The Spitz estimate

Equation (5) assumes that the signal PEF is known in advance. This argument is circular since we are estimating the signal needed to compute ${\bf S}$! Nonetheless, Spitz (1999) shows that ${\bf S}$ can be estimated directly from the data PEF ${\bf D}$and the noise PEF ${\bf N}$. Again, we assume that we are able to compute a model for the coherent noise we wish to attenuate. In equation, the signal PEF can be estimated as follows:  

$${\bf S} \approx {\bf D/N}.$$ (8)

In the next section, I show on a simple 1D example that this estimate makes the overlap of the signal and noise operators ${\bf L_s}$ and ${\bf L_n}$impossible