Transmission mode time-reversal super-resolution imaging

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Abstract
The theory of time-reversal super-resolution imaging of point targets embedded in a reciprocal background medium [A. J. Devaney, “Super-resolution imaging using time-reversal and MUSIC,” J. Acoust. Soc. Am. (to be published)] is generalized to the case where the transmitter and receiver sensor arrays need not be coincident and for cases where the background medium can be nonreciprocal. The new theory developed herein is based on the singular value decomposition of the generalized multistatic data matrix of the sensor system rather than the standard eigenvector/eigenvalue decomposition of the time-reversal matrix as was employed in the above-mentioned work and other treatments of time-reversal imaging [Prada, Thomas, and Fink, “The iterative time reversal process: Analysis of the convergence,” J. Acoust. Soc. Am. 97, 62 (1995); Prada et al., “Decomposition of the time reversal operator: Detection and selective focusing on two scatterers,” J. Acoust. Soc. Am. 99, 2067 (1996)]. A generalized multiple signal classification (MUSIC) algorithm is derived that allows super-resolution imaging of both well-resolved and non-well-resolved point targets from arbitrary sensor array geometries. MUSIC exploits the orthogonal nature of the scatterer and noise subspaces defined by the singular vectors of the multistatic data matrix to form scatterer images. The time-reversal/MUSIC algorithm is tested and validated in two computer simulations of offset vertical seismic profiling where the sensor sources are aligned along the earth’s surface and the receiver array is aligned along a subsurface borehole. All results demonstrate the high contrast, high resolution imaging capabilities of this new algorithm combination when compared with “classical” backpropagation or field focusing. Above and beyond the application of seismo-acoustic imaging, the time-reversal super-resolution theory has applications in ocean acoustics for target location, and ultrasonic nondestructive evaluation of parts.