## 4 Analysis of the Experiment Data
### Channel Temporal Coherence and Cluster Analysis  
This subsection distinguishes and identifies the path clusters with different arrival paths and analyzes the temporal coherence of channels and single-path clusters. Single-path clusters were separated using the method in [11]. During the experiment, the transmitting ship drifted while the receiving hydrophone array was anchored to the sea bottom by a sinker. The relative motion of the transmitter and receiver caused a Doppler frequency shift in the received signal. The experimental records revealed constant speed and direction of the ship during the measurement period. The Doppler frequency shift in the received signals was removed as described in [14]. The temporal coherence of channels at different receiving depths was then calculated using Equation (7). The temporal coherence results at different receiving depths are shown in Figure 15.  
At the shallow depths of the shadow zone (depths shallower than 500 m), the temporal coherence of the channel usually remained at 0.2 throughout the CIR measurement period. The coherence at 246 m was selected for further analysis (see Figure 16). As is shown in Figure 16a, clusters arrived in the order of S, B, SB, BS, and SBS, and all of them provided clear contributions to the channel. Figure 16c indicates that the temporal coherence of all path clusters related to the sea surface was very low due to the fluctuation of the sea surface. Meanwhile, the temporal coherence of B declined slowly over time. Figure 14: Three-dimensional plots of CIR at (**a**) 1805 m (inset is a partial enlargement of the results of B and SB) and (**b**) 1905 m (inset is a partial enlargement of the results of B and SB). Clusters with high randomness that contributed more energy to the channel led to low temporal coherence at shallow depths in the shadow zone. As the receiving depth increased, B and SB, with high energy contributions to the channel, had an obvious influence on the temporal coherence of the channel. The temporal coherence of the channels differed between the depths of 1805 m and 1905 m, as shown in Figures 17b and 18b. Based on Figures 17a and 18a, it was determined that the main energy of the channel at both depths was mainly sourced from B and SB, but the energy contributions of B and SB were more similar at the former depth than at the latter depth. At 1905 m, the main energy source of the channel was SB, with higher randomness than B. Figures 17c and 18c indicate that the temporal coherence of B exceeded 0.98 at 1805 m but decreased with time at 1905 m, respectively. Considering a coherence coefficient of 0.5 as the evaluation standard, the channel coherence time at 1805 m reached 160 s. The clusters related to the sea surface exhibited poor temporal coherence because random scattering paths were introduced by sea surface fluctuations. At depths greater than 2605 m in the shadow zone, the propagation distances of the rays in B were shorter than those at shallow depths, so the expansion and absorption losses were reduced. In most cases, B and SB dominated the energy contributions to the channel. Stable B, with high contribution to the channel, led to higher temporal coherence of the channel, which led to higher temporal coherence (0.5-0.6) of the channel than (0.2-0.5) at shallow receiving depths in the shadow zone. Figure 16: (**a**) Temporal variability in CIR at 246 m (inset is a partial enlargement of the results of the last four clusters); (**b**) temporal coherence versus lag time; (**c**) temporal coherence versus lag time for selected clusters. Figure 15: Temporal coherence at different depth ranges: (**a**) shallower than 500 m; (**b**) deeper than 500 m.  
In the direct-arrival zone at depths beyond 3405 m, the temporal coherence largely increased to 0.6-0.8. The additional contribution from high-energy high-temporal-coherence D with no interface loss led to the high channel temporal coherence in this zone. The main energy contributions to the channels of this zone were D, S, B and SB.