Comparison of a subrank to a full-rank time-reversal operator in a dynamic ocean
The R/V Henlopen was moored in approximately 95-m deep water and is depicted with the source-receiver array (SRA) deployed from the A-frame. The array focused sound on the echo-repeater/probe source which was married beneath a short vertical receive array (VRA) deployed from the R/V ENDEAVOUR, which was slowly drifting away in 85-m deep water. A typical soundspeed profile (SSP) is shown.
(a) Twenty-one thermistors sampled the temperature field along the aperture of the SRA every . (b) Salinity measurements were inferred three times daily with CTD casts. (c) Calculated sound speed showing an upward refracting profile that traps energy in the water column. (d) The geoacoustic model for the experimental site area off the coast of New Jersey.
A gray scale plot of three measured time-reversal foci are shown over depth and time. A diagram to the right of the time series shows the nested vertical-receiver array and its placement above the probe source. The probe source transmitted a Tukey windowed pulse which was measured on the source-receiver array about 2.8-km away. The signal was windowed, time-reversed, and retransmitted. The vertical-receiver array is measuring only the upper part of the focus.
Modeled backpropagation of probe-source signal data recorded on the SRA using the environmental measurements described in Fig. 1. (a) Single frequency ambiguity surfaces simulated at by backpropagating a measured probe-source data signal. The nominal range/depth of the probe-source is . (c) Coherent broadband simulation of the received time-reversal focus as it would be received on the VRA (three different realizations of the sweep are shown). (b) and (d) Tracking the target range and depth versus time. (b) Stacked plot of horizontal slices of the ambiguity surfaces at the nominal probe source depth. The solid line indicates the GPS estimated distance between the ships, one of which was freely drifting. (d) Vertical slices of the ambiguity surfaces at the nominal probe-source range. The solid line shows the measured depth of the probe source, which was different by .
Modeled TRO focusing simulation using 64 simulated beams. (a) Single frequency TRO focus of the first eigenvector in an inhomogeneous, range dependent, and static version of the typical ocean environment during the TREX-04 experiment and excluding ship drift. (b) Incoherent average of the broadband TRO focus. (c) Single frequency TRO focus in a dynamically changing ocean including estimated ship drift. (d) Incoherent average of the dynamic broadband TRO focus. The black line represents the target collocated with the VRA which is drifting. Measuring all 64 beams, at one beam a minute, takes more than a hour which leads to a broadening of the focus. Note that the ship has drifted out of the center of the focal region.
Simulated single frequency TRO focusing using multiple eigenvectors in a dynamic ocean. (a) TRO focus using the second eigenvector and (b) TRO focusing using both the first and second eigenvectors weighted by their respective eigenvalues. No significant enhancement is seen. Over the used to measure the full-rank TRO the target has been spread into five significant incoherent eigenvalues (the other eigenvalues are noise). In the static environment [Figs. 5(a) and 5(b)], only one strong eigenvalue was present and corresponded to the target.
Comparison of modeled backpropagation of simulated sub-rank TRO and measured subrank TRO. The subrank TRO was measured over a period using every fourth beam during the TREX-04 experiment. Backpropagation was modeled using a TRO constructed with simulated target response in (a) and (b) and from measured at-sea target response in (c) and (d). Subrank TRO focusing of simulated scatter: (a) Single frequency TRO focus of the first eigenvector in an inhomogeneous range-dependent and dynamic ocean with a drifting target. (b) Incoherent average of the broadband TRO focus. Sub-rank TRO focusing of experimentally measured scatter: (c) Single frequency TRO focus of the first eigenvector. (d) Incoherent average of the broadband TRO focus. In both cases, when the subrank TRO was estimated over a (instead of ) period, the target was incoherently smeared into just two eigenvalues. In this dynamic case, the focus associated with the subrank TRO is superior to the focus of the full-rank TRO shown in Fig. 6.
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