## 2 Theory and Experimental Methods
### Experimental Measurement and Signal Processing  
A schematic of the attenuation experiments is illustrated in Figure 1. The acoustic transmitter was a half-omnidirectional transducer (T335, Neptune Sonar; Kelk Lake, Kelk, UK) in the mid-frequency band range of 3-7 kHz. The receiver was a hydrophone (TC-4032, Teledyne RESON; Slangerup, Denmark). The transmitter and receiver were installed at a depth of approximately 3.3 m, and the net cage was positioned at 2.8-3.8 m below the sea surface and between the transmitter and the receiver at a distance of 2 m.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Experiments** & **Individual Fish** & **Explanation** & **Remark** \\ \hline Exp1 & 0 ind. & Non-net (empty) & \\ Exp2 & 0 ind. & Only-net (net) & Figure 2a \\ Exp3 & 100 ind. & & Figure 2b \\ Exp4 & 200 ind. & & Figure 2c \\ Exp5 & 300 ind. & Fish schools in a net cage & Figure 2c \\ Exp6 & 400 ind. & & Figure 2d \\ Exp7 & 500 ind. & & Figure 2d \\ \hline \hline \end{tabular}
\end{table}
Table 1: Attenuation experiments with varying number of individual fish (Japanese horse mackerel).  
The transducer transmitted the pulse wave signals every 1 s, and the pulse length was 1 ms. The pulse signals that traveled through the net cage with and without the fish schools were received by the hydrophone [6]. A total of 100 and 300 pings were received at 0-300 and 400-500 individual fish, respectively. The sampling frequency was 100 kHz. Direct current (DC) noises were removed from all the received signals. The signals used a band-pass filter range of \(\pm\)1 kHz on the basis of each frequency. The filtered signals were enveloped using Hilbert transform and converted into the received level (\(RL\)) in decibel scales. In this study, the 90% confidence limits for reliability were extracted from the \(RL\)s; the mean \(RL\) was calculated by applying the cumulative sum because the attenuation characteristics of fish schools were the main purpose of this work [25].  
To calculate the attenuation of fish schools, the insertion losses (\(IL\)s) with and without the fish schools were incorporated in the experiment [26; 27]. The \(IL\) was present between the transmitter and the receiver from the mean \(RL\) (see Equation (3)):  
\[IL\ =RL_{non-fish\_school\ (ref.)}-RL_{fish\_schools} \tag{3}\]  
where \(RL_{non-fish\_school\ (ref.)}\) is the mean \(RL\) without the fish school (only net cage), and \(RL_{fish\_schools}\) is the mean \(RL\) with the fish schools. \(IL\) was converted to \(\alpha\) (dB/m) when the net cage with fish school size was 1 m.  
During the attenuation measurements, the seawater temperature was 13.4 \({}^{\circ}\)C, and the salinity was 31.6 psu at a depth of 3.3 m. Thus, the sound speed was 1497.6 m/s. Table 2 lists the details of the transmitter, receiver, and measured environmental factors.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & Frequency (kHz) & 3, 4, 5, 6, 7 \\ Transmitter & Pulse length (ms) & 1 \\  & Ping rate (pps) & 1 \\  & Total pings (ping) & 100, 300 \\ \hline  & Sampling frequency (kHz) & 100 \\ Receiver & Hydrophone RVS (dB/V) & \(-\)170 \\  & Gain (dB) & 0 \\ \hline  & Water temperature (\({}^{\circ}\)C) & 13.4 \\ Environments & Salinity (psu) & 31.6 \\  & Sound speed (m/s) & 1497.6 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Transmitter, receiver, and measured environmental factors for sound attenuation by fish schools.  
Figure 1: Schematic of the experimental system used to measure sound attenuation from the fish schools (Japanese horse mackerel) at mid-frequency bands. Transmitter, receiver, net cage, and underwater camera were set at a depth of 3.3 m below the sea surface.