Model-building with image segmentation and fast image updates

Generalized wavefields and phase encoding

While restricting the domain and datuming the wavefields as described above significantly lessened the computational expense of updating the image, the process still occurs over a matter of minutes, rather than the seconds required to approach the level of interactivity we seek. One possibility to improve the performance of shot-profile migration is to use phase encoding (Romero et al., 2000), in which data from $N$ shots are combined into a generalized source gather:

$$\hat P(\omega,x;j) = \sum_{i=1}^N \epsilon_{i,j}(\omega)P(\omega,x;\mathbf{s}_i).$$ (5)

Here, the $\epsilon$ term is a complex weight value assigned to each shot.

A simple experiment combines all shots into a single generalized source gather, and uses a single generalized plane-wave source function for migration. Figure 6 is the perfect-velocity image resulting from this procedure. While information from unwanted crosstalk terms have significantly degraded the image, the salt body and its boundaries are still visible. When the two possible salt-flood velocity models in Figures 4(a) and 4(b) are used, we obtain the zoomed-in images in Figures 7(a) and 7(b), respectively. While the differences between these two images is not as apparent as for Figures 5(a) and 5(b), the salt canyon walls appear more continuous for the first model, especially near the location indicated by the arrow. These migrations were completed in less than five seconds; although this is only a 2D example, this is approaching a level at which interactive imaging becomes feasible.

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Figure 6. A perfect-velocity migration in which all shots have been combined into a single generalized source gather, and a single plane-wave is used as the generalized source function. Crosstalk artifacts have significantly degraded the image, but the salt body is still clearly visible.

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Figure 7. Generalized wavefield migrations corresponding to the velocity models in Figures 5(a) and 5(b). While crosstalk artifacts obscure the differences between the two images to a much greater extent than in Figures 5(a) and 5(b), the salt canyon wall is still noticeably more continuous near the indicated location in (a).

Further improvents are necessary to obtain cleaner images than in Figures 6, 7(a) and 7(b). One option is to define the weighting coefficients from equation 5 as having only imaginary (phase) components:

$$\epsilon_{i,j}(\omega)=\frac{e^{i\phi_{i,j}}(\omega)}{\sqrt{M}},$$ (6)

where $M$ is the number of generalized sources. By making $\phi$ a random phase function, it is possible to attenuate the crosstalk terms that arise from combining information from different shots (Morton and Ober, 1998). The implementation of a scheme combining image segmentation, re-datumed wavefields and phase-encoding could allow interpreters to interactively view high-quality images of several salt-interpretation scenarios.

Model-building with image segmentation and fast image updates