Acoustic backscattering by a dense solid elastic sphere. (a) The full-wave solution to the sphere (scattering amplitude, ; thin curve) which involves a summation of all partial waves and is shown to be strongly dependent upon frequency, containing numerous strong and narrow resonances. The partial-wave solution (scattering amplitude, ; thick curve) for the echo from the front interface of the sphere which is calculated from the first arrival of the impulse response in Fig. 1(b) and is shown to be weakly dependent upon frequency for higher frequencies. Both solutions for the scattering amplitude are normalized by . In this example, a tungsten carbide sphere of diameter was used. The circles correspond to two standard frequencies (38 and ) used in fisheries acoustics. (b) Impulse response of scattering.
(Color online) Effects of pulse-compression processing of a broadband signal. (a) A 2-ms-long (raw) chirp signal applied to Reson transducer, (b) frequency spectrum of signal from (a), (c) envelope of pulse-compressed signal in which autocorrelation function of signal shown in (a) is calculated, (d) frequency spectrum of pulse-compressed signal (before envelope was calculated) from (c). Dots: Spectrum calculated using -long window shown in (c). Solid: spectrum calculated using 10-ms-long window, which involves beginning with the signal within the -long window and zero padding each side.
Time-domain analysis of calibration signal. Top panel: Envelope of pulse-compressed echo from air-filled aluminum spherical shell in at-sea measurement. The echo was cross correlated with echo measured in a tank experiment with the system aimed up at the smooth air-water interface. Middle panel: Impulse response of predicted echo from spherical shell through calculating inverse Fourier transform of exact modal series solution. Bottom panel: Envelope of the convolution of the impulse response from middle panel and the applied transmitter signal. Each plot is normalized to unity. The data were collected on September 11, 2006 with the 41.5-cm-diam sphere suspended below the towbody.
Spectra of signals and system response associated with calibration measurement with air-filled spherical shell. Upper panel: Spectrum of (partial wave) echo from front interface (thick line) compared with spectrum of (full wave) echo from all partial waves (thin line). The spectra were calculated using the pulse-compressed signal illustrated in the top panel of Fig. 3. Lower panel: System response of broadband transducer as derived through partial-wave analysis using echo from front interface.
Sensitivity analysis of full-wave (upper panels) and partial-wave (lower panels) echoes for aluminum spherical shell, whose shell thickness is about 1% of the diameter. Material properties (density, compressional sound speed, and shear sound speed) of spherical shell are varied by about 1% between two sets of predictions in the left panels. Shell thickness is varied by 7% between two sets of predictions in the right panels.
(Color online) Design curves for minimum diameter of calibration sphere that can be used in partial-wave analysis. Combinations of solid elastic and air-filled elastic shell for aluminum (“AL”) and stainless steel (“SS”) are given. A separation between the echo from the front interface and the next major partial wave is assumed to be two times the inherent temporal resolution of the system (i.e., two times the inverse bandwidth). A larger than minimum diameter will allow for a longer processing gate and corresponding improved spectral resolution.
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