Introduction

In the Fourier-domain flattening methods presented previously Lomask et al. (2005); Lomask and Claerbout (2002); Lomask (2003) the data has to be mirrored in order to eliminate Fourier artifacts. This means that the data is replicated and reversed so that the boundaries are periodic. This requires four times the memory in 2D and eight times in 3D. In a world where post-stack data cubes can easily be tens of gigabytes in size, efficient memory usage is extremely important.

Here we apply a discrete cosine transform (DCT) approach developed for 2D phase unwrapping Ghiglia and Pritt (1998); Ghiglia and Romero (1994) to our flattening method. As a result, we the reduce memory requirements of the transforms in 2D by a factor of four and in 3D by a factor of eight. We reap an additional factor of two savings from using real instead of complex numbers. Furthermore, the reduction in size significantly reduces computation time as well. We demonstrate its use on a simple 3D synthetic model.