Signal-Waveform Distortion Caused by Reflection off Lossy-Layered Bottoms

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Abstract
The acoustic theory for the reflection of a single-frequency plane wave from a fluid layer lying between two semi-infinite fluid media, where the layer and the bottom medium are subject to attenuation, is reviewed. Applying the experimental fact that the attenuation is proportional to the first power of frequency to this theoretical model of the ocean bottom, we show that the effect on impingent plane waves may be treated as a parallel linear-filtering operation with a component transfer function of the basic form H (f) = exp[−2πb|f|+iε sgn (f)]. The parameters b and ε depend on the media physical constants, the angle of incidence, and the particular reflected component under consideration. Here, f is frequency in cycles per second, 2πb is attenuation in nepers per cycles per second, ε is phase shift in radians, and sgn (f) = 1 for f>0, −1 for f <0. For this basic type of transfer function, the component reflected pulse is first derived generally in terms of the incident pulse, the attenuation, and the phase shift. Component reflected-pulse shapes for some specific incident pulses, including a carrier, amplitude-modulated by a rectangular pulse, a sinc pulse, an exponential pulse, and a Gaussian pulse with linear frequency modulation (FM), are then derived in terms of tabulated functions and are numerically evaluated. A method is presented which can treat the total reflected signal in complete generality for arbitrary amounts of loss and angle of incidence, and a variety of waveshapes with arbitrary Q, phase, and bandwidth. The answer is given by amplitude scaling, delay, and summation of component pulses, several of which are presented. Furthermore, the method is applicable to media with several lossy layers, once the components are individually identified and their coefficients, delays, and attenuations are computed.

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