homogeneous half-space. Finally, for a realistic simulation, the ambient noise signal of a white Gaussian noise type is added to the sensor data. Figure 11 shows the modeled reverberations of ping 107 and 324, described in Section 3. The results of Figures 9 and 11 show very similar features. In Figure 11a, a longer reverberation time is observed for the downslope direction than for the upslope direction. To examine this feature precisely, the beam time series shown in Figure 11a is sliced at starboard and port, which corresponds to the upslope and the downslope directions, respectively. Figure 10: Spectrogram of data received at a single particular sensor in the event of CW ping 120 and CW ping 121. (**a**) Pulse duration 1 s, (**b**) Pulse duration 0.1 s.  
Figure 9: Beam time series at two different sites for the time and relative beam angle measured clockwise from the bow direction. (**a**) Ping 107 (CW ping, pulse duration 1 s, \(z_{s}=135\) m, \(z_{r}=129\) m), and (**b**) ping 324 (LFM ping, pulse duration 1 s, bandwidth 1 kHz, \(z_{s}=135\) m, \(z_{r}=129\) m). Figure 12 shows the results. To remove the random fluctuation of the reverberation, the measured data were time-averaged with the window of 0.06 s. The dotted line indicates a noise floor of 40 dB and 60 dB, respectively. In the starting region of measured data, ghost signal is observed by the electric coupling of source and receiver array. After about 0.5 s, the direct blast is arrived. We note again that the time signal with a large voltage are clipped. For the case of ping 107 that the water depth is shallower, it is seen that the direct blast is mixed with multi-path signals and reverberation signals. Totally, the modeled results (solid line) agree well with the measured results (dashed line), except that a longer tail appears in the latter. This tail may be a consequence of the scattering from sea-floor layering or volume inhomogeneity. In Figure 13, the modeled spectrogram for the CW with the 1 s duration and 3 kHz center frequency is given and compared with the results obtained without the platform motion. The environmental parameters used are the same as for Figure 11. Comparing Figures 10a and 13a, it is clear that our model describes the spectrum broadening well. In Figure 13b, we can see that the model without Doppler correction fails to predict realistic reverberation. Figure 11: Modeled beam time series. (**a**) Ping 107 (CW reverberation) and (**b**) ping 324 (LFM reverberation). Figure 12: Comparison of the modeled reverberation intensity and the data at both broadsides for ping 107 and ping 324. (**a**) 90\({}^{\circ}\) for ping 107, (**b**) 270\({}^{\circ}\) for ping 107, (**c**) 90\({}^{\circ}\) for ping 324, and (**d**) 270\({}^{\circ}\) for ping 324. Finally, Figure 14 shows the change of the extracted Doppler shift for the motion of the source and receiver arrays using Equation (6). The reverberation data of ping 120 with a 3 kHz center frequency and a 1 s duration is chosen.