Reconstructing surface wave profiles from reflected acoustic pulses

Surface wave shapes are determined by analyzing underwater reflected acoustic signals. The acoustic signals (of nominal frequency 200 kHz) are forward scattered from the underside of surface waves that are generated in a wave tank and scaled to model smooth ocean swell. An inverse processing algorithm is designed and implemented to reconstruct the surface displacement profiles of the waves over one complete period. The inverse processing uses the surface scattered pulses collected at the receiver, an initial wave profile (two are considered), and a broadband forward scattering model based on Kirchhoff’s diffraction formula to iteratively adjust the surface until it is considered optimized or reconstructed. Two physical length scales over which information can be known about the surface are confirmed. An outer length scale, the Fresnel zone surrounding each specular reflection point, is the only region where optimized surfaces resulting from each initial profile converge within a resolution set by the inner length scale, a quarter-wavelength of the acoustic pulse. The statistical confidence of each optimized surface is also highest within a Fresnel zone. Future design considerations are suggested such as an array of receivers that increases the region of surface reconstruction by a factor of 2 to 3.