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Space-shift imaging condition

A generalized prestack imaging condition (Sava and Fomel, 2005) estimates image reflectivity using cross-correlation in space and time, followed by image extraction at zero time:
$\displaystyle U \left ({ \bf m},{ \bf h}, t \right )$ $\textstyle =$ $\displaystyle U_r \left ({ \bf m}+{ \bf h}, t \right )\ast
U_s \left ({ \bf m}-{ \bf h}, t \right )\;,$ (3)
$\displaystyle R \left ({ \bf m},{ \bf h}\right )$ $\textstyle =$ $\displaystyle U \left ({ \bf m},{ \bf h},t=0 \right )\;.$ (4)

Here, ${ \bf h}= \left[ h_x,h_y,h_z \right]$ is a vector describing the space-shift between the source and receiver wavefields prior to imaging. Special cases of this imaging condition are horizontal space-shift (Rickett and Sava, 2002) and vertical space-shift (Biondi and Symes, 2004).

For computational reasons, this imaging condition is usually implemented in the Fourier domain using the expression

\begin{displaymath}
R \left ({ \bf m},{ \bf h}\right )= \sum_\omega
U_r \left...
...ga \right )
U_s^* \left ({ \bf m}-{ \bf h},\omega \right )\;.
\end{displaymath} (5)

The $^*$ sign represents a complex conjugate applied on the receiver wavefield $U_s$ in the Fourier domain.


next up previous [pdf]

Next: Time-shift imaging condition Up: Imaging condition in wave-equation Previous: Imaging condition in wave-equation

2013-08-29