In the preceding sections we have talked qualitatively about "signal to noise ratio" (SNR), but we have not yet defined it in any formal way. While our goal is to provide only a cursory introduction to acoustics as it applies to sonar systems, it is instructive to look at the equation for SNR, if only briefly.
First we can define a bunch of terms, each of which are represented in decibels (dB):
SL = Source Level or the amount of sound energy that we "ping" into the water.
TS = Target Strength or the amount of sound energy that is reflected from an object (in our case the sea floor).
PL = Propagation Loss or the amount of energy lost to absorption and spreading of sound energy in the water column.
N = Noise or the amount of sound energy from other sources including reverberation, other ships, own ship, sea life, you name it. This term also includes electronic noise that is not "acoustic" in origination.
Armed with these definitions we can then write an equation for SNR, but before we do, we could review some quick math so it makes more sense. Remember that these values are expressed in dB, which is the log of the ratio of the sound intensity level to some standard level. Our "ratio" is a ratio of sound intensities, so when writing these as logarithms, to multiply the sound intensities we add the logarithms and to divide the sound intensities we subtract the logarithms. Now for the equation:
SNR = SL - PL + TS - PL - N
Reading left to right this equation makes perfect sense. Our signal starts with the source level from the transducer array (SL). The level is then reduced during propagation to the sea floor target (PL). Some amount of signal is reflected from the target (TS). This target signal is then decreased again by propagation loss back to the transducers (PL). The received signal is then reduced by are ability to discern it from the surrounding noise (N).
Written more compactly:
SNR = (SL + TS) - (2PL + N)
It is helpful to consider this equation when considering the possible sources of poor sonar performance and data quality.