## 3 Results and Discussion
### Impact of Acoustic Transmission Characteristics on Acoustic Signal Propagation
#### 3.4.3 Acoustic Transmission Loss  
Multipath signals also result in acoustic energy transmission loss (\(TL\)), and the transmission loss of the acoustic signal can be assessed as follows [38]:  
\[TL(d,f)=k\times 10\log(d)+0.11\frac{f^{2}}{1+f^{2}}+\frac{44f^{2}}{4100+f^{2} }+3\times 10^{-4}f^{2}+3.3\times 10^{-3} \tag{11}\]  
where \(d\) is the distance between the station and the user, \(f\) is the signal frequency, and coefficient \(k\) represents the propagation geometry space.  
Figure 9a,b show the transmission loss when the base station was at a depth of 500 m. Figure 9a shows that the transmission loss increased from 40 dB to 80 dB within the horizontal distance of 5 km. The transmission loss then increased slowly and approached 100 dB when the horizontal distance was 10 km. However, there was an obvious caustic curve above the depth of 2500 m--the transmission loss changed significantly from the left side of the curve to the right side. On the right side of the caustic curve, the rays reflected by the seafloor or the sea surface with large reflection loss, and the zone of large transmission loss decreased with increasing station depth. Therefore, for the station in shallow water, such as a subsurface buoy, the acoustic signals had a large transmission loss in the shallow water. Figure 9b shows the rapid increase in the transmission loss. When the user was at the depth of 100 m, there was a drastic change in the transmission loss at a horizontal  
Figure 8: Propagation time deviation between the reflected signal and the direct signal. (**a,b**) Propagation time deviation of the base station at depths of 500 m and 2998 m, respectively. Blue, orange, yellow, purple, and green colors denote user depths of 100 m, 500 m, 1000 m, 2500 m, and 2900 m, respectively.  
distance of 6 km, while the drastic change occurred at a horizontal distance of 10.5 km when the user was at the depth of 1000 m.  
Figure 9c,d show the transmission loss when the base station was at a depth of 2998 m. Figure 9c shows that, when the horizontal distance was within 2.5 km, the transmission loss gradually increased from 40 dB to 70 dB, and then the increase in the transmission loss slowed down. When the horizontal distance was 15 km, the transmission loss was close to 100 dB. Two obvious caustic curves could be found, and the depth of the turning point was about 500 m. For the caustic curve above 500 m, the zone of large transmission loss decreased with increasing station depth. In contrast, the zone of large transmission loss increased with increasing station depth for the other caustic curve. Figure 9d shows the rapid increase in the transmission loss when the base station was at a depth of 2998 m. When the user was at a depth of 100 m, the horizontal distance of drastic change increased to 16.5 km, and when the user was at a depth of 1000 m, the horizontal distance increased to 21.5 km. Therefore, for the base station in deep water, the acoustic signals had a large transmission loss in both shallow and deep water.  
From the above analysis, when the base stations were located at 500 m and 2998 m depths simultaneously, they could compensate for the signal transmission loss in shallow and deep water, which further indicates the necessity of deploying the subsurface buoy and seafloor base stations.