Predicted Deepwater Bathymetry From Satellite Altimetry: Non-Fourier Transform Alternatives

Robert Parker (1972) demonstrated the effectiveness of Fourier Transforms (FT) to compute gravitational potential anomalies caused by uneven, non-uniform layers of material. This important calculation relates the gravitational potential anomaly to sea-floor topography. As outlined by Sandwell and Smith (1997), a six-step procedure, utilizing the FT, then demonstrated how satellite altimetry measurements of marine geoid height are inverted into seafloor topography. However, FTs are not local in space and produce Gibb’s phenomenon around discontinuities. Seafloor features exhibit spatial locality and features such as seamounts and ridges often have sharp inclines. Initial tests compared the windowed-FT to wavelets in reconstruction of the step and saw-tooth functions and resulted in lower Root Mean Square (RMS) error with fewer coefficients. This investigation, thus, examined the feasibility of utilizing sparser base functions such as the Mexican Hat Wavelet, which is local in space, to first calculate the gravitational potential, and then relate it to sea-floor topography, with the aim of improving satellite derived bathymetry maps

A geometric investigation of acoustical wavefront scattering and healing induced by ocean internal waves

Observed ocean acoustic wavefronts show surprising stability in long range acoustic transmission experiments. This suggests that ocean scattering processes tend to re-distribute acoustic energy dominantly along the wavefront rather than across it. The purpose of this thesis is to elucidate the physical mechanism for this type of scattering by presenting a ray based physical model. Analytic formulae are presented that predict wavefront distortions caused by ocean internal waves and other processes. Applications of this study include wavefront healing near underwater obstacles, out of plane scattering and the vertical redistribution of energy of off axis sources.http://archive.org/details/ageometricinvest109453672US Navy (USN) author.Approved for public release; distribution is unlimited