This paper presents a summary of the fundamental properties of the Radon transform, including delay effects, data shifting, rotation, scaling, windowing, bowtie events, energy conservation, etc., and includes representative examples on standard data sets such as 2-D delta functions, boxcar events, Gaussian bell, and conic sections which reinforce the basic concepts of the Radon transform.
A Radon transform mapping is developed which allows correct migration below plane sloping layers to be achieved. The mapping, which is the P-τ equivalent of a Fourier transform mapping, consists of p shifting and weighting. The effect of the mapping is to move the recording plane to a sloping interface. Migration then becomes conventional migration in a horizontally layered medium. Breaking the process into a sequence of steps gives a high level of insight into this particular wave‐field‐extrapolation problem. Applying the Radon transform mapping to a synthetic example of migration below a sloping layer produces excellent results. However, the method is accurate only for planar reflectors.
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