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Introduction

In this paper we establish some rules of thumb as to when anti-aliasing is required in Kirchhoff migration. The same criteria are applicable to other processes such as DMO, velocity analysis, and wave-equation datuming.

There are many methods of handling operator aliasing. Gray (1992) presented a method which involves low-pass filtering data traces with a variety of pass bands and then selecting input data from these sets of traces so that operator aliasing does not occur. Spatial trace interpolation is another method of dealing with the operator aliasing problem (Yilmaz, 1987). A draw back of the latter two methods is increased data volumes. Methods which limit the dip or aperture of the operator reduce aliasing without increasing the data volume, but at the expense of losing high-angle and wide-aperture information. An attractive and computationally efficient method of handling operator aliasing has been implemented by Claerbout (1992). His dip-dependant triangular weighting method does not require multiple copies of the data to be kept in memory since the weights are generated and applied quickly on-the-fly.

Claerbout's triangular weighting method has been demonstrated to be efficient for 2-D (Bevc and Claerbout, 1993,1992) and 3-D (Lumley, 1993; Lumley et al., 1994) Kirchhoff time and depth migration. It has also been successfully adapted to DMO and wave-equation datuming operators (Blondel, 1993; Bevc, 1992). Even though the triangular weighting method is very efficient, it still involves an extra computational cost. When the anti-aliased algorithm is implemented on the Connection Machine in FORTRAN 90, calls to an indirect addressing subroutine are required to extract data points from individual traces for summing into output locations. These calls turn out to be a bottleneck. In order to perform an anti-aliased migration with linear interpolation, six calls to the indirect addressing subroutine are required for each input trace location. For a 3-D migration, the indirect addressing is substantial.

Because this anti-aliasing is currently expensive on the CM5, we are motivated to determine when we can get away with not using it. While doing away with anti-aliasing is generally not a good idea, there are situations in which we may be able to live without it. For example, if we are running trial migrations to determine velocity models we may concentrate our efforts on portions of the data where operator aliasing is not a factor.

After developing criteria which link frequency and dip content of seismic data, we migrate a 2-D salt dome data set with and without anti-aliasing. The examples illustrate the effects of operator aliasing, how it can be ameliorated by aperture limitation and triangle weighted migration, and when anti-aliasing is unnecessary.


next up previous [pdf]

Next: OPERATOR ALIASING Up: Bevc and Lumley: Anti-aliasing? Previous: Bevc and Lumley: Anti-aliasing?

2015-03-26