In the top of Figure is an image of the lower portion of a salt boundary from the Gulf of Mexico. Overlain on this image is a single horizon that results from the unconstrained flattening method. The horizon fails to track the boundary accurately. In the lower image, two picked horizons have been added as hard constraints. Notice that the center horizon now does an overall much better job of tracking the boundary than its unconstrained counterpart. Unfortunately, the price paid is that by applying regularization in time, the constrained horizon does not track the character of data locally as well.
In Figure is a 3D North Sea data set. The top shows several horizons that result from unconstrained flattening. Although some of the horizons are well tracked, several are not. In the lower figure, we picked the brightest horizon and passed it into the flattening method as a hard constraint. Notice that the reflectors above it now tend to more accurately track their respective events.
Also in Figure , notice how the reflectors at the top of the cube are tracked more accurately without constraints. This is as expected because the regularization is causing the reflectors to conform to one another. To mitigate this, we could have passed an upper picked horizon from the unconstrained result as an additional hard constraint to the lower result.