(A) Locations of source and receiver during GOME'06 (Refs. 5 and 6). Isobath contours have the unit of m. The sound speed profiles shown in Fig. 2(A) were collected roughly at the beginning, middle, and end of each receiver track and at the source locations. (B) Normalized histogram of the number of transmissions as a function of source and receiver separation or range.
(A) Sound speed profiles and (B) buoyancy frequency profiles obtained from XBT and CTD measurements at the experimental site. A total of 185 sound speed profiles and 35 buoyancy frequency profiles are shown.
Example of source waveform and received broadband signal at a range of 7.6 km for the Tukey-windowed linear frequency modulated pulse centered at = 415 Hz. (A) Source waveform, (B) source spectrum, (C) received signal waveform, and (D) received signal spectrum. The results are normalized for a 0 dB re 1 μPa at 1 m source level.
Modeled transmission loss for 50-Hz bandwidth Tukey-windowed broadband signals centered at (A) = 415 Hz and (B) = 1125 Hz, calculated using the range-dependent parabolic equation model (Ref. 34). Transmission losses are obtained by averaging over 20 independent Monte Carlo realizations of the broadband signal in the Gulf of Maine environment randomized by internal waves.
Histograms showing distribution of measured log-transformed bandwidth-averaged energy spectral densities received in the 7 to 9 km range for two center frequencies = 415 Hz (left) and = 1125 Hz (right) with (A) and (B) 0.5 Hz bandwidth (nearly monochromatic components), and (C) and (D) 50 Hz bandwidth Tukey windowed signals with an effective bandwidth of 42 Hz. The histograms are overlain with thetheoretical exponential-Gamma distribution modeled using Eq. (8) (black curve), with the number of frequency correlation cells determined from the data mean and standard deviation. The exponential-Gamma distribution corresponding to assumed is also shown for comparison.
Mean and standard deviation of the log-transformed energy spectral density Lε as a function of frequency for broadband signals received between the 7 and 9 km range, centered at (A) = 415 Hz and (B) = 1125 Hz.
(A) Empirically measured standard deviations of the log-transformed bandwidth-averaged energy spectral densities obtained from broadband transmissions in the Gulf of Maine shown as points. (B) The number of frequency correlation cells are obtained from the measured signal standard deviations via Eq. (10). The dotted curves in (A) and (B) are obtained from the minimum mean-squared error fit to the data points using the equation and coefficients in Table II. The error bar shown applies to all data points.
Measured SIs in the Gulf of Maine for all four center frequencies as a function of relative bandwidth. The error bar shown applies to all data points.
Average energy spectral density correlation coefficient calculated from received broadband signals at the four center frequencies shown as a function of frequency shift within the signal bandwidth.
Log-transformed time-averaged energy spectral density calculated from received broadband signals in the 7 to 9 km range for thewaveforms centered at (A) = 415 Hz and (B) = 1125 Hz.
Two-sided chi-squared test results to verify the distributions of the log-transformed bandwidth-averaged energy spectral density for the four scenarios shown in Fig. 5. A significance level of α = 0.05 gives χ 2 within the range from lower-tail to upper-tail critical values for both the Gamma and exponential distributions.
Empirically determined number of frequency correlation cells is related to relative bandwidth by the “inverted exponential decay” relationship , with coefficients A and k determined by curve fitting as shown in Fig. 7. The case corresponds to one unique independent fluctuation. When B becomes very large, tends to A, its upper saturation value for each center frequency, which is 3 for the lowest frequency = 415 Hz and 1.6 for the highest frequency = 1125 Hz.
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