Acoustic scattering from a solid aluminum cylinder in contact with a sand sediment: Measurements, modeling, and interpretation
Top: experiment facility. Bottom area identified in diagram is area covered by sand. Bottom: rail and mobile tower system used. The rail consisted of 3 rail sections each 7 m in length, resulting in a 19.1 m span over which the tower could be moved. Insert is a schematic of the experiment viewed from above, range to cylinder is approximate, see text for exact geometry. The underwater photograph includes side view of array used. The diver is in the background, the overall vertical extent of the array is approximately 1 m.
Each panel shows pulse compressed and basebanded (i.e., signals downshifted by the center frequency) backscattering returns for a proud 60 cm long aluminum cylinder for 480 transmissions as the rail tower translated the central 12 m of the rail. The cylinder’s orientation is different in each panel. The axis of the cylinder relative to the path of the rail tower for each case is (a) 0° (broadside), (b) 25°, (c) 47°, and (d) 70°. The dB scale is relative to the brightest pixel in each panel.
The SAS images of the proud 60 cm long cylinder resulting from processing the data presented in Fig. 2. The dB scale is relative to the brightest pixel in each panel. Note that range 0 in the figure is relative to 9.5 m—the nominal horizontal distance from transmitter/receiver array to the center of the cylinder.
(a) shows the experimental result for the absolute target strength of the proud cylinder as a function of azimuthal angle and frequency. (Note that 0° is broadside and 90° is azimuthally end-on but still at a vertical angle of about 21.5° to the center of the cylinder.) The other subplots show FE results, all but the last use axial symmetry and 2-D FE: (b) absolute target strength of the free field cylinder as a function of azimuthal angle and frequency calculated assuming source and receiver at infinity; (c) absolute target strength of the proud cylinder as a function of azimuthal angle and frequency calculated assuming source and receiver at infinity and using image cylinders to account for cylinder/interface interactions; (d) absolute target strength of the proud cylinder calculated using actual experiment geometry and with second order accurate layered medium Green’s functions; (e) absolute target strength of the proud cylinder calculated using actual experiment geometry and with first order accurate layered medium Green’s functions; (f) 3-D FE computation of absolute target strength of the proud cylinder as a function of azimuthal angle and frequency.
Paths included in FE calculation in Sec. IV C. Top panel shows all paths and the bottom four panels show the separate paths. Paths 2 and 3 are reciprocal and include one bottom bounce, path 4 includes two bottom bounces.
Comparison broadside target strength: data (black), free field FE calculation (red), and proud FE calculation (green) using Eq. (3).
(a) Target strength as a function of frequency at broadside aspect and cylinder orientation parallel to the rail, computed by taking into account the actual source-target-receiver geometry of the experiment. Strong variations of the target strength as a function of sensor location along the vertical receive array are evident. The red curve shows the effect of applying the beamforming to the model results. (b) Variation of the simulated beamformed array response caused by changes in the vertical receive array tilt angle. (c) Computed target strength for broadside insonification, obtained by two different combinations of cylinder orientation relative to the rail and tower displacement. (d) Sensitivity of the beamformed array response to changes in the grazing angle (keeping the range constant), and to changes in the range (keeping the grazing angle constant), for broadside insonification and cylinder orientation 0° with respect to the rail. (e) Computed target strength for broadside insonification, obtained using different approximations of the layered medium Green’s function. The first order accurate Green’s functions are equivalent to those used in Sec. IV C, however, the first order result here includes the actual experimental geometry instead of the assumption of plane wave incidence and scattering.
Comparisons of data (black), FE results using plane wave incident and scattering angles (green), and FE results using experimental geometry with first order accurate Green’s function (magenta): (a) broadside [note that the green curve is the same as that in Fig. 6 and magenta curve is the same as the green curve in Fig. 7(e)], (b) 17° relative to broadside, (c) 23° relative to broadside, (d) 33° relative to broadside.
Left: geometry of FE model for target region. Right: enlarged end view of cylinder.
(a) Comparison of 3-D FE model and experimental data at broadside insonification. (b) Comparison of the FE model results at broadside insonification using quadratic (red) and cubic (green) elements.
Comparisons of data (black), FE results using plane wave incident and scattering angles (left column, green curves), and FE results using experimental geometry with first-order-accurate Green’s function (center column, magenta curves), 3-D FE results (right column, red curves): top row: broadside, top center row: 17° relative to broadside, bottom center row: 23° relative to broadside, bottom row: 33° relative to broadside.
Definition of angles and unit vectors needed to get and in terms of and .
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