The target strength or acoustic size is a measure of the area of a sonar target. This is usually quantified as a number of decibels. For fish such as salmon, the target size varies with the length of the fish and a 5 cm fish could have a target strength of about -50 dB. The target strength of a fish also depends on the orientation of the fish at the moment of sonification, which in turn changes the scattering cross-section of the fish and any air-filled cavities of the fish. The effect of this means that behavioral reaction affects observed biomass, for example fish evading the research vessel at night due to strong lights and vibrations from the hull and machinery. Target strength is often observed on or near a specific frequency where the target is most resonant. Narrowband (CW) pulses has historically been used, but there is ongoing research into using wideband (FM) pulses for improved classification.
Formula For some simple shapes, target strength can be derived mathematically. For other objects like fish, where the size of the air bladder is the main factor, target strength is commonly derived empirically. Target strength (TS) is referenced to 1 meter from the acoustic center of the target, assuming isotropic reflection:
T S = 10 ⋅ log ( I r I i ) d B = 10 ⋅ log [ σ 4 π ] d B {\displaystyle TS=10\cdot \log \left({\frac {I_{r}}{I_{i}}}\right)dB=10\cdot \log \left[{\frac {\sigma }{4\pi }}\right]dB}
Where:
I r {\textstyle I_{r}} is the reflected intensity from target
I i {\textstyle I_{i}} is the incident intensity on target
σ {\displaystyle \sigma } is the backscattering cross-section Target strength of a sphere with radius a {\displaystyle a} , large compared to the wavelength, assuming reference distance 1 meter:
σ = π ⋅ a 2 {\displaystyle \sigma =\pi \cdot a^{2}}
T S = 10 ⋅ log [ σ 4 π ] d B = 10 ⋅ log [ a 2 4 ] d B {\displaystyle TS=10\cdot \log \left[{\frac {\sigma }{4\pi }}\right]dB=10\cdot \log \left[{\frac {a^{2}}{4}}\right]dB}
Thus, for a sphere of radius 2 meters, the target strength is 0 dB. NOAA has a calculator that can be used to inspect the target strength of calibration spheres made out of copper or tungsten carbide in relation to physical parameters found in the ocean.
References
Further reading "Introduction to the use of sonar systems for estimating fish biomass, FAO Fisheries Technical Paper No. 191, Revision 1, FAO 1982" Fisheries Acoustics Simmonds, E John and MacLennan, David N (2005) Blackwell Publishing. ISBN 978-0-632-05994-2 C. S. Clay & H. Medwin, Acoustical Oceanography (Wiley, New York, 1977). ISBN 978-0-080-53216-5