THE MEANING OF THE DSR EQUATION

The double-square-root equation contains most nonstatistical aspects of seismic data processing for petroleum prospecting. This equation, which was derived in the previous section, is not easy to understand because it is an operator in a four-dimensional space, namely, (z,s,g,t). We will approach it through various applications, each of which is like a picture in a space of lower dimension. In this section lateral velocity variation will be neglected (things are bad enough already!). Begin with

$$\begin{eqnarray} {dU \over dz }\ \ &=&\ \ { -\,i \omega \over v }\ \left( \ \sqr... ...qrt {1\ -\ (Y+H)^2 } \ \ +\ \ \sqrt { 1\ -\ (Y-H)^2 }\ \right) \ U\end{eqnarray}$$ (54) (55)