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Old 14th May 2011, 12:22
  #1325 (permalink)  
Join Date: Jun 2009
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Posts: 660
auv-ee, the spreading or square law loss is about 20 log10( 1700 ) if we use 1700 meters as the ultimate range. That's only 65dB (pulling it off a calculator rather than my semi-memorized log tables.) Add in a generous 10dB for the extra attenuation of H2O at that frequency - as somebody else cited, and you get slightly less than 75dB. So gives about 86 dB above 1 micro Pascal. If the noise level is only 36dB give or take a few dB we still have about 50 dB more attenuation to cover. We are working one way rather than radar range calculations that raise exponents.

That extra 50dB comes from ???? Antenna loss and other properties are figured in already on the sensitivity and sound pressure at 1 meter figures.
That hints the range at noise floor is about 300 times 1700 meters.

Ah, I had not allowed for bandwidths. I presume the figures you gave are in the traditional 1Hz bandwidth. If we use 100Hz FFT that's 20dB of the 50 dB right away. If we use 100kHz bandwidth and simply look for an amplitude change that could account for the full 50 dB and why Thales may have figured post processing with say a 1kHz set of FFT windows should bring it right out.

(That was a stupid omission in my original analysis. Learning the actual measurement method would probably lead to better answers, too. I bet that would take a REAL lot of digging.)

For the onlookers:

It's called square law or spreading loss because the signal has to cover more area on the surface of a sphere as the signal expands out from the source. The area of the surface of a sphere is an r^2 or range squared function. So the power drops with the range squared.

Noise is usually figured in decibels, 10 log10( power ratio), and are a logarithmic ratio with no units. A very handy measurement when dealing with signals in noise is the amount of noise at the frequency you are operating in a known bandwidth, usually 1Hz. Since the noise is usually incoherent noise doubling the bandwidth doubles the power.

So we end up with a "20 log10( distance ratio) + 10 log10( power ratio) + incidental numbers" sort of calculation. I hope that filled in gaps for most people.
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