# Cause Analysis and Preventive Measures against False Bottoms in Echosounder Data
## 2 Materials and Methods
### The Influence of False Bottoms on Echosounder Detection and Its Causes
#### 2.3.1 The Second Reflection of the Same Ping Signal Forms a False Bottom  
One possible cause of the formation of a false bottom is the occurrence of two reflections of the bottom echo being received by the receiver during an echosounder reception cycle. This leads the receiver to perceive the two reflections as a single reflection echo signal originating from the false bottom's location (see Figure 1a). Consequently, the time for the receiver to receive the signal for one cycle can be expressed as follows:  
\[t_{m}=\frac{2d_{m}}{v} \tag{1}\]  
\[2d_{r1}=vt_{r1} \tag{2}\]  
where the propagation speed of sound waves in seawater is denoted by \(v\), \(t_{m}\) is each ping during the cycle duration, \(d_{m}\) is the maximum detection depth, \(t_{r1}\) is the time of the true-bottom echo transmission of the first type, and \(d_{r1}\) is the seabed depth of the first type.  
Figure 1: _Cont._  
Within a signal cycle, two reflections of the bottom echo are received by the receiver; therefore, the following equation can be used:  
\[t_{f1}=2t_{r1} \tag{3}\]  
where \(t_{f1}\) is the sonar transmission time of the formation of the first type of false bottom. The receiver should be able to receive the secondary echo signal within one cycle, and the following requirement must be met:  
\[t_{m}>t_{f1} \tag{4}\]  
It is not difficult to derive the following equation from the above formula:  
\[d_{r1}<\frac{d_{m}}{2} \tag{5}\]  
It is apparent from Formula (5) that the second reflection of the same ping signal generates a false bottom, where the true depth of the seabed (\(d_{r1}\)) must be less than half of the maximum detection depth (\(d_{m}\)), as depicted in Figure 2a of the echosounder image. The false-bottom echo, compared with the genuine bottom echo signal, experiences two additional reflections (one from the seabed and one from the water surface) and travels a greater distance in the water. Consequently, the acoustic signal undergoes more significant attenuation, resulting in a weaker signal being received in comparison to the actual bottom. Given the shallow depth of the genuine bottom (\(d_{r1}<\frac{d_{m}}{2}\)), the transmission distance of the genuine bottom echo is small, yielding a relatively strong echo intensity for the bottom target. Hence, the false-bottom image can be readily distinguished. In this scenario, the  
Figure 1: Sonar diagram of different types of false bottom. (**a**) First type. (**b**) Second type. (**c**) Third type. \(d_{0}\)—sea surface depth [0 m]; \(d_{r1}\)—seabed depth of first type [m]; \(d_{r2}\)—seabed depth of second type [m]; \(d_{r3}\)—seabed depth of third type [m]; \(d_{m}\)—echo range [m]; \(d_{f1}\)—false-bottom depth of first type [m]; \(d_{f2}\)—false-bottom depth of second type [m]; \(d_{f3}\)—false-bottom depth of third type [m]; \(t_{0}\)—start time of first ping [0s]; \(t_{r1}\)—time of arrival of the true-bottom echo of first type [s]; \(t_{r2}\)—time of arrival of the true-bottom echo of arrival of the true-bottom echo of second type [s]; \(t_{r3}\)—time of arrival of the true-bottom echo of third type [s]; \(t_{r1}\)—interval between adjacent ping receiving cycles [s]; \(t_{m}\)—each ping receiving cycle duration [s]; \(t_{f1}\)—formation of false-bottom sonar transmission time [s]; \(t_{f2}\)—time between the start of second ping and the arrival of the second bottom echo from previous ping [s]; \(t_{f3}\)—time between the start of second ping and the arrival of the first bottom echo from previous ping [s].  
depth of the false bottom is twice that of the actual bottom (\(d_{f1}=2d_{r1}\)). However, it is important to note that the false bottom does not occur in the same area as the target echo, and therefore does not significantly affect target detection.