Application of the DORT method to the detection and characterization of two targets in a shallow water wave-guide

The decomposition of the time-reversal operator (DORT in French) is an active array detection technique. It requires the measurement of the array response matrix K(/spl omega/) and consists in the analysis of the eigenvalues and the eigenvectors of the time-reversal operator K*K which provides information on the presence and localization of scatterers in the medium. It was shown that the DORT method allows to separate and localize pointlike scatterers in a shallow water wave-guide [J. Acoust. Soc. Am. Mordant et al. (1998) and Fotegot et al. (2003)]. Here, we extend the study to the detection and frequency characterization of two spherical targets. Small scale ultrasonic experiments are performed with a 3.9 MHz 24 elements transducer array and two spheres of 2 and 3 mm diameter in a 31 mm deep wave-guide. These scatterers correspond to 15 < ka < 25 leading to a non-isotropic scattered field. We have developed a theoretical model taking into account the wave-guide and the acoustic properties of the spheres and using the partial waves decomposition of the scattered field. We calculate the singular values of the array response matrix. This theoretical approach is in good agreement with the experimental results. This 1/325/sup th/ scale ultrasonic experiment corresponds to a shallow water experiment with a 12 kHz Vertical Linear Array (VLA).