Two univariate problems

Communication channels tend to mix information in the way equations (1) and (2) do. This is ``crosstalk.'' Everything on the right sides of equations (1) and (2) is unknown. This problem can be formulated in an elaborate way with estimation theory. Here we will postpone the general theory and leap to guess that the pressure-wave field $\bold p$will be some linear combination of $\bold v$ and $\bold h$,and the shear-wave component $\bold s$will be something similar:

$$\begin{eqnarray} \bold p &=& \bold v \ -\ \alpha \bold h \ \bold s &=& \bold h \ -\ \alpha' \bold v\end{eqnarray}$$ (3) (4)

We will understand the crosstalk question to ask us to find the constant value of $\alpha$ and of $\alpha'$.Although I will describe only the mathematics of finding $\alpha$,each figure will show you the results of both estimations, by including one part for $\alpha$ and one part for $\alpha'$.The results for $\alpha$ and $\alpha'$ differ, as you will see, because of differences in $\bold p$ and $\bold s$.