Of the approaches to generating stochastic realizations of reverberation time series, the simple point scatterer model (PSM) is appealing because the statistics evolve naturally as the number of scatterers increases. Unfortunately, the number of eigenrays required is often overwhelming, especially for broadband signals. The more common ‘‘variance factorization model’’ (VFM) uses far fewer eigenrays to compute a time-dependent estimate of the variance of the reverberation, and applies the spectral factorization theorem to generate a sequence of short-time spectra, which is inverse transformed and concatenated to form the desired time series. However, the variance and factorization steps scale with the square and the cube, respectively, of the number of receiver channels, so the advantage is lost for element-level simulations of complex receivers. The ‘‘noiselet model’’ is conceptually similar to the PSM, but the transmit pulse is replaced by an ensemble of precomputed ‘‘noiselets,’’ which are sums of randomly weighted and delayed copies of the original transmit pulse. The number of eigenrays is thus comparable to the VFM, but scaling is linear in the number of channels, rendering this method tractable for real-time broadband element-level simulation. Examples are shown for a linear FM pulse at 10 kHz and 400-Hz bandwidth.

The noiselet reverberation model, instead of transmitting the pulse itself, transmits a superposition of many copies of the pulse, each copy with a random amplitude and phase. This allows the simulation to mimic the point scatterer method without requiring a prohibitively large number of scatterers. It uses the GRAB ray model to introduce the propagation information. It provides a real-time high-fidelity simulation, providing element-level time series as an output for a planar array of receivers. However, it is presently limited by the phase shift calculations required by the frequency-domain beamformer to about 20 receivers without an unacceptable trimming of the number of rays used. Here, an approach is demonstrated that significantly improves the speed of this computation by identifying those receivers requiring the same phase shift to within a given specified error, such that only a single phase shift computation is required. These receivers fall onto a finite width strip, or quasi stave, that is not required to be parallel to element rows or columns. Along with providing a significant speed-up to the calculation, the approach becomes more efficient as the number of receivers increases, thereby allowing real time simulations using receiver arrays of over 100 elements.