(Color online) Diagram of the experimental setup drawn to scale. A broadband, approximately 2–40 kHz, spherical source is positioned directly above target objects, buried at depths of 10 cm below the sediment–water interface. A two-dimensional receive array is generated synthetically by scanning a single hydrophone in a 1 m × 1 m patch directly above targets in steps of 3 cm.
(Color online) Bottom panel: Temporal band-limited scattering impulse responses on a logarithmic scale versus time (ms) and receiver position (m), measured experimentally by scanning a single hydrophone at a height of 20 cm above the sediment–water interface in a line directly above the UXO buried at a depth of 10 cm below the sediment–water interface. Superimposed on the direct-path and sediment-interface returns are time-of-flight estimates predicted numerically through geometric constraints. Top panel: Time trace extracted from the central receiver position in the bottom panel. The direct-path pulse width is approximately 15 μs, corresponding to an approximately 1.1 cm spatial resolution. In both panels, all ray paths are labeled according to their type.
(Color online) Acoustic images generated from experimental scattering data collected from a cinder block (first row), a natural rock (second row), and a rocket UXO (third row). Images in the bottom row are generated from scattering data generated with a finite-element-analysis (FEA) based simulation of scattering from the rocket. Left: Volumetric images. Center: Plan-view images generated by projecting the maximum value from volumetric images, as a function of depth, onto a single plane. Right: Single-slice beam-view images taken from the volumetric image at x = 0. The sediment interface and outlines of the targets are highlighted with solid and dashed lines, respectively. Circles in the two bottom right panels highlight the predicted location for the manifestation of a 0+ antisymmetric Lamb waves. In all beam-view images, scattering components are labeled according to their type and the image bandwidth is presented. All images are shown on the same linear scale, depicted in the top right panel. The PSF of the imaging algorithm, the image resulting from application of the algorithm to a single perfectly broadband point scatterer, is presented as an inlay in the second row.
(Color online) Depiction of the ray paths contributing to acoustic images in Fig. 3. Top: Trace showing the relative arrival times of the rays depicted on the left-hand side of the bottom panel. The leftmost ray is generated by scattering from the water–sediment interface. The central ray represents the specular return from the face of the target proximal to the sediment interface. The rightmost ray arises due to multiple scattering between the target and sediment interface. The ray tracing the circumference of the shell in the bottom panel indicates the approximate path traveled by antisymmetric Lamb waves.
(Color online) Top: Monostatic scattering form function for an infinitely long cylindrical shell possessing the same properties as the rocket examined in pool experiments. Bottom: Predicted phase and group velocities of the lowest order antisymmetric Lamb wave. The dashed line is for an air-filled shell and the solid line is for a shell with elastic filler. The shaded region on both plots indicates the bandwidth employed to generate acoustic images from experimentally measured data.
(Color online) Far-field directivity estimates of a 0.4 m by 0.127 m rigid plate of the same cross-sectional dimensions as the rocket UXO. The receiver sweeps in angle along the longest dimension of the rocket. (a) Analytical solution for plane-wave incidence and receivers in the far field. (b) Numerical computation employing the Helmholtz–Kirchhoff integral, with the source and receivers at ranges of 100 m. (c) Solution of the Helmholtz–Kirchhoff integral with the point source in the same location as in pool measurements and receivers in the far field. (d) Directivity estimated through angular spectrum extrapolation, where scattered waveforms are collected over the same aperture as in pool measurements with the source in the same position as in (c). The top panel presents the axial response from (c) and (d) along with the axial response resulting from the same procedure as in (d) but with the aperture doubled in size.
(Color online) Far-field target strength (dB) referenced to 1 m as a function of frequency (kHz) and bistatic angle (deg) of objects buried in water-saturated medium grained sand at a depth of 10 cm. The top row presents the target strength as a function of the beam aspect, whereas the bottom row is for the receiver angle sweeping lengthwise along the target. The three columns on the right-hand side are generated from experimental data with the object type labeled over each column. The first column on the left is generated from a time-harmonic finite-element-analysis (FEA) based simulation assuming the rocket is in a configuration identical to that from the experiment used to generate the result in second column.
(Color online) Correlations representing the symmetry of plan-view acoustic images in the second column from Fig. 3 as a function of the mirror angle (deg). The acoustic image used to generate the “Cinder Block 45” result does not appear in Fig. 3. The horizontal dashed line represents the maximum correlation value observed for the clutter objects.
(Color online) Localized symmetry versus target strength correlation; whitened feature values from experimental measurements of the 127 mm diameter rocket UXO buried horizontal, at 30° and 60° pitch, the 155 mm diameter artillery shell buried horizontal, and at 30° pitch, the cinder block horizontal and rolled 45°, and the natural rock where the data are contaminated with numerically generated random noise with signal-to-noise ratios of 25–40 dB. The manually placed boundary indicates the class separation between the target UXO objects, labeled with crosses of varying shade, and clutter objects, labeled with circles of varying shade.
Material properties used in the three-dimensional time-harmonic finite-element-based simulation of bistatic scattering from the fully buried rocket UXO.
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