Synthetic Data

First, realistic synthetic data are used to illustrate the benefits of filtered GDM to reduce noise in the migration image for imaging the salt-flank model in Figure . The white lines in Figure a depict the raypath for a 3rd-order reflection that can significantly contribute to the migration image. Imaging of reflection points at $A$ and $C$ demands the filtering of upgoing and downgoing components for the Kirchhoff-like migration kernel in equation . In contrast, the migration image at point $B$ requires the filtering of leftgoing and rightgoing events for the last GDM kernel in equation .

Figure: RTM results associated with the salt model. a) Salt velocity model overlaid by the raypath of a single source-receiver pair. b), c) and d) are RTM images of this model. Shallow part of the image is overwhelmed by strong artifacts. A high-pass filter is effective in suppressing these artifacts but large residuals still remain.

Figure: Up-down separation of Green's function. a) shows the model. b) is the Green's function recorded along the vertical receiver line. It is then filtered into c) upgoing and d) downgoing components.

Figure: Left-right separation of Green's function. a) shows the model. b) is the Green's function recorded along the horizontal receiver line. It is then filtered into c) leftgoing and d) rightgoing components.

To filter such events, the Green's function for the migration kernel are computed by a finite-difference solution to the wave equation, and Figures  and show the shot gathers recorded along vertical (Figure b) and horizontal (Figure b) receiver lines; here the shot is at the surface. These shot gathers are easily dip filtered into their corresponding one-way components, either upgoing (Figure c) and downgoing (Figure d) waves for the vertical line, or leftgoing (Figure c) and rightgoing (Figure d) waves for the horizontal line. The Kirchhoff-like kernels in either equation  or equation  can then be used to get the, respectively, artifact-free RTM images of a single recorded shot gather in Figures a and Figures b. The artifacts are successfully eliminated in Figure c and the image quality is noticeably improved compared to Figure d. Figure  shows a stacked image of 126 such individual single-shot images.

Figure: Applying the Kirchhoff-like migration kernels in equations  and  to recorded data gives, respectively, a) and b). Stacking a) and b) gives c). d) is the standard RTM image.

Figure: Applying the Kirchhoff-like migration kernels in equations  and  to all 126 shot gathers gives, respectively, a) and b). c) is the stacking image of a) and b). The high-pass filtered RTM image is shown in d).