Introduction

When flattening seismic data, it is important that the relative position of adjacent data points be preserved. In other words, it is important that the process be continuous and monotonic. If the flattening process is not monotonic, then points can be swapped creating artifacts in the data. This is important if the flattened data is to be unflattened or if multiple iterations are to be performed as these artifacts can worsen with each iteration. Simply smoothing the dip in depth prior to integrating should achieve a monotonic result, however, it is more desirable to penalize roughness in depth in a least squares sense while the dip is being integrated. In short, we want to apply an adjustable model styling goal to insure smoothness of the dip integration result.

In Lomask and Claerbout (2002); Lomask (2003) dips are integrated (summed) by a Fourier method with regularization. However, this regularization was not adjustable. Although it did insure that the integrated dip result was smooth, in many cases the depth regularization goal over-whelmed the dip integration goal, causing the result to be too smooth.

In this paper, we present a modification to the analytical flattening method that uses an adjustable weighting parameter for regularization in depth. This method is applied to several 2D field gathers provided by WesternGeco and compared to 2D field gathers that are flattened without regularization. A 2D section created by applying NMO prior to stacking is compared to the same 2D section created by flattening prior to stacking. We show that applying the analytical flattening method with regularization can preserve the integrity of the data even after multiple passes of flattening.