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The pseudospectral time-domain (PSTD) method is an accurate and efficient scheme for solving the acoustic wave equation numerically. It provides a good basis for a general sonar simulation model because all of the fundamental processes on which sonar depend occur as natural consequences of solving the wave equation. Propagation, interference, and spreading and absorption losses are intrinsic to this solution; reflection and scattering are governed by the distribution of materials within the simulated environment. These processes are analogous to those in the physical system being modeled. The method generates the full spatial and temporal evolution of the acoustic field for a specified model environment. This paper presents the application of a PSTD model to the simulation of a sidescan sonar system operating in deep water. Synthetic sidescan images of sand ripples are simulated using a directional fractal surface as the model sea bed. Different forms of time-varying gain are applied to the received signals to investigate its effects on the statistics of the resulting images. These images are visually realistic and have significantly non-Rayleigh histograms. Rayleigh distribution, Rayleigh mixtures with up to four modes, and K distribution fits to these histograms demonstrate that the form of the applied time-varying gain has a substantial effect both on the derived distribution parameters and on the probability that the data are drawn from that distribution. They also demonstrate that, with a greater chi-square test probability and with fewer fitting parameters, the K distribution provides the more appropriate description of the reverberation from the simulated sand-ripple sea bed generated with the model sonar system.