The present invention is a system that mathematically simulates acoustic waves that are reflected off an ocean floor from a SONAR transducer mounted on a ship, submarine, or other water navigable craft. By varying the number of mathematical equations, the form of the equations, and the parameters of the equations, many different conditions may be simulated in the laboratory before testing and implementing a SONAR system at sea. The system can simulate either a spatial hydrophone SONAR system or a temporal hydrophone SONAR system for all ship speeds (i.e. all velocity components). The novel equations used in the system are based on the physics of correlation SONAR, and are applied in real time simulation environments to provide for accurate SONAR simulation of a ship's velocity.