Spatio-temporal invariants of the time reversal operator

Abstract

The decomposition of the time reversal operator, known by the French acronym DORT, is a technique to extract point scatterers' monochromatic Green's functions from a medium. It is used to detect, locate, and focus on scatterers in various domains such as underwater acoustics, medical ultrasound, and nondestructive evaluation. A limitation of the method arises from its single-frequency nature, when the signals used in acoustics are often broadband. Reconstruction of the broadband Green's functions from the single-frequency Green's functions can be very difficult when numerous scatterers are present in the medium. Moreover, the method does not take advantage of the axial resolution associated with broadband signals. Time domain methods are investigated here as an answer to these problems. It is shown that the time reversal operator in the time domain takes the form of a tensor. The properties of the invariants are discussed. It is shown they do not have all the expected properties. Another method is proposed that requires a priori information on the medium.

Time Reversal and Fractional Fourier Transform-Based Method for LFM Signal Detection in Underwater Multi-Path Channel

“…They also validated this theory by acoustic and seismic imaging experiments. Furthermore, they proposed TR cavity [20], iterative TR [21], TR operator decomposition (DORT) [22] and other methods [23,24] for target detection. Kuperman et al verified the focusing ability of TR in ocean experiments [25][26][27].…”

Coherent and Noncoherent Joint Processing of Sonar for Detection of Small Targets in Shallow Water

“…Meanwhile, several vertical transmitting arrays are widely-spaced to illuminate the likely target from different angles. The vertical diversity is exploited by the time-reversal (TR) mirror [ 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 ] to enhance target echoes and suppress reverberation by spatial-temporal focusing. For improving robustness of time-reversal focusing, an adaptive iterative strategy is considered in the processing framework.…”

Experimental implementation of reverse time migration for nondestructive evaluation applications

“…As with time reversal techniques, RTM is limited in its spatial resolution by the diffraction limit (in the present case it is a half wavelength for the guided, bending wave in the plate). Time reversal may be used to image linear scatterers through a series of time reversal experiments and complex processing, 19,20 or it may be used to directly image nonlinear scatterers (which are the sources of new frequency content). [21][22][23][24] However, the typical aim of time reversal is to localize sources, [25][26][27][28][29][30] whereas the aim of RTM is to directly image linear scatterers without the need for complex processing, or the requirement that the scatterers be nonlinear.…”