Fig. 1. State transition matrix of water. (a) State transition matrix MT. (b) State transition matrix raised to the 15th power MT15.

Fig. 2. Normalized angular probability distribution for increasing number of collisions nc.

Fig. 3. Normalized probability distribution of the number of collisions nc for increasing transmission distance DT.

Fig. 4. Energy loss on the receiving plane versus transmission distance DT. (a) Jerlov IB: a = 0.06 m⁻¹, b = 0.084 m⁻¹. (b) Pool water: a = 0.117 m⁻¹, b = 0.182 m⁻¹.

Fig. 5. Transmission procedures of the successive layering model, nc=1 and nc=2.

Fig. 6. Temporal distributions of different transmission distances. (a) DT=20m, (b) DT=40m, (c) DT=60m, (d) DT=80m.