Introduction

The parabolic radon transform (PRT) is extensively used to transform the data into a domain where multiples and primaries are separable. This multiple-attenuation method proceeds as follows: the data are sorted in common midpoint (CMP) gathers, flattened with a normal moveout (NMO) correction, and then radon transformed. The multiples are then muted in the radon domain and subtracted from the input data. The final result depends heavily on the mapping of the primaries and multiples in the radon domain.

The limited aperture of the recording geometry and the spatial data sampling might considerably affect the separability of primaries and multiples Kabir and Marfurt (1999). This data sampling issue is called data aliasing. It causes many artifacts that dramatically affect focusing in the radon domain (Figure 2).

A second source of problem can stem from aliasing of the radon transform operator. The operator aliasing creates noise in the radon domain by the summation action of the PRT operator on the CMP gather Abma et al. (1999); Lumley et al. (1994).

In this paper, I present solutions to correct for both operator and data aliasing. We can antialias the operator by imposing dip limitations on the summation path of the PRT. These dip limits translate easily into frequency limits. I also show that when using inverse theory, data-aliasing artifacts can be attenuated by imposing some constraints on the sparseness of the radon domain.

 

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Figure 1 Left: A parabolic radon model (s.km^-2). Right: Data derived from the left panel using the PRT (offset in km).

 

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Figure 2 Left: The radon domain obtained by applying the adjoint PRT ${\bf L'}$ to the input data shown in Figure 1. The straight lines are caused by the limited aperture of the recording geometry. The other noisy events correspond to data-aliasing noise. Right: Reconstructed data applying the forward operator L to the left panel.