Advances in Acoustics and Vibration

Review Article

Advanced Applications for Underwater Acoustic Modeling

Box 3

Sonar performance models are based upon the sonar equations, which are the basic building blocks for both monostatic and bistatic sonar geometries.
Active sonar equations (monostatic)
(i) Noise background
    S L − 2 T L + T S = N L − D I + R D 𝑁 .
(ii) Reverberation background
    S L − 2 T L + T S = R L + R D 𝑅 .
Passive sonar equation
    S L − T L = N L − D I + R D .
SL: source level; TL: transmission loss; TS: target strength; NL: noise level; DI: receiving directivity index;
RL: reverberation level; RD: recognition differential.
Active sonar equations (bistatic)
The signal excess (SE) can be represented as:
(i) S E = E S L − T L 1 − T L 2 − [ ( 𝑁 0 − A G 𝑁 ) ⨁ 𝑅 0 ] + T S − Λ − 𝐿 ,
the energy source level (ESL) is related to the intensity source level (SL) as:
(ii) E S L = S L + 1 0 l o g 1 0 𝑇
where 𝑇 is the duration of the transmitted pulse,
The echo energy level (EEL) received from the target at a hydrophone on the receiver array is then:
(iii) E E L = E S L − T L 1 − T L 2 + T S ,
where TS is the target strength, 𝑁 0 is the noise spectral level, 𝑅 0 represents the reverberation spectral level, A G 𝑁 is the array
gain against noise, Λ is the threshold on the signal-to-noise ratio (SNR) required for detection,
𝐿 is a loss term to account for time spreading and system losses,
⨁ represents power summation, TL1 is the transmission loss from source ( 𝑆 ) to target ( 𝑇 ),
and TL2 is the transmission loss from target ( 𝑇 ) to receiver ( 𝑅 ).