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Time-angle sensitivity kernels for sound-speed perturbations in a shallow ocean
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10.1121/1.4809650
/content/asa/journal/jasa/134/1/10.1121/1.4809650
http://aip.metastore.ingenta.com/content/asa/journal/jasa/134/1/10.1121/1.4809650
View: Figures

Figures

Image of FIG. 1.
FIG. 1.

(Color online) Pekeris waveguide used for the PE simulation. Seawater properties: Sound speed  = 1500 m/s; density  = 1000 kg/m; and attenuation  = 0 dB/λ. Seabed properties: Sound speed  = 1600 m/s; density  = 1600 kg/m; and attenuation  = 0.1 dB/λ. The elements of the 48-m source-receiver arrays are represented by dots. The acoustic arrivals are indexed by the number of reflections of the corresponding acoustic path. The sign of the reception angle gives the sign of the acoustic arrival/path. The bold black line represents acoustic path number 4, which is further used in Figs. 3–5 .

Image of FIG. 2.
FIG. 2.

(Color online) Iso-surface (3.33 × 10 Pa) of the 3D-received signal envelope in the double-beamformed domain (, , ). The signal was recorded in the configuration shown in Fig. 1 and the nine “bubbles” represent the nine acoustic arrivals that correspond to the eigenray that is also shown in Fig. 1 .

Image of FIG. 3.
FIG. 3.

(Color online) 2D-TT-SKs corresponding to ray path number 4 of Fig. 1 (here a white plain line) for different apertures of the source-receiver arrays: (a) 3, (b) 11, and (c) 31 elements (3, 15, and 45 m span, respectively). The white dashed line shows the ray path with the same TT, but with opposite DOA and DOD. The three numbered circles represent different locations of possible positive perturbations.

Image of FIG. 4.
FIG. 4.

(Color online) 2D-DOA-SKs corresponding to ray path number 4 of Fig. 1 (here a white plain line) for different apertures of the source-receiver arrays: (a) 3, (b) 11, and (c) 31 elements (3, 15, and 45 m span, respectively). The white dashed line shows the ray path with the same TT, but with opposite DOA and DOD. The three numbered circles represent different locations of possible positive perturbations.

Image of FIG. 5.
FIG. 5.

(Color online) 2D-DOD-SKs corresponding to ray path number 4 of Fig. 1 (here a white plain line) for different apertures of the source-receiver arrays: (a) 3, (b) 11, and (c) 31 elements (3, 15, and 45 m span, respectively). The white dashed line shows the ray path with the same TT, but with opposite DOA and DOD. The three numbered circles represent different locations of possible positive perturbations.

Image of FIG. 6.
FIG. 6.

(Color online) Ray paths used for the T-A-SK validation that correspond to the four-times-reflected eigenrays taken between the center of each subarray (dots). Sound-speed perturbations are 2D-Tukey (tapered cosine) windows with their maximum values at: 0.3 m/s (0.02% of the sound-speed background). The perturbation shape is given in the “A” case, as shown. The four circles A, B, C, and D show the four locations of the sound-speed perturbations. The reference sensors of the different source-receiver arrays are shown by the dots.

Image of FIG. 7.
FIG. 7.

Flowchart of the main steps of the observable variation measurements carried out with PE simulations. and are the reference and the perturbed Green's functions, respectively. and are the 3D signals recorded in the reference and the perturbed states, respectively, and is the emitted signal. and represent the observables of the acoustic arrival in the reference and perturbed states, respectively. (, , ) are the observable variations measured on the PE-simulated signals shown in the figure.

Image of FIG. 8.
FIG. 8.

Flowchart of the observable estimation scheme using the T-A-SKs. Observable variations are induced by a perturbation, , located at a point in the waveguide. is the emitted signal, is the reference Green's functions, (.) is the gradient operator, and (, , ) are the estimates of the observable variations obtained with the T-A-SKs shown in the figure.

Image of FIG. 9.
FIG. 9.

(Color online) (a) TT variations normalized by the signal period  = 4 × 10 s. (b) DOA variations normalized by the main lobe size  = 2.9°. (c) DOD variations normalized by the main lobe size  = 2.9°. From left to right, these observable variations are caused by the sound-speed perturbations A, B, C, and D represented in Fig. 6 . Circles correspond to measurements made on PE simulations (the ground truth), and dots to the respective T-A-SK estimates.

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/content/asa/journal/jasa/134/1/10.1121/1.4809650
2013-07-11
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Time-angle sensitivity kernels for sound-speed perturbations in a shallow ocean
http://aip.metastore.ingenta.com/content/asa/journal/jasa/134/1/10.1121/1.4809650
10.1121/1.4809650
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