In the previous chapter, some of the theory behind solving a system of regressions by characterizing both the signal and the noise was presented. It was shown there that the weighting of the various parts of the system and the initialization of the system are important considerations.
In this chapter I apply the ideas of the previous chapter to remove two different types of noise. The first applications involve removing noise that is limited to either a single trace or to a small number of nearby traces within a given shot. The second example is the removal of coherent noise, in this case, ground roll.
The signal and noise separation techniques in this chapter are developed in a sequence of four steps. The first step is characterizing the signal and noise by amplitude only, the second step adds characterization of the signal and noise by one-dimensional filters, the third step makes the signal filter a two-dimensional filter, and the fourth step characterizes both the signal and the noise by two-dimensional filters as well as by amplitude. Examples of the results of the various techniques are demonstrated on synthetics and real data.