Phase Distortion of a Pulse Caused by Bottom Reflection

The phase distortion of a plane-wave pulse owing to bottom reflection at incident angles more grazing than the critical angle is considered. Two general methods of investigation, using the time and frequency domains, are given; they employ, respectively, the Hilbert transform of the incident pulse and the complex envelope signal. Applications to two typical SONAR pulses—a carrier frequency amplitude-modulated by a rectangular pulse and a Gaussian pulse—are given, along with graphs of the results. It is concluded that negligible distortion occurs, there being only a phase shift of the carrier, when the Q of the waveform is moderately larger than unity, the exact value depending on the smoothness of the transmitted pulse.