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During the Sediment Acoustics Experiment 2004 (SAX04), a synthetic aperture sonar (SAS) was used to detect simple targets that were either proud or buried below a water-sediment interface, where the nominal grazing angle of incidence from the SAS to the point above a buried target was well below the critical grazing angle. SAS images from other measurements below the critical angle have also produced target detections of buried spheres and finite cylinders. Models and numerical simulations are developed to investigate these proud and buried target detections. For buried targets, the simulations include estimates of reverberation from the rough seafloor, the subcritical penetration through the seafloor, scattering from a target, and propagation back to the SAS. For proud targets, the simulations include the scattering from the target where interaction with the seafloor is included through simple ray models. The simulations used environmental and material parameters measured during SAX04. The environmental measurements include profiles of small-scale surface roughness and superimposed ripple structure. The SAS simulations and model/measurement comparisons over a frequency range of 10-50 kHz further support scattering from sediment ripple structure as the dominant mechanism for subcritical penetration in this range.