Demonstration at sea of the decomposition-of-the-time-reversal-operator techniquea)
The error of the signal level is shown as a function of . The noise matrix has statistically independent, Gaussian-distributed random elements. Averages were found to two significant figures. Note that the error in echo level is less than at .
The accuracy of the steering vectors as a function of . The product of accuracies of the receiver and source steering angles is only approximately 0.9 at .
The values of the singular values as a function of . The singular values have been normalized. Note that at very low SNR the singular value spectrum is that of a matrix with statistically independent, Gaussian-distributed elements. At very high values of SNR the spectrum has only one nonzero value.
A map of the experimental area. The experiment was performed in the vicinity of and .
The signal received on the SRA produced by matched filtering, squaring, and summing the signal from each element. The first four peaks are the responses from a sequence of four broadside transmissions. The signal at the right was transmitted for a different experiment and should be disregarded.
The matched-filtered signal is displayed as recorded in the upper panel as a function of phone depth in meters and time in seconds. The lower panel shows the signal transformed into angle-time (beam-time) space with the angles in units of degrees and time in seconds.
The result of time shifting the signal by so a set of four peaks are aligned. Each panel from top to bottom is given a different source index. Only in the time window from 2.00 to are all four source signals present.
The four singular values of oceanic noise recorded and processed exactly the same as the echoes. The singular values are normalized. There is little frequency dependence on the singular values. The average over frequency of each singular value is displayed on the plot.
(Color online) The first, and highest, normalized singular value resulting from four broadside transmissions in the various bands. The first singular value is plotted with respect to frequency in the top plot, with respect to wind speed in the middle and with respect to range of the echo/repeater in the bottom plot.
The back-propagation image of one ping from 500 to versus depth and time with . Each panel displays the back-propagation image with an identical color scale with dynamic range. The top panel displays the image from the largest singular vectors that are associated with the echo-repeater signal. The expected depth of the echo repeater is and is displayed with a black line in each image. The depth of the bottom is also shown as a black line at .
The back-propagation images using noise-free, numerically simulated echoes that exactly correspond to the back-propagation Green’s functions. The dynamic range of each image is . The lower three panels have the same scale as the top panel.
The back-propagation images using noise-free, numerically simulated echoes from two identical scatterers, one at and the other at . The dynamic range of each panel is and the scales are identical. The two signals are separated to a high degree, but not perfectly.
The normalized singular spectra of various-sized matrices composed of statistically independent, Gaussian-distributed elements.
Sequence of transmissions.
Sound speed profile.
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