The effect of coherence and noise on the decomposition of the time reversal operator

Active sonar in shallow water in shallow water is often reverberation-limited and the detectability is often limited by the presence of too many false alarms. The decomposition of the time reversal operator (DORT) is a method that potentially alleviates this problem by separating echoes from different depths in the water column. For example, DORT can separate a target in the water column from reverberation on the bottom. DORT requires a set of echoes recorded on a line array that result from a set of independent transmissions from a source array. A short derivation of DORT using the sonar equation is given. Because DORT is inherently a frequency-domain method, the time-frequency domain is derived to implement the algorithm on the data. Lastly, the similarity of DORT to adaptive beam forming is shown. In this paper, data taken on the Atlantic shelf, east of Cape May, NJ, during Geoclutter 03 and TREX-04 experiments, is processed and shown. The data was taken with a 64 element vertical line array of source-receiver elements. The target was an echo repeater using an XF4 source from 500 to 2500 Hz or an ITC 200 source from 2500 to 3500 Hz. The data cover six 500 Hz-bands from 500 Hz to 3500 Hz. The data are processed using DORT in the time-frequency domain. The analysis produces singular values in the time-frequency domain and in the time-delay domain. It also produces singular vectors that are used with a broad-band propagation model to form back-propagation images in the range, depth, frequency or range, depth, time domain. The analysis shows that the limiting factors in this data set arise from 1) motion that causes a lack of time-invariance, 2) additive noise and 3) the independent transmission scheme. The lack of time invariance is shown to spread the echo energy into several singular indices. Additive noise is shown to contaminate the singular values and back-propagation images. The particular transmission scheme used, time division multiplexed LFMs, is shown to c- - reate large side lobes in the time domain. Alternative transmission sequences, as well as alternative source and receiver orientations, are discussed