Hmm... I bet you are going to be getting into the secrets of what makes the 'Bird work so well. Responses are going to be slim.
If it were me and I were going to try and figure this out I'd pick up my oscilliscope and put it between the unit and the transducer with a good charged battery and read my voltages - narrow it down to their signal in hz. (Depending on which frequency you are testing, then take the best amperage reading I could). Some involved math could tell you the intensity of the ping in amps/hz would be my guess. (and I would suspect it to be in mA, as the whole unit for the biggest they have draws like 2.5 amps.)
Unless you were going to try and reverse engineer a sonar system- what would a guy need this information for?
Good luck on your thesis- stay with it. I gave up on mine 7 years ago- wish I would've hung in there now.