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# Examples

Our first example corresponds to a synthetic model with flat reflectors and v(z) velocity. The left panel in Figure  is a representative CMP for this model. Most of the energy in the CMP is multiples. The right panel in Figure  depicts a corresponding CIG. Again, most of the energy in the gather is multiples, which have non-flat moveout that distinguishes them from the flat primaries.

Figure  shows from left to right: (D) the data = primaries + multiples, in the image space; (P) the data transformed to the Radon domain, where the flat primaries are represented in the vicinity of q=0, in contrast to the multiples at non-zero q; (N) the multiples isolated in the Radon domain and transformed back to the image domain; (S) the primaries left after subtraction of the multiples (N) from the data (D).

Figure  shows a comparison between RT using the parabolic equation (left), and the more accurate tangent equation (right). Not surprisingly, we observe better focusing using the tangent equation, which makes it easier to isolate the multiples.

Figure  corresponds to a real dataset filled with multiples over a region with mildly varying velocity. Similarly to the case of the preceding synthetic example, we show: (D) the data = primaries + multiples, in the image space; (P) the data transformed to the PRT domain; (N) the multiples isolated from the PRT panel and transformed back to the image domain; (S) the primaries left after subtraction of the multiples (N) from the data (D).

mDSN
Figure 4
Field data example. Signal/Noise separation in the image space: (D) signal + multiples (data); (P) data the Parabolic Radon domain; (N) multiples (noise); (S) primaries (signal);

Next, we present the case of a synthetic example over a salt dome model. Figure  follows the pattern used in the preceding two examples: from left to right, the data (D), the PRT domain (P), the noise (multiples) (N), and the signal (primaries) (S). Figure  shows the corresponding stacks before (D) and after (S) multiple suppression. Most of the multiple energy is removed from the image (around a depth of 16 kft).

bDSN
Figure 5
BP synthetic example. Signal/Noise separation in the image space: (D) signal + multiples (data); (P) data the Parabolic Radon domain; (N) multiples (noise); (S) primaries (signal).

 bcomp Figure 6 BP synthetic example. Images obtained by angle-domain stacks: (D) signal + multiples (data); (S) primaries (signal). Multiples at a depth of 16 kft are removed.

We also apply our technique to a Gulf of Mexico dataset from a salt dome environment. This is a more complicated example, since it illustrates many of the difficulties encountered by multiple suppression in complicated areas, around salt bodies and in the presence of notable 3-D effects. Following the pattern used in the preceding example, Figures  and show our multiple analysis at two different locations in the data. The first figure, corresponds to an area more or less away from the salt body, while the second one corresponds to a region right under the salt. From left to right, we present the data (D), the Radon domain (P), the noise (multiples) (N), and the signal (primaries) (S).

In both cases, primaries and multiples separate remarkably well in the Radon domain. We obtain the noise model after mute in the Radon domain and inverse RT, and the signal model by subtracting the noise from the data.

For comparison, in both Figures  and we include one more panel (C) which represents the same image gather obtained by migration of the signal obtained by multiple suppression in the data space using a high resolution HRT with Cauchy regularization. The image space multiple suppression creates cleaner CIGs, compared with the data space method, although some of the inherent noise associated with RT can be still observed in the image.

Figure  shows the stacks of the images obtained without multiple suppression (D), with multiple suppression in the image space (S), and with multiple suppression in the data space (C). Our image space method removes more of the multiple energy than the data space method.

gDSN1
Figure 7
Gulf of Mexico example. S/N separation in the image space: (D) signal + multiples (data); (P) data the Parabolic Radon domain; (N) multiples (noise); (S) primaries (signal) separated in the image space; (C) primaries (signal) separated in the data space.

gDSN2
Figure 8
Gulf of Mexico example. S/N separation in the image space: (D) signal + multiples (data); (P) data the Parabolic Radon domain; (N) multiples (noise); (S) primaries (signal) separated in the image space; (C) primaries (signal) separated in the data space.

gsmall
Figure 9
Gulf of Mexico example. Images obtained by angle-domain stacks: (D) signal + multiples (data); (S) primaries (signal) after separation in the image space; (C) primaries (signal) after separation in the data space.

Next: Discussion Up: Sava and Guitton: Multiple Previous: Multiple suppression
Stanford Exploration Project
7/8/2003