Kirchhoff PreSDM Interactive Dip-gather Stacking and Dip Illumination Panel Generation Fuhao Qin, Bin Wang, Po Zhang, Audebert, F., CGG Americas, Inc., Houston, U. S. A. Summary

Kirchhoff Pre-Stack Depth Migration (PreSDM) is used to output image gathers in structure dip angle instead of the traditional offset attributes gathers in sub-salt areas that are hard to image. These new image gathers can help processors and/or interpreters to better define geological structures through interactively stacking the image gathers in dip within various dip angle ranges based on different interpretations. Illumination panels can also be obtained for structures with different dips. They can be used to determine if observed amplitude anomalies are caused by geology or seismic acquisition and imaging processes. We demonstrate using the Sigsbee 2A synthetic dataset that partial dip-angle gather stacking and illumination compensation can be used to effectively suppress sub-salt migration artifacts.

Introduction

All migration methods, especially the single arrival Kirchhoff PreSDM, produce images that suffer from serious migration artifacts especially at near- and sub-salt areas. These artifacts are caused by: the inability of single-arrival Kirchhoff migration to process all arrivals (other arrivals are noise), the insufficiency of the asymptotic approximations made in the application of the Kirchhoff integral to in simulating wave propagation in complex media by the Kirchhoff integral, the inability of most migration method to overcome the irregularities of illumination related to an irregular acquisition or a complex propagation. These migration artifacts often appear as aliased migration smiles cutting through or extending beyond the true seismic events. Sometimes, the true seismic events are completely buried by the artifacts and interpretations for model building and exploration are made very difficult.

To suppress the migration artifacts, Audebert et al (2000) and Audebert et al (2004) proposed to output common reflection gathers (CIG) according to a variety of angle attributes. Their main focus was to apply a hit-count technique to suppress migration artifacts and balance the migration amplitude. Chen (2004) proposed to suppress migration aliasing artifacts by searching for specular rays that contribute the most to the diffraction stack and to migrate only rays within a vicinity of those specula rays.

In this abstract, we propose a simple dip-angle CIG approach. We arrange the output by the dip angle instead of offset. Dip angle, here, means the migration dip. It describes the direction of the migration slowness vector at the depth point, pointing along the normal to the migration isochrone. The total slowness vector is the sum of the

source and the receiver related slowness vectors, fulfilling the Snell’s law at the image point. The CIGs in dip angle, which we call dip gathers, can be supplied to the interpreters alongside a stacked image. The users can then do their interpretations based on the stacked image. In complex areas with low S/N ratio, such as near or sub-salt areas with conflicting dips or without apparent dips at all, several educated guesses can be made to re-stack the image within several limited dip angle ranges. The better images thus achieved might lead to a geologically reasonable interpretation.

Wu, et al (2002) used beamlet propagator to generate direction illumination maps. In our approach, the number of traces that contribute to the image point for a certain dip direction are accumulated to yield an illumination map for this dip. This map is the dip illumination panel. It can be used to balance the final PreSDM image and can help in identifying the cause of amplitude anomalies visible on the seismic image.

Dip gathers and interactive stacking

The dip angle here means the angle between the vertical axis and the normal direction of the reflector that can reflect the incoming ray from the shot to the receiver (Figure 1). In Kirchhoff depth migration, it can be obtained by calculating the negative gradient direction of the sum of traveltimes from shot to the image point and from receiver to the image point.

Migration schemes with dip constraints have been used for a long time in Kirchhoff PreSDM (CGG internal reports). They need a predefined dip model and use the dip model input to specify the migration aperture in terms of a relative dip range around the predefined model. The resulting image enhances the coherent events that agree with the dip model while all other events in the input seismic are attenuated or suppressed.

αn

S R

Figure 1. Geometry of the reflector and rays from the shot location and the receiver location to the reflector. The dip angle, here, means the angle between the normal of the reflector n and the vertical axis for 2D. And it will have an azimuth component in 3D case.

Kirchhoff PreSDM Interactive Dip Gather Stacking and Dip Illumination generation

A problem of the above approach is that the dip model is hard to specify, especially in areas where it is most needed. One user’s dip model interpretation may be very much different from the others. This is very common in near- and sub-salt areas. A new migration has to be run every time the dip model is changed. Another problem is that there are often conflicting dips at faults and/or diffractor locations. Out of all these possibly valid dips, only one can be kept by the Kirchhoff PreSDM method with dip constraint.

The dip gather output (CIG in dip angle) solves the above problems. In producing these gathers, we cause no loss of information, we perform only a different sorting of the output: the offset dimension is (optionally) stacked but the

migration dips are separated. Figure 2 shows a dip gather obtained from migrating the Sigsbee 2A synthetic data at CDP 631. It can be observed that the appearance of a dip gather is different from an offset gather. Most events are concentrated in a relatively narrow angle range since most events have well-defined dips. However point diffractors tend to leave an imprint spread over the entire dip range (at depth 17000 ft and 25000 ft) permitted by the acquisition and/or migration apertures. The locations with conflicting dips, such as the fault at the depth of 18000 ft, have show more than one peak of energy along the dip angle axis.

Once we have all the dip gathers, we can chose reasonable dip ranges to partially stack the dip gathers to get optimized stack images. A dip range is defined by the extreme dip angles containing the specular dip plus some aperture around it. We can do as many partial stacks as we want and keep the one that makes the best geological sense and gives the best image. A fixed dip range (constant or even varying with depth only) is not going to fit the whole mode, since the actual speclular dip may change in all spatial directions. A reasonable dip model can be used to control the stack. For complicated low S/N region, stacks should be done on the fly by the interpreters. Different interpretations should be tested and the best will be identified.

Figure 3 is an image of the Sigsbee 2A synthetic dataset, migrated with the exact velocity model, and obtained by partial stacking of dip gathers. To show the robustness’ of this method, we did not use point-to-point varying dip ranges. Instead, the model was divided into 6 big blocks each with a different dip range. Comparing it with Figure 4 which is the conventional Kirchhoff PreSDM result, we can see that the partial stacking of the dip gathers (Figure 3) produced an image with very much improved quality, where almost all the faults are interpretable. This is by far the best single arrival Kirchhoff PreSDM sub-salt image of the Sigsbee 2A model we have seen from the literature. We also notice that the images of some of the diffraction points and some of the fault surfaces in the sub-salt area are less well defined. This is expected since we have to stack the entire dip angle range to really collapse the diffraction energy.

We can also form CIG in both dip angle and offset dimension, if we plan to use the offset information, at the cost of increased output volume of course. However, it is more advantageous not to include the offset dimension in the gather. First, the computation is faster, due to the computer memory saving. Second, it is easier to handle a smaller number of volumes for those who need to stack the gathers interactively.

Illumination panels

When we migrate the seismic into dip gathers, we can keep track of the number of traces (with migration weighting) that contribute to the image for every dip class at all the image points. This will form an illumination panel for each dip class.

Figure 5 is an illumination panel for the dip angle class around –25 degree and Figure 6 is the migration image for the same dip angle class. It can be seen that the illumination intensity for the sub-salt structure with the –25 degree dip angle is strongly affected by the salt. This suggests that even for a reflector with constant dip and constant reflection strength the amplitude of the image will not be constant in the sub-salt areas. Reservoir properties

-85 +85 0

Figure 2. A dip gather from the Sigsbee 2A model at CDP 631. The dip angle range is from –85 degree (the left most trace) to +85 degree (the right most trace). The large dip spread at depth 17000 ft and 25000 ft indicates diffraction points and the break of amplitude along dip axis at depth 18000 ft is caused by conflicting dips between the bedding and a fault.

Kirchhoff PreSDM Interactive Dip Gather Stacking and Dip Illumination generation

predicted by the amplitude information will have to be corrected or weighted by the illumination factor.

Illumination for the final image can be generated by selectively summing the relevant angle illumination panels the same way as the final migration image is generated. It can be used to balance the migration image (Figure 3 is the final illumination balanced image). However, to accurately determine the illumination for a particular seismic horizon, information should be extracted from the illumination panels based on the exact normal direction of that horizon.

Discussions

Although conventional Kirchhoff PreSDM only handles single arrival from shot and receiver on the surface, it does contain useful information upon sub-salt structures even though they might be difficult to image. The migration noise may have different origins such as Kirchhoff method’s inability to collapse diffraction energy in complex media (thus the migration smiles), aliasing artifacts due to irregularities of the traveltime maps or more general illumination problems caused by acquisition irregularities and wave propagation in a complex medium. The problem is how to extract the useful information from the overlaying noise. Dip angle is one of the efficient and reasonable attributes to be included in the imaging process.

Interactive PreSDM process is still far out of reach, but interactively partial stacking of CIG can be done efficiently. In our proposed scheme, the CIGs are produced with the dip angle as an attribute, and the interactive stacking is based on a selection of the local structural dip. The interactive partial stacking and the improved images it produces may help processing personnel to better delineate the base-salt where clear picking from conventional Kirchhoff PDM migration images are often difficult. It can also help interpreters to obtain more reliable sub-salt horizon mappings.

Computer programs may be developed to automatically select the optimal dip for partial stacking using the spatial continuity of the geological structure. However, attention should be paid to point diffractors and faults where dips are discontinuous.

The illumination map for the final image can be generated by selectively summing the relevant angle illumination panels in the same way as the final migration. It can be used to balance the migrated image. However, to accurately determine the illumination for a particular seismic horizon, information should be extracted from the illumination panels based on the exact normal direction of that horizon.

Acknowledgements

We would like to thank the SMAART JV consortium for the Sigsbee2A data used in this study. We would also like to thank CGG Americas for allowing us to submit this abstract.

References

Audebert, F., Froidevaux, P., Huard, I., Nicoletis, L., and Svay-Lucas, J., 2000, True amplitude migration in the angle domain by regularization of illumination: 70th SEG Expanded Abstracts: 515-520.

Audebert, F., Nicoletis, L., Froidevaux, P. and Rakotoarisoa, H., 2003, True amplitude migration in the angle domain by regularization of illumination: 73rd SEG Expanded Abstracts: 515-520.

Chen, J., 2004, Specular ray parameter extraction and stationary-phase migration, Geophysics, Vol. 69, No. 1, 249-256.

Wu, R. and Chen, L., 2002, Mapping directional illumination and acquisition-aperture efficacy by beamlet propagators: 72nd SEG Expanded Abstracts.

Figure 3. Kirchhoff PreSDM image of the Sigsbee 2A model using partial dip angle stacking is balanced by its

illumination distribution..

Kirchhoff PreSDM Interactive Dip Gather Stacking and Dip Illumination generation

Figure 6. Migration image for dip angle of –25 degree.

Figure 5. Illumination panel for the dip angle of –25 degree. The red color indicates more reflection ray hits. And the blue color means less.

Figure 4. Conventional Kirchhoff PreSDM image of the Sigsbee 2A synthetic model data.