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2-D crosscorrelation

The zero lag of the 2-D crosscorrelation of the source and the receiver wavefields in (xs,t) is the same as the zero lag of the 1-D crosscorrelation in the time domain with a stack across the shot position axis. A simple example with matrices illustrates the concept. If we take the 2-D crosscorrelation of 2 matrices,
\begin{displaymath}
\left[\begin{array}
{cc}
 1 & 2 \  2 & 3 \  \end{array}\ri...
 ... 14 & 4 \  11 & 25 & 12 \  2 & 11 & 5 \  \end{array}\right],\end{displaymath} (5)
the zero lag coefficient is 25. If instead we crosscorrelate the columns,
\begin{eqnarray}
\left[\begin{array}
{c}
 1 \  2 \  \end{array}\right]
\star 
...
 ...=
 \left[\begin{array}
{c}
 3 \  17 \  10 \  \end{array}\right]\end{eqnarray} (6)
(7)
take the zero lag, and stack over the rows, the result is also 25. This illustrates the relationship that exists between the 1-D and the 2D crosscorrelation.


next up previous print clean
Next: 2-D deconvolution Up: 2-D imaging conditions in (xs,t) Previous: 2-D imaging conditions in (xs,t)
Stanford Exploration Project
7/8/2003