Introduction

As described by Lomask and Guitton (2006), flattening algorithms often need to be constrained. Although a key selling point of flattening without picking Lomask et al. (2006) is that it requires no picking, it is useful to have the ability to add some geological constraints to restrict the flattening result in areas of poor data quality while allowing it to efficiently tackle other areas where the dips are accurate. Furthermore, constraints can also be used to force the flattening result to conform to data points besides dip alone such as correlations across faults.

In this paper, I present a flattening method with hard constraints that exploits Discrete Cosine Transforms (DCTs) to increase computational efficiency. It is a modification of the constrained Gauss-Newton flattening method Lomask and Guitton (2006) using an improved preconditioner. The preconditioner, an unconstrained flattening method that uses DCTs, was presented by Lomask and Fomel (2006). Instead of approximating the inverse of the Laplacian with the helical transform, the DCT is exploited to more accurately invert the Laplacian. The resulting algorithm converges faster than previous constrained flattening methods while the memory usage is similar. Here, I first review the constrained Gauss-Newton flattening method. I then demonstrate its use on a faulted 3D field data set from the Gulf of Mexico.