The decomposition of the time reversal operator (DORT) is a single frequency method of spatially isolating scatterers with a multiple-source/multiple-receiver system [C. Prada et al., J. Acoust. Soc. Am. 99, 2067–2076 (1996)]. The application of the DORT technique to a broadband sonar system is explained by showing its relationship to the sonar equation. The orthogonal matrices are related to source and receiving steering vectors and the singular values to the echo levels of the various signal components. The structure of a coherent, reverberation-limited, broadband, numerical sonar model is shown. Numerical results from this sonar model are processed by windowing and Fourier transforming. Then DORT is applied and the depth isolated target components are identified through projecting source and receiver steering vectors with modeled propagation matrices. The ability of this procedure to isolate scatterers from distributed bottom reverberation is shown for a set of source/receiver geometries with the scatterer at various depths and ranges. Both range-independent and range-dependent environments are considered. [Research sponsored by ONR.]