� � � � � Geophysical Institute, Karlsruhe University W I T Common-Reflection-Surface Stack and Wavefield Attributes J¨ urgen Mann, Rainer J¨ ager, German H¨ ocht, and Peter Hubral Overview Comparison of different stacking operators Eigenwave based CRS stacking operator Synthetic example vs. forward modeled attributes Real data example: imaging a salt dome Conclusions and outlook
Summary The common reflection surface (CRS) stack is a macro velocity model independent method to simulate zero-offset (ZO) sec- tions from multi-coverage seismic reflection data for 2-D me- dia. The CRS stacking operator depends on attributes of hypothet- ical wavefronts observed at the surface that allow to perform a subsequent inversion. The CRS stacking operators fitting best to actual reflection events in the data set have to be determined by coherency analysis. The main task is the determination of these opera- tors by variation of the attributes in a reasonable computation time preserving a sufficient accuracy.
Stacking operators of NMO/DMO/stack and pre-stack depth migration PreSDM stacking surface MZO stacking surface t t 0.6 0.6 Depth [m] Time [s] Depth [m] Time [s] 0.4 0.4 h h P 0 P 0 0.2 0.2 0 0 X 0 X 0 x x −200 −200 ZO isochrone 400 400 R R −400 −400 300 300 200 200 −600 −600 Half−offset [m] Half−offset [m] 100 100 −1000 −1000 −500 −500 0 0 0 0 500 500 Midpoint [m] Midpoint [m] 1000 1000
CRS stacking operator Eigenwave experiments 0.2 R x NIP 0 0 α -0.2 CRS stacking surface Depth [km] R -0.4 t 0.6 -0.6 Depth [m] Time [s] 0.4 -0.8 h 0.6 0.8 1 1.2 1.4 1.6 Distance [km] 0.2 P 0 0.2 R N x 0 0 α 0 X 0 x -0.2 −200 Depth [km] C R 400 R R -0.4 −400 300 200 −600 Half−offset [m] -0.6 100 −1000 −500 0 0 500 Midpoint [m] 1000 -0.8 0.6 0.8 1 1.2 1.4 1.6 Distance [km]
☛ ✙ ✠ ✬ ✂ ✁ ✠ ☎ ✂ ✁ ✪ ✦✩ ✦ ✙ ✥ ★ ✦✧ ✥ ✘ ✞ ✆ ✠ ✜ ✛ ✛ ✂ ✂ ✛ ✥ ✘ ✂ ✕ ✤ ✢ ✑ ✁ ☎ ✱ ★ ✦✧ ✑ ✦✩ ✙ ✔ ☞ ✪ ✦✩ ✂ ✙ ✰ ✯ ✭✮ ✪ ✛ ✛ ✚ ✙ ✤ ✁ ✔ ✒ ✂ ✜ ✛ ✛ ✛ ✚ ✑ ✞ ✂ ✆ ✘ ✖✗ ✕ ✔ ✁ ✏ ✎ ✎ ✎ ✍ ✞ ★ ✕ ✘ ✎ ✦✧ ✥ ✂ ✠ ✒ ✦ ✥ ✂ ✆ ✏ ✞ ✎ ✎ ✙ ✑ ✎ ✍ ✎ Common-reflection-surface stacking operator ✑✣✢ ✁✄✂ ☛✌☞ ☎✝✆ ✟✡✠ ✑✓✒ : half offset between shot and receiver : midpoint distance : emergence angle of the normal ray : radius of curvature of the NIP wave : radius of curvature of the normal wave In the CMP gather in terms of the stacking velocity : ☛✌☞ ✑✫✒
Synthetic example: model and ZO section of multi-coverage data set v = 1250 m/s v = 1400 m/s v = 1800 m/s R v = 2400 m/s v = 3200 m/s v = 4500 m/s Distance [km] 0 2 4 6 8 10 2 Time [s] 3 4
Coherence in the wavefield attribute domain
Synthetic example: result of the optimized CRS stack Distance [km] Distance [km] 0 2 4 6 8 10 0 2 4 6 8 10 0.40 0.35 0.30 2 2 0.25 Time [s] Time [s] 0.20 0.15 3 3 0.10 0.05 0 4 4 simulated ZO section coherency section
✴✵✶ ✳ ✲ Synthetic example: attribute sections Distance [km] Distance [km] 0 2 4 6 8 10 0 2 4 6 8 10 30 5000 4500 20 2 2 4000 10 3500 Time [s] Time [s] 3000 0 2500 3 3 -10 2000 1500 -20 1000 4 500 4 -30 emergence angle [ ] radius of curvature [m]
✴ ✳ ✳ ✴ Synthetic example: attribute sections Distance [km] 0 2 4 6 8 10 1.0 0.8 0.6 2 0.4 0.2 Time [s] 0 -0.2 3 -0.4 -0.6 -0.8 -1.0 4 x104 radius of curvature [m] model-derived vs. data-derived
✳ ✴✵ ✶ Synthetic example: attribute sections model-derived vs. data-derived emergence angle model-derived vs. data-derived
✸ ❊ ✸✹ ✺ ✿ ❀ ✺ ✸✹ ❃ ❄ ❅ ❆ ❇ ❈ ❉✹ ✿ ✷ ✾ ✾ ✼ ✻ ✸ ❀ ❊ ✹ ❊ ❅ ❆ ❇ ❈ ✷ Real data example: NMO/DMO/stack vs. CRS stack CMP location CMP location approx. 13km approx. 13km 0.5 0.5 1 1 1.0 1.0 Time [s] Time [s] 1.5 1.5 2.0 2.0 2 2 5 5 4a 4b 4a 4b 2.5 2.5 3 3 3.0 3.0 NMO/DMO/stack Optimized CRS stack Data courtesy of and . ✺❂❁ ✻✽✼✾ ✻●❋
✸✹ ❊ ❄ ❃ ❇ ❈ ✺ ❀ ✿ ❉✹ ✺ ✸✹ ✷ ✸ ✷ ✿ ❆ ✾ ✾ ✼ ✻ ✸ ❀ ❊ ✹ ❊ ❅ ❆ ❇ ❈ ❅ Real data example: conventional NMO/DMO/stack CMP location approx. 13km 0.5 1 1.0 Time [s] 1.5 2.0 2 5 4a 4b 2.5 3 3.0 Data courtesy of and . ✺❂❁ ✻✽✼✾ ✻●❋
✸✹ ❊ ❄ ❃ ❇ ❈ ✺ ❀ ✿ ❉✹ ✺ ✸✹ ✷ ✸ ✷ ✿ ❆ ✾ ✾ ✼ ✻ ✸ ❀ ❊ ✹ ❊ ❅ ❆ ❇ ❈ ❅ Real data example: optimized CRS stack CMP location approx. 13km 0.5 1 1.0 Time [s] 1.5 2.0 2 5 4a 4b 2.5 3 3.0 Data courtesy of and . ✺❂❁ ✻✽✼✾ ✻●❋
✸✹ ❊ ✷ ✺ ✿ ❀ ✺ ✸✹ ❃ ❄ ❅ ❆ ❇ ❈ ❉✹ ✿ ✸ ✾ ✾ ✼ ✻ ✸ ❀ ❊ ✹ ❊ ❅ ❆ ❇ ❈ ✷ Real data example: post-stack depth migrated sections CMP location CMP location 13km 13km 0 0 1 1 1 1 2 2 Depth [km] Depth [km] 3 3 2 4 2 4 4 4 3 3 5 5 NMO/DMO/stack Optimized CRS stack Data courtesy of and . ✺❂❁ ✻✽✼✾ ✻●❋
❅ ✿ ❃ ❄ ❅ ❆ ❇ ❈ ❉✹ ❊ ✾ ❆ ✾ ✼ ✻ ✸ ❀ ❊ ✹ ❇ ❊ ✸✹ ✺ ❀ ✷ ✿ ❈ ✺ ✸✹ ✷ ✸ Real data example: post-stack depth migrated NMO/DMO/stack CMP location 13km 0 1 1 2 Depth [km] 3 2 4 4 3 5 Data courtesy of and . ✺❂❁ ✻✽✼✾ ✻●❋
❅ ✿ ❃ ❄ ❅ ❆ ❇ ❈ ❉✹ ❊ ✾ ❆ ✾ ✼ ✻ ✸ ❀ ❊ ✹ ❇ ❊ ✸✹ ✺ ❀ ✷ ✿ ❈ ✺ ✸✹ ✷ ✸ Real data example: post-stack depth migrated CRS stack CMP location 13km 0 1 1 2 Depth [km] 3 2 4 4 3 5 Data courtesy of and . ✺❂❁ ✻✽✼✾ ✻●❋
❍■ ❖P ❏ ❑▲ ▼◆ Conclusions The CRS stack is a model independent seismic imaging method and thereby can be performed without any ray tr ac- ing and macro velocity model estimation. Only the knowledge of the near surface velocity is required. As a result of a CRS stack one obtains in addition to each simulated ZO reflection time important wave-field attributes: the angle of emergence and the radii of curvature of the and the wave. The application to real and synthetic datasets showed notewor- thy results with respect to the stack section and the determined attributes. In view of the authors, the proposed strategies offer an exciting approach to improve the stack section and to allow for a subsequent inversion.
❴ ❯ ❭ ❯ ❨ ❪ ❨ ❫ ❱ ❵ ❨ ❲ ❙ ❨ ❱ ❛ ❳ ❜ ❝ ❨ ❞ ❪❡ ❞❢ ❬ ❩ ❪ ❨ ❯ ❨ ❳ ❛ ❬ ❜ ❨✐ ❱ ❤ ❯ ❳ ❯ ❛ ◗ ◗❘❙ ❚❯ ❘ ❙ ❱ ❲ ❳ ❨ ❣ References Berkovitch, A., Gelchinsky, B., and Keydar, S. (1994). Basic formulae for multifocusing stack. 56th Mtg. Eur. Assoc. Expl Geophys., Extended Ab- stracts, page Session: P140. de Bazelaire, E. (1988). Normal moveout revisited – inhomogeneous media and curved interfaces. Geophysics , 53(2):143–157. de Bazelaire, E. and Thore, P . (1987). Pattern recognition applied to time and velocity contours. 57th Annual Internat. Mtg., Soc. Expl. Geophys., Expanded Abstracts, page Session: POS2.14. Schleicher, J., Tygel, M., and Hubral, P . (1993). Parabolic and hyperbolic paraxial two-point traveltimes in 3D media. Geophys. Prosp. , 41(4):459– 513. Acknowledgements This work was kindly supported by the sponsors of the , Karlsruhe, Germany and , Pau, France.
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