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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.

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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 H ankel 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.

The conclusion that simultaneous vibroseis recording does not provide adequate signal separation (Martin & Bacon 1993) is, in my opinion, short-sighted, as it takes into account only the individual records. A 30 dB separation cannot be easy to accept by a field geophysicist, but in real field surveys we never use individual records for interpretation.If we take into account the fact that, in 3D surveys, coverage will seldom be below 1200%, if not much higher, and differences in offset and azimuth among interfering sweeps will add to the separation of energy coming from different vibroseis locations, the 30 dB separation will improve considerably and will easily reach 40 or 50 dB. When using up-and-down sweeps, crossover problems can be attenuated or eliminated by choosing sweeps that cross at 50 Hz, where high-line rejection filters are normally present. T h e suggestion of using more seismic lines simultaneously in land acquisition, like multistreamer operations, does not take into account the much higher down-time expected by increasing the number of seismic lines in Europe's highly populated areas.The success of surveys using much worse separation methods in comparison with today's efficient electronics and better understood interference phenomena, demonstrates that the conclusions of Martin's experiment cannot be applied to 3D field surveys without additional investigation of other interference attenuation factors.