Characterization of an elastic target in a shallow water waveguide by decomposition of the time-reversal operator

Abstract

This paper reports the results of an investigation into extracting of the backscattered frequency signature of a target in a waveguide. Retrieving the target signature is difficult because it is blurred by waveguide reflections and modal interference. It is shown that the decomposition of the time-reversal operator method provides a solution to this problem. Using a modal theory, this paper shows that the first singular value associated with a target is proportional to the backscattering form function. It is linked to the waveguide geometry through a factor that weakly depends on frequency as long as the target is far from the boundaries. Using the same approach, the second singular value is shown to be proportional to the second derivative of the angular form function which is a relevant parameter for target identification. Within this framework the coupling between two targets is considered. Small scale experimental studies are performed in the 3.5 MHz frequency range for 3 mm spheres in a 28 mm deep and 570 mm long waveguide and confirm the theoretical results.

Imaging and tracking of targets in clutter using differential time-reversal techniques

“…Time-reversal (TR) techniques [7][8][9][10][11][12][13] have shown to be very useful for applications in remote sensing and imaging utilizing either acoustic/elastic waves [8,11] or electromagnetic waves [9,10,12,13]. These techniques exploit the time invariance of the wave equation in lossless media under TR [14,15].…”

Propagation of guided waves through weak penetrable scatterers

“…In the context of dielectric waveguides, as used in optical communication, interest lies in the understanding of the effects of impurities due to material defects and in the possibility of utilizing deliberate isolated impurities as passive optical components. [1][2][3] The detection and the characterization of buried defects or targets motivates research in the context of acoustic waves, 4-6 water waves, 7,8 and in the context of elastic waves. 9,10 The problem of scattering by a single scatterer centered in a waveguide is analogous to the scattering problem by a periodic array of scatterers.…”

Construction of the temporal invariants of the time-reversal operator

“…2(a) and 2(b) by plotting the focal spot at target distance as a function of frequency. Difficulties can arise if SV switching occurs, especially in the case of target resonances as presented by Philippe et al 17 As predicted by the image theory, the focusing pattern is made of several focus spots for one target: one in the vertical extension corresponding to the guide and eight others outside the guide. The depth of the target in the guide is extracted from the directivity diagram in Fig.…”