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Claerbout's imaging principle

According to Claerbout's (1971) imaging principle, a reflector exists where the source and the receiver wavefields coincide in time and space. Claerbout expresses the imaging condition as follows:  
 \begin{displaymath}
{\bf r}(x,z)=\frac{ {\bf u}(x,z,t_{d})}{ {\bf d}(x,z,t_{d})},\end{displaymath} (1)
where x is the horizontal coordinate, z is the depth, and td is the time at which the source wavefield ${\bf d}(x,z,t_{d})$ and the receiver wavefield ${\bf u}(x,z,t_{d})$ coincide in time and space. This principle states that the reflectivity strength ${\bf r}(x,z)$ depends only on the source and the receiver wavefields at time td. The time td is not known a priori, therefore we need a practical way to locate the reflector position in the (x,z) plane and compute its strength.
next up previous print clean
Next: 1-D Crosscorrelation Up: 1-D imaging conditions Previous: 1-D imaging conditions
Stanford Exploration Project
7/8/2003