Sonar single transducer element SNR vs array SNR
I'm going to take a stab at this though I don't know if it applies to sonar. If you have a signal received on a transducer there will be both signal and noise. If you have two transducers (in an array) it can be presumed that the same signal is received on both but the noise on each is likely gaussian and not coherent.

The upshot of this is that when you add the two signals from the two transducers the signal will double (+6dB) but the noise will add as per: -

Noise = \$\sqrt{A^2+B^2}\$ i.e. it will only increase by 3dB

This means the SNR has risen by 3dB

Each time you double the number of transducers, the SNR increases by 3dB

Hope this helps.