Stacking angle-domain common-image gathers for normalization of illumination

ANGLE-DOMAIN COMMON-IMAGE GATHERS

ADCIGs can be produced both by Kirchhoff methods (Hoop and Ursin, 2003; Xu et al., 2001) and wave-equation methods (Xie and Wu, 2002; Mosher and Foster, 2000; Sava and Fomel, 2003; Prucha et al., 1999; Biondi and Symes, 2004). In wave-equation migration methods, angle gathers can be produced either in the data space during imaging or in the image space after imaging (Fomel, 2004). These methods can be also applied in source-receiver migration (Sava and Fomel, 2003), shot-profile migration Rickett and Sava (2002), and reverse-time migration (Zhang et al., 2007; Biondi and Shan, 2002).

To extract ADCIGs, in wave equation migration we first compute subsurface offset-domain common-image gathers (ODCIGs) using crosscorrelation imaging condition in space and time, followed by extraction at zero time Sava and Fomel (2006):

$$I(\mathbf{m} ,\mathbf{h}) = \sum_\omega U_s(\mathbf{m} - ... ...f{h} ,\omega) U_r^\ast (\mathbf{m} + \mathbf{h} , \omega) \;.$$ (1)

Here, $I(\mathbf{m} , \mathbf{h})$ is the subsurface-offset dependent image, $\mathbf{m} = \left[m_x,m_y,m_z\right]$ is a vector of locations of image points, $\mathbf{h} = \left[h_x,h_y,h_z\right]$ is a vector of local source-receiver separation in the image space, and $\ast$ means the conjugate.

In two dimensions, angle-domain common-image gathers $I(\mathbf{m} ,\theta)$ can be obtained by a simple slant-stack operation on ODCIGs $I(\mathbf{m} , \mathbf{h})$ after migration (Sava and Fomel, 2003; Weglein and Stolt, 1999; Stolt and Weglein, 1985). For three dimensions, we can extract ADCIGs after applying imaging condition by transforming local offset gathers in the depth domain (Sava and Fomel, 2005; Fomel, 2004), in which local structural dips need to be estimated. In examples herein, we extract ADCIGs in the image space after applying imaging conditions and test our proposed method on a 2D case.

Stacking angle-domain common-image gathers for normalization of illumination