MOVEBOAT2006 chart presenting Vilanova i la Geltru harbor, isobath line, hydrophone’s position, fish farm and typical tracks (parallel to the shoreline above the 15 meter isobath) of cooperative DOMIGO trawler.
Schematic RDC curves in the (k, f) plane. For frequencies lower than f 2 only mode 1 propagates, no interference exists. For frequencies in [f 2, f 3] modes 1 and 2 propagate and interfere together to create a single curve between f 1 and f 2 along k 2(f) − k 1(f). For frequencies higher than f 3, modes 1, 2, and 3 propagate ant interfere together to created three relative dispersion curves located along k 2(f) − k 1(f), k 3(f) − k 1(f), and k 3(f) − k 2(f).
Inversion scheme diagram.
Flowchart to define and optimize the objective function J. Measurement are processed in box B 1 to compute I mes(k, f). In the box B2, the map I mes(k, f) is matched to a synthetic binary map M(k, f, θ) obtained from simulation. Applied on I mes(k, f) the goal of M(k, fθ) is to extract the power contained by the measurement around some simulated RDC. To do so, for a given θ the simulated RDC are computed in box B 3, RDC appear to have an ideal infinite resolution in the (k, f) plane. To account for the bounded range R max − R min of the measurements, each RDC is broaden by the expected resolution of Im (k, f) [i.e., 2π/(R max − R min)] to form a binary masking map in the (k, f) plane with one around the simulated RDC and zero elsewhere. An optimization procedure is applied on θ to optimize the amount of power of Im (k, f) contained in the mask M(k, f, θ).
Accuracy of our inversion scheme versus SNR, mean value and standard deviation of compressional sound speed of the bottom estimates (N = 100 runs of independent simulations for each SNR value). For SNR < 6 dB, estimates are biased, for SNR > 6 dB estimates are unbiased and have a standard deviation less than 3 m s−1.
(a) Shape of objective function J: SNR = 2.5 dB (dots); SNR = 5.58 dB (triangles); SNR = 10,70 dB (crosses); SNR = 23.6 dB (circle); SNR = 63.5 dB (diamond); (b) comparison of normalized criterium shape depending on SNR values. The highest the SNR is, the greater the maximum value of the objective function (a) and the narrower the peak around the maximum (b).
Estimated compressional sound speed of half space bottom for different thick nesses of the sediment layer (crosses); rock basement compressional sound speed (circles); compressional sound speed of the sediment layer (triangles). For a thin sediment layer (area 1), the estimated compressional sound speed is similar to the basement one; for thick sediment layer (area 3), the estimated compressional sound speed in similar to the sediment layer ones, whereas for a middle thickness (area 2), the estimated compressional sound speed is a depth average between sediment and basement ones.
(a) Shape of the cost function J depending on the upper layer thickness versus relative compressional sound speed of the guessed sediment layer (i.e., value - value which optimizes J): 10 m thick sediment layer (circle); 5 m intermediate sediment layer (crosses); 0.25 m thin sediment layer (points). (b) Normalized criterion depending on the layer thickness with the same meaning as below; a middle thickness of sediment layer (curves with crosses) creates a small decrease in the maximum value of J [(a) from 0.6 to 0.56], and a small widening of the peak around the maximum (b).
(a) and (b) I mes(t, f) for tracks 1 and 2, white boxes identify the data used to compute I mes(k, f), the ship’s range in these boxes is approximately 1500 m between 300 m and 1800 m, striations are clearly visible on I mes(t, f). (c) and (d) I mes(k, f) for tracks 1 and 2, and corresponding inverted RDC curves (in black) a good match between local maxima of Im (k, f) and optimal theoretical RDC is visible. (e) Objective functions for track 1: real data SNR = 12.5 dB (continuous line); simulated data with ship’s range = 1500 m and SNR = 12.5 dB (crosses); simulated data with ship’s range = 750 m and SNR = 12.5 dB (triangles). (f) Objective functions for track 2: real data SNR = 9.8 dB (continuous line); simulated data with ship’s range = 1500 m and SNR = 9.8 dB (crosses); simulated data with ship’s range = 750 m and SNR = 9.8 dB (triangles).
Recorded data during the MOVEBOAT2006 experiment.
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