Oppenheim Alan V.

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Oppenheim
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Alan V.
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  • Technical Report
    Computation of the Hankel transform using projections
    (Woods Hole Oceanographic Institution, 1981-04) Oppenheim, Alan V. ; Frisk, George V. ; Martinez, David R.
    In this paper two new algorithms for computing an nth‐order Hankel transform are proposed. The algorithms are based on characterizing a circularly symmetric function and its two‐dimensional Fourier transform by a radial section and interpreting the Hankel transform as the relationship between the radial section in the two domains. By utilizing the property that the projection of a two‐dimensional function in one domain transforms to a radial section in the two‐dimensional Fourier transform or inverse Fourier transform domain, several efficient procedures for computing the Hankel transform exploiting the one‐dimensional FFT algorithm are suggested.
  • Technical Report
    A technique for measuring the plane-wave reflection coefficient of the ocean bottom
    (Woods Hole Oceanographic Institution, 1981-04) Frisk, George V. ; Oppenheim, Alan V. ; Martinez, David R.
    A new technique for the measurement of the plane-wave reflection coefficient of a horizontally stratified ocean bottom is described. It is based on the exact Hankel transform relationship between the reflection coefficient and the bottom reflected field due to a point source. The method employs a new algorithm for the numerical evaluation of the Hankel transform which is based on the "projection-slice" theorem for the two-dimensional Fourier transform. The details of the algorithm are described in the companion paper. Although the algorithm is applied to the case of an isovelocity ocean, the general theory for measuring the plane-wave reflection coefficient in a refracting ocean is developed. The technique provides information about the reflection coefficient, not only for real incident angles, _but also for complex angles, thus potentially providing substantial additional structural information about the bottom. The method is shown to yield excellent results with synthetically generated data for the cases of a hard bottom and slow isovelocity bottom.