Directions in 3-D imaging - Strike, dip, both?

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1 Stanford Exploration Project, Report 113, July 8, 2003, pages Short Note Directions in 3-D imaging - Strike, dip, both? Marie L. Clapp 1 INTRODUCTION In an ideal world, a 3-D seismic survey would have infinite extents and dense shot and receiver grids over the entire x-y plane. This would provide the best illumination possible everywhere in the subsurface. In our world, our limited source-receiver geometries allow energy to leave the survey and the density of our shot and receiver arrays depends on the equipment available. For 3-D surveys, the geometry leads to limited azimuth ranges dependent on the direction in which the survey is shot. The illumination itself depends on the subsurface structure. For all of these reasons, shooting our surveys in different directions will result in different subsurface illumination. Some studies have been done comparing strike direction and dip direction surveys, which can be considered to be a special case of any two surveys shot in different directions over the same area. O Connell et al. (1993) found that for many CMP-based processes, strike direction datasets had advantages over dip directions. Etgen and Regone (1998) showed that there are differences in multiple attenuation and illumination between strike and dip direction surveys. In this paper, I will examine the results of common azimuth migration of 3-D datasets oriented along the dip and the strike directions of the Amoco 2.5-D Carpathian Mountains overthrusting the North Sea. I will explain how the differences in the images might be used to compensate for illumination problems and theorize that these problems may be overcome by using a regularized inversion of both datasets to produce images that combine the illumination of both. AMOCO 2.5-D DATASET Synthetic dataset The Amoco 2.5-D dataset juxtaposes the complex folding of the Carpathian mountains with the classic salt structures of the North Sea. A 2-D slice of the velocity model can be seen 1 marie@sep.stanford.edu 363

2 364 M. Clapp SEP 113 in Figure 1. This slice can be replicated along a third dimension to create the 2.5-D velocity model. Naturally, the second dimension is the dip direction and the third dimension is the strike direction. The data for this synthetic model were created by finite difference modeling. It was done as a 3-D survey shot in the dip direction. Since this modeling was done over a 2.5-D velocity structure, it is a simple matter to manipulate the data to generate a strike line survey as well, although the inline and crossline geometries will be different from the dip line survey. Figure 1: Velocity model for the Carpathians over the North Sea. marie3-vel [ER] Migration results I ran common azimuth migration for both the dip and strike direction 3-D data. Since we are dealing with a 2.5-D subsurface and we know the data was acquired in the true strike and dip directions, the common azimuth assumption is valid. The result of the dip direction common azimuth migration can be seen in the top panel of Figure 2 and the strike direction common azimuth migration is in the bottom panel. The large difference in amplitudes between the mountain side of the model and the sea side is expected because of the very different impedances that are apparent from the velocity model. For these experiments, this difference in amplitudes should not concern us greatly, as our primary consideration is the illumination, which can be examined in the areas with better impedances. The illumination problems can be seen most clearly along the flat reflector at a depth of 4 km and at the base of the salt. Comparing the dip direction and strike direction common azimuth migration results is interesting. The strike direction result has stronger artifacts in the area from 1 to 2 km depth under the overthrust, but shows better continuity in the deeper region. Along the flat reflector

3 SEP 113 Strike, dip, both? 365 at depth=4 km, the strike direction migration shows illumination problems that are different from those seen in the dip direction results. Similar behavior can be seen along the base of the salt, which is patchy in both results but is clear in different regions. The differences in illumination that are evident from these results is what drives the question: can we use these two datasets to get one model that combines the best illumination of both datasets? Figure 2: Zero offset ray parameter slices. Top: common azimuth migration of the dip direction data. Bottom: common azimuth migration of the strike direction data. marie3-mig [CR] JOINT INVERSION It is difficult to combine the information from two surveys shot in different directions to take advantage of the different illumination patterns. If we believe that our results are accurately imaged in space, it is tempting to just add them, including some equalization term to account for amplitude differences. The result of adding the common azimuth results of the dip and strike direction data is in Figure 3. Simply adding the migration results is not wise. Migration

4 366 M. Clapp SEP 113 operators essentially sum along complex hyperboloids and the migration result is the summation of all of those hyperboloids. Ideally all of the summations will cancel out artifacts. However, in complex areas, we do not have the data necessary to cancel out all of the artifacts. The differences in artifacts and frequency content in the migration results in Figure 2 have degraded the image. The illumination problems visible on the flat reflector at depth=4 km and along the salt base are still present in the added result (Figure 3). Figure 3: Result of simply adding the common azimuth results of the dip and strike direction data seen in Figure 2. marie3-added [CR] The problems that migration encounters in complex areas are well known. These problems can be solved to some degree by imaging through regularized least-squares inversion (Nemeth et al., 1999; Duquet and Marfurt, 1999; Ronen and Liner, 2000). This inversion process can be described by the fitting goals Lm d (1) ɛam. These fitting goals relate one dataset, d, to one model, m, using a linear imaging operator L. This first goal is the data fitting goal. The second goal is the model styling goal, wherein a regularization operator, A, acts on the model to help compensate for poor illumination. The regularization parameter ɛ allows us to balance the strength of the model styling goal against the data fitting goal. We can replicate these fitting goals to obtain two models from two datasets: [ ][ ] [ ] L1 m1 d1 (2) L 2 m 2 [ ][ ][ ɛ1 A1 m1 ɛ 2 A 2 m 2 d 2 ]. (3)

5 SEP 113 Strike, dip, both? 367 In these fitting goals, L 1 and L 2 are linear imaging operators such as the downward continuation migration operator presented by Prucha and Biondi (2002) that relates the individual models, m 1 and m 2, to the individual datasets d 1 and d 2. The regularization operators A 1 and A 2 are individually applied to the two different models and should be designed to compensate for poor illumination. However, these expanded fitting goals do not take advantage of the fact that we are imaging the same areas of the subsurface using two different datasets. We need an additional fitting goal that will allow us to regularize the models based on each other. One potential scheme for jointly inverting two datasets shot over the same area is based on regularization between stacks of the models. This inversion can be expressed in terms of three fitting goals that combine the two datasets: [ ][ ] [ L1 m1 d1 L 2 m 2 d 2 [ ][ ][ ] ɛ1 A1 m1 ɛ 2 A 2 ɛ 3 [S 1 ES 2 ] m 2 [ m1 m 2 ] (4) (5) ]. (6) The third fitting goal is the key to regularizing the illumination between the two models. S 1 and S 2 are stacking operators for the two models. E is a cross-equalization operator that compensates for differences in amplitudes and wavelets between the two models. E can be created from the migration result of each dataset (Rickett et al., 1997; Rickett and Lumley, 1998). The ɛs are weights that are used to balance the different fitting goals. These fitting goals will result in two models that have been regularized to help fill in areas that are illuminated differently by the two surveys. Either of these models should have better illumination than the result of migration of the individual datasets. Ideally, if both datasets have the same angular coverage, the stacks of the models should be the same, but the information along the ray parameter axes will be different. This difference is due to the fact that the ray couples for each survey are traveling through different media. The directions of the surveys will cause the rays to have different illumination problems and encounter other problems such as anisotropy, attenuation, and velocity contrasts that may cause evanescence. FUTURE WORK I plan to apply these fitting goals to the Amoco 2.5-D datasets. Proper construction of the regularization, stacking, and cross-equalization operators is essential. Preconditioning these fitting goals may not help to speed convergence, particularly because of the stacking operators, which will tend to act slowly when unstacking. I may choose to develop a different fitting goal to replace the stacking fitting goal. After I have satisfactorily applied my joint fitting goals to this synthetic, I hope to obtain two real 3-D surveys to further test this joint inversion scheme.

6 368 M. Clapp SEP 113 ACKNOWLEDGMENTS I would like to thank BP-Amoco for allowing us to use this 2.5-D dataset and Dennis Yanchak for getting the data to SEP. REFERENCES Duquet, B., and Marfurt, K. J., 1999, Filtering coherent noise during prestack depth migration: Geophysics, 64, no. 4, Etgen, J., and Regone, C., 1998, Strike shooting, dip shooting, widepatch shooting - Does prestack depth migration care? A model study.: 68th Ann. Internat. Mtg, Soc. Expl. Geophys., Expanded Abstracts, Nemeth, T., Wu, C., and Schuster, G. T., 1999, Least-squares migration of incomplete reflection data: Geophysics, 64, no. 1, O Connell, J. K., Kohli, M., and Amos, S., 1993, Bullwinkle: A unique 3-D experiment: Geophysics, 58, no. 01, Prucha, M., and Biondi, B., 2002, Subsalt event regularization with steering filters: 72nd Ann. Internat. Meeting, Soc. Expl. Geophys., Expanded Abstracts, Rickett, J., and Lumley, D., 1998, A cross-equalization processing flow for off-the-shelf 4-D seismic data: SEP 97, Rickett, J., Lumley, D., and Martin, H., 1997, An amplitude bias correction for 4D seismic cross-equalization: SEP 95, Ronen, S., and Liner, C. L., 2000, Least-squares DMO and migration: Geophysics, 65, no. 5,