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Imaging condition in wave-equation imaging

A traditional imaging condition for shot-record migration, often referred-to as $U D^*$ imaging condition (Claerbout, 1985), consists of time cross-correlation at every image location between the source and receiver wavefields, followed by image extraction at zero time:
$\displaystyle U \left ({ \bf m}, t \right )$ $\textstyle =$ $\displaystyle U_r \left ({ \bf m}, t \right )\ast
U_s \left ({ \bf m}, t \right )\;,$ (1)
$\displaystyle R \left ({ \bf m}\right )$ $\textstyle =$ $\displaystyle U \left ({ \bf m},t=0 \right )\;,$ (2)

where the symbol $\ast$ denotes cross-correlation in time. Here, ${ \bf m}= \left[ m_x,m_y,m_z \right]$ is a vector describing the locations of image points, $U_s({ \bf m},t)$ and $U_r({ \bf m},t)$ are source and receiver wavefields respectively, and $R({ \bf m})$ denotes a migrated image. A final image is obtained by summation over shots.