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![]() | Theory of 3-D angle gathers in wave-equation seismic imaging | ![]() |
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Common-azimuth migration (Biondi and Palacharla, 1996) is a downward continuation imaging method tailored for narrow-azimuth streamer surveys that can be transformed to a single common azimuth with the help of azimuth moveout (Biondi et al., 1998) Employing the common-azimuth approximation, one assumes the reflection plane stays confined in the acquisition azimuth. Although this assumption is strictly valid only in the case of constant velocity (Vaillant and Biondi, 2000), the modest azimuth variation in realistic situations justifies the use of the method (Biondi, 2003).
To restrict equations of the previous section to the common-azimuth
approximation, it is sufficient to set the cross-line offset
to zero
assuming the
coordinate is oriented along the acquisition azimuth. In
particular, from equations (8-9), we obtain
Under the common-azimuth approximation, the angle-dependent relationship (13) takes the form
The post-imaging equation (16) transforms to the equation
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![]() | Theory of 3-D angle gathers in wave-equation seismic imaging | ![]() |
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