intro.tex

\section{What the equation doesn't tell us}

Equation \ref{eq:traveltime} relates travel-times: the one we can measure ($t$)
and the one we want to know ($t_0$).
But the data in our CMP gather are actually a matrix of \textit{amplitudes}
measured as a function of time ($t$) and offset.
Our NMO corrected gather will also be a matrix of amplitudes as a function of
time ($t_0$) and offset.
So what we really have to do transform one matrix of amplitudes into the other.
\textit{But the equation has no amplitudes}!

This is a major divide between the formula we've all seen before and what
actually goes on in the software that implements it.
You have probably never thought about it -- I certainly hadn't --
so let's bridge this divide.
Next, I'll explain an algorithm that maps the amplitudes in the CMP to
amplitudes in an NMO corrected gather.