Time-Domain Analysis of Echoes from Solid Spheres and Spherical Shells with Separated Transmit-Receive Configurations
Abstract
The complexity of bistatic echo pulse sequences surpasses that of monostatic echo pulse sequences. Based on the scattering acoustic field of elastic spheres and spherical shells, a method is employed to calculate the time-domain echoes of solid spheres and spherical shells with transceiver separation under the condition of plane wave incidence. This is achieved by constructing the incident signal and performing a multiplication operation in the frequency domain with the target scattering acoustic field. Employing the contour integral method, we derive phase velocity and group velocity dispersion curves for circumferential waves propagating around these structures. Furthermore, under the assumption of plane wave incidence, we analyze the propagation paths of Rayleigh echoes for solid spheres and anti-symmetric Lamb waves for spherical shells. Estimation formulas for the arrival times of separated transmit-receive echoes are provided for both solid spheres and spherical shells. Our findings indicate that bistatic waves can be classified into clockwise and counterclockwise circulation patterns around the surfaces of these structures. Through a comparison with the time-angle spectrum of echoes, we demonstrate the accuracy of the proposed estimation formulas for echo arrival times. This study offers valuable insights for the identification of underwater targets.Keywords:
dispersion curves, time-domain echoes, bistatic configuration.References
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24. Williams K.L., Marston P.L. (1985), Backscattering from an elastic sphere: Sommerfeld–Watson transformation and experimental confirmation, The Journal of the Acoustical Society of America, 78(3): 1093–1102, https://doi.org/10.1121/1.393028
25. Xia Z., Li X., Meng X. (2016), High resolution time-delay estimation of underwater target geometric scattering, Applied Acoustics, 114: 111–117, https://doi.org/10.1016/j.apacoust.2016.07.016
26. Yu X., Peng L., Yu G. (2014), Extracting the subsonic anti-symmetric lamb wave from a submerged thin spherical shell backscattering through iterative time reversal, Journal of Ocean University of China, 13: 589–596, https://doi.org/10.1007/s11802-014-2166-8
2. Apostoloudia A., Douka E., Hadjileontiadis L.J., Rekanos I.T., Trochidis A. (2007), Crack detection on beams by time-frequency analysis of transient flexural waves, Archives of Acoustics, 32(4): 941–954.
3. Ayres V.M., Gaunaurd G.C., Tsui C.Y., Werby M.F. (1987), The effects of Lamb waves on the sonar cross-sections of elastic spherical shells, International Journal of Solids and Structures, 23(7): 937–946, https://doi.org/10.1016/0020-7683%2887%2990088-6
4. Bednarz J. (2017), Operational modal analysis for crack detection in rotating blades, Archives of Acoustics, 42(1): 105–112, https://doi.org/10.1515/aoa-2017-0011
5. Diercks K.J., Hickling R. (1967), Echoes from hollow aluminum spheres in water, The Journal of the Acoustical Society of America, 41(2): 380–393, https://doi.org/10.1121/1.1910349
6. Ding D., Chen C.X., Kong H.M., Fan J., Peng Z.L. (2023), Acoustic coding based on high frequency time domain echo of layered elastic spherical shells in water [in Chinese], Applied Acoustics, 42(4): 781–791.
7. Fan W., Fan J., Wang X.N. (2012), Application of the SWT method to scattering from water-filled elastic spherical shells [in Chinese], Journal of Ship Mechanics, 16(6): 705–715.
8. Fawcett J.A. (2015), Computing the scattering from slightly deformed spherical shells, IEEE Journal of Oceanic Engineering, 41(3): 682–688, https://doi.org/10.1109/JOE.2015.2478995
9. Gaunaurd G., Überall H. (1985), Relation between creeping-wave acoustic transients and the complex-frequency poles of the singularity expansion method, The Journal of the Acoustical Society of America, 78(1): 234–243, https://doi.org/10.1121/1.392564
10. Gaunaurd G.C., Überall H. (1983), RST analysis of monostatic and bistatic acoustic echoes from an elastic sphere, The Journal of the Acoustical Society of America, 73(1): 1–12, https://doi.org/10.1121/1.388839
11. Gaunaurd G.C., Werby M.F. (1987), Lamb and creeping waves around submerged spherical shells resonantly excited by sound scattering, The Journal of the Acoustical Society of America, 82(6): 2021–2033, https://doi.org/10.1121/1.395646
12. Gaunaurd G.C., Werby M.F. (1991), Sound scattering by resonantly excited, fluid-loaded, elastic spherical shells, The Journal of the Acoustical Society of America, 90(5): 2536–2550, https://doi.org/10.1121/1.402059
13. Gunderson A.M., España A.L., Marston P.L. (2017), Spectral analysis of bistatic scattering from underwater elastic cylinders and spheres, The Journal of the Acoustical Society of America, 142(1): 110–115, https://doi.org/10.1121/1.4990690
14. Kargl S.G., Williams K.L., Thorsos E.I. (2012), Synthetic aperture sonar imaging of simple finite targets, IEEE Journal of Oceanic Engineering, 37(3): 516–532, https://doi.org/10.1109/JOE.2012.2200815
15. Li X., Wu Y. (2019), Feature extraction for acoustic scattering from a buried target, Journal of Marine Science and Application, 18: 380–386, https://doi.org/10.1007/s11804-019-00102-9
16. Long Y.L., Wen X.L., Xie C.F. (1994), An implementation of a root finding algorithm for transcendental functions in a complex plane [in Chinese], Journal on Numerical Methods and Computer Applications, pp. 88–92.
17. Marston P.L., Sun N.H. (1992), Resonance and interference scattering near the coincidence frequency of a thin spherical shell: An approximate ray synthesis, The Journal of the Acoustical Society of America, 92(6): 3315–3319, https://doi.org/10.1121/1.404181
18. Qiao S., Shang X., Pan E. (2016), Elastic guided waves in a coated spherical shell, Nondestructive Testing and Evaluation, 31(2): 165–190, https://doi.org/10.1080/10589759.2015.1079631
19. Su J., Wang F., Du S. (2017), An elastic wave enhancement method based on modified bright point model, [in:] 2017 IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC), pp. 1–4, https://doi.org/10.1109/ICSPCC.2017.8242491
20. Tang W.L., Fan J., Ma Z.C. (2018), Elastic acoustic scattering mechanism of targets in water, The Acoustic Scattering of Underwater Target [in Chinese], pp. 79–84, Science Press, China.
21. Thompson M. (2023), Time-frequency sonar detection of elastic wave reradiation, Ph.D. Thesis, Electrical and Computer Engineering, Auburn University.
22. Too G.P., Lin Y.W., Ke Y.C. (2014), Echoes analysis from spherical elastic shells by using iterative time reversal mirror, [in:] OCEANS 2014 – TAIPEI, pp. 1–5, https://doi.org/10.1109/OCEANS-TAIPEI.2014.6964463
23. Überall H., Gaunaurd G.C., Murphy J.D. (1982), Acoustic surface wave pulses and the ringing of resonances, The Journal of the Acoustical Society of America, 72(3): 1014–1017, https://doi.org/10.1121/1.388232
24. Williams K.L., Marston P.L. (1985), Backscattering from an elastic sphere: Sommerfeld–Watson transformation and experimental confirmation, The Journal of the Acoustical Society of America, 78(3): 1093–1102, https://doi.org/10.1121/1.393028
25. Xia Z., Li X., Meng X. (2016), High resolution time-delay estimation of underwater target geometric scattering, Applied Acoustics, 114: 111–117, https://doi.org/10.1016/j.apacoust.2016.07.016
26. Yu X., Peng L., Yu G. (2014), Extracting the subsonic anti-symmetric lamb wave from a submerged thin spherical shell backscattering through iterative time reversal, Journal of Ocean University of China, 13: 589–596, https://doi.org/10.1007/s11802-014-2166-8
