NOTE Conti et al.; Measurements of the total scattering spectra from Sebasfes paucispinis) 



155 



Figure 2 



Diagram of the experimental setup: a computer with integrated function generator 

 (CompuGen 1100, GageApplied, Montreal, Canada) and analog to digital acquisition 

 system (CompuScope 1610, GageApplied, Montreal, Canada) connected to the emitters 

 in black (ITCIOOIB, ITC1032, ITC1042; ITC Transducers Company, Santa Barbara, CA) 

 and receivers in gray (one ITClOOl, one ITC1032, and two ITC1042; ITC Transducers 

 Company, Santa Barbara, CA) in the tank. The transmitted signal is amplified with a 

 power amplifier (Krohn-Hite 7500, Krohn-Hite Corporation, Brockton, MA). 



an ITC1042 emitter (/; = 105 kHz) (ITC Transducers 

 Company, Santa Barbara, CA). The transducers were 

 inserted from the top of the aquarium. The amplitude of 

 the chirps from the function generator was 1 volt peak- 

 to-peak, amplified 100 times (40 dB) with a Krohn-Hite 

 7500 amplifier (Krohn-Hite Corporation, Brockton, MA). 

 The corresponding reverberation time series were re- 

 corded at a 500-kHz sampling rate, for at least 90 ms 

 on a four transducer array consisting of one ITClOOl, 

 one ITC1032, and two ITC1042 transducers. 



To increase the signal-to-noise ratio, the recorded 

 reverberation time series were cross correlated with 

 the transmitted signal to obtain the impulse responses 

 hi^it). The measurements for the lowest (f^=25 kHz) and 

 highest (/"j.=105 kHz) frequencies bands were repeated 

 11 times. The measurements for the center frequency 

 {f,=50 kHz) band were repeated 20 times. For f^=25, 50, 

 and 105 kHz, the total scattering cross sections were 

 estimated from the signals on the ITClOOl, ITC1032, 

 and two ITC1042 receivers, respectively. 



Results 



The mean weight (W) and total length (L) of the 20 

 bocaccio were 1.37 kg (ranging from 0.73 to 2.73 kg; 

 standard deviation (SD) = 0.57 kg), and 468 mm (rang- 

 ing from 382 to 563 mm; SD = 45.5 cm), respectively 

 (Table 1). Fish masses did not correlate well to fish 

 lengths (Fig. 1). The mean deviation was about 25%, 

 for fish weight to fish length-to-the-third-power. This fit 

 may indicate heterogeneity in the shapes (i.e., long and 

 thin versus short and wide) and could be observed from 

 visual inspection of the fish. 



Because the fish were not moving very actively during 

 the experiments, the time between consecutive shots ST 

 had to be increased to assure uncorrelated positions of 

 the fish. This was effectively achieved by considering 

 the shots k and ^-h20 instead of ^ and ^-i-l to estimate 

 -S,(t), resulting in ^^,= 40 s between the shots. By in- 

 creasing the time between shots, the measured total 

 scattering cross section reached a stable plateau at 

 Of 0.01 m~ for each of the considered frequency bands 

 (Fig. 3). This plateau indicated that the positions of 

 the fish were uncorrelated between shots, and the mea- 

 sured total scattering cross section was not biased by 

 the correlation of fish positions (Conti et al., 2006a). 

 The measurement variance was conspicuously higher 

 in the lowest and highest frequency bands because of 

 decreased signal-to-noise ratios. The differences in sig- 

 nal-to-noise ratio with frequency was due to the experi- 

 mental setup at high frequency, and the lack of acoustic 

 modes propagating in the tank at low frequencies. The 

 total scattering cross section was equivalent to the one 

 expected for a rigid sphere of diameter 90 mm in water 

 (Fig. 4; Faran, 1951), which is of the order of the size of 

 the swimbladder for the fish in the tank (Foote, 1979). 

 The largest discrepancies between the measurements 

 and expectations were at the lowest and highest fre- 

 quencies, again because of lower signal-to-noise ratios. 



The total scattering cross-sectional area was virtu- 

 ally the same for each of the three frequency bands 

 because all three measurements were in the geometric 

 scattering domain for these fish. In other words, in 

 all three frequency bands the radius of the equivalent 

 scattering sphere was greater than half the wavelength. 

 In the geometric domain, the scattering cross-section 

 increased with the square of the frequency, in contrast 



