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1-D Crosscorrelation

A practical way to compute the reflectivity strength in equation (1) is discussed in Claerbout (1971). He computes the reflector strength and position as the zero lag of the crosscorrelation of the source and the receiver wavefields in the time dimension (Figure [*]).

 
match1
Figure 2
Source and receiver wavefields to be matched in the time dimension.
match1
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The previous concept is expressed in the formula :  
 \begin{displaymath}
{\bf r}(x,z)= \sum_{x_s}\sum_{\omega}{\bf U}(x,z,\omega,x_s) {\bf D}^{*}(x,z,\omega,x_s),\end{displaymath} (2)
where ${\bf r}(x,z)$ is the zero lag coefficient of the crosscorrelation, which is computed by summation over the frequencies and ${\bf U}(x,z,\omega)$ and ${\bf D}(x,z,\omega)$ are the one-dimensional Fourier Transforms of the receiver and the source wavefields, respectively. The contribution of each shot (located at xs) is added to form the final image.


next up previous print clean
Next: 1-D Deconvolution Up: 1-D imaging conditions Previous: Claerbout's imaging principle
Stanford Exploration Project
7/8/2003