SNR for an underwater acoustic signal

[JAP]

TL;DR

How could I find the SNR of an acoustic signal knowing its sound level (db ref uPa @1m)

Hi, I'm trying to model the transmission loss and SNR of an acoustic signal underwater. I'm using this expression to modelize the transmitted signal:

y = sqrt(P)*exp(1i*2*fr*pi*t)'​

where P is the transmission power in watts, fr is the transmission frequency and t is the acquisition time.
The only data I have to find P is the sound level (SL) of my source that is supposed to be 142 dB ref 1uPa at 1 meter from the source. According to the Matlab documentation site (https://fr.mathworks.com/help/phased/ug/sonar-equation.html) sound level can be defined as:

SL = 10log10(I/Iref)​

where I is the intensity from the source in W/m^2 and Iref is the reference intensity of sound in water which value is 6.667*10^-19 W/m^2. Knowing the SL value, I can isolate I to find the acoustic pressure p_rms and then the power P because I can be defined as follows:

I=p_rms^2/ρc and I = P/4*pi*r^2​

where p_rms: signal acoustic pressure in Pascal, ρ: water density (1000kg/m^3), c: sound speed in water (1500 m/s)
Putting these two equations together, I can find P that should be :

P = p_rms^2*(4*pi*r^2)/(ρc)​

However, when I use the value of my source (142 dB), I get a power of 1.33 mW! I believe it doesn't make sense 'cause the signal source should be detected at the receiver at least at 500 m from the source.
With regard to the SNR, I use the passive sonar equation, however I find very optimist results (i.e. more than 20 dB for a range of 800m...) so I'm not really sure my calculations are right. If there's any pro in the underwater acoustics field that could give me a hand to resolve this, I will be very grateful.
Thanks!

JAP

 

[jedishrfu]

While you are waiting for help here, this manual may be sufficient to answer your question:

https://docslide.net/documents/fleet-oceanographic-and-acoustic.html