Acoustic echo formation-a filter theory approach

The response of a reflecting boundary, such as an ocean bottom, to an impinging acoustic pulse involves several processes and variables. One group of these processes is associated with the formation of an acoustic transmitting/receiving beam and with the parameters of the transmitted acoustic pulse. Another group is associated with the complex physical processes involved in sound reflection and scattering from the surface and the volume of the ocean bottom. The complexities of these phenomena often obscure an intuitive understanding of the underlying principles of echo formation and its reception. In this paper, we propose a simplistic model for this complex process using filter theory. The bottom is represented as a surface reflector with an acoustic wave front sweeping over it with time-varying velocity. The impulse response of a smooth flat bottom is characteristic of a low pass-filter that will greatly attenuate the impinging high frequency pulse. On the other hand, bottom undulations will modulate the reflected signal such that it can be represented by the impulse response of a band-pass filter. The received echo can be represented as the response of such filter to a high frequency probing pulse. The characteristics and amplitude of the echo are dependent on frequency spectrum overlap between the transmitted pulse spectrum and the filter frequency response. In the paper, we discuss several cases of interest with the intent to provide an intuitive understanding of echo formation from a system point of view.