Analytical path-summation imaging of seismic diffractions

2D field data example

We tested the proposed workflow on a vintage Gulf of Mexico dataset (Fomel et al., 2007; Claerbout, 2005). A stacked section of diffractions separated using plane-wave destruction filter is shown in Figure 4a. The path-summation migration image, which was calculated directly according to equation (6), is shown in Figure 4e. The integration limits corresponded to $1.4\ [km/s]$ - $2.6\ [km/s]$ . Diffractions collapse to form an image of faults.

Path-summation migration image with Gaussian weighting evaluated with $1.4\ [km/s]$ - $2.6\ [km/s]$ integration limits, $v_{bias}=2.0\ [km/s]$ and $\beta =10$ is shown in Figure 4f. The image in comparison with the regular path-summation migration image appears to have higher resolution. Tail artifacts appear to be suppressed as well. However, some velocity bias is noticeable in the upper part of the section.

The migration velocity field acquired by division of double path-summation integral by path-summation integral and the corresponding image of diffractions are shown in Figures 4c and 4b. Velocity values in the regions without diffraction energy are associated with noise. Strong velocity anomalies at the boundaries of the section are associated with edge effects. A possible extension of the workflow would include velocity model weighting by diffraction probability at selected locations.

The image derived from double-path-summation velocity has the highest resolution. A full image with both reflections and diffractions imaged using the same velocity field is shown in Figure 4d. Discontinuities in seismic reflections align with faults imaged by path-summation diffraction imaging.

a-bei-pwd,a-dpi-vel,a-dpi-slice,a-refl-image,a-pi-nw-nwi,a-pi-gaussian-nwi
Figure 4. Gulf of Mexico dataset: (a) separated diffractions; (b) velocity model from division of double path-summation integral by path-summation integral; (c) diffraction's image generated with the velocity field (b); (d) reflections and diffractions migrated with the same velocity field (b); (e) path-summation migration image; (f) path-summation migration image with Gaussian weighting.

Analytical path-summation imaging of seismic diffractions