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Geophysical Institute, Karlsruhe University

W I T

Common-Reflection-Surface Stack and Wavefield Attributes

J¨ urgen Mann, Rainer J¨ ager, German H¨

• cht, 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

−1000 −500 500 1000 100 200 300 400 −600 −400 −200 0.2 0.4 0.6

Depth [m] Time [s] Half−offset [m]

P0 X0 R x h t MZO stacking surface

Midpoint [m]

ZO isochrone

−1000 −500 500 1000 100 200 300 400 −600 −400 −200 0.2 0.4 0.6

Depth [m] Time [s] Half−offset [m]

P0 X0 R x h t PreSDM stacking surface

Midpoint [m]

CRS stacking operator

−1000 −500 500 1000 100 200 300 400 −600 −400 −200 0.2 0.4 0.6

Depth [m] Time [s] Half−offset [m]

P0 X0 R x h t CR CRS stacking surface

Midpoint [m]

Eigenwave experiments

• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.6 0.8 1 1.2 1.4 1.6

R R x

NIP

Distance [km] Depth [km]

α

• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.6 0.8 1 1.2 1.4 1.6

R R x

N

Depth [km] Distance [km]

α

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

R

v = 2400 m/s v = 1800 m/s v = 1400 m/s v = 3200 m/s v = 4500 m/s v = 1250 m/s

2 3 4 Time [s] 2 4 6 8 10 Distance [km]

Coherence in the wavefield attribute domain

Synthetic example: result of the optimized CRS stack

2 3 4 Time [s] 2 4 6 8 10 Distance [km] 2 3 4 Time [s] 2 4 6 8 10 Distance [km] 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

simulated ZO section coherency section

Synthetic example: attribute sections

2 3 4 Time [s] 2 4 6 8 10 Distance [km]

• 30
• 20
• 10

10 20 30 2 3 4 Time [s] 2 4 6 8 10 Distance [km] 500 1000 1500 2000 2500 3000 3500 4000 4500 5000

emergence angle [

] radius of curvature

[m]

Synthetic example: attribute sections

2 3 4 Time [s] 2 4 6 8 10 Distance [km]

• 1.0
• 0.8
• 0.6
• 0.4
• 0.2

0.2 0.4 0.6 0.8 1.0 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

0.5 1.0 1.5 2.0 2.5 3.0 Time [s] CMP location

• approx. 13km

3 2 4a 4b 5 1 0.5 1.0 1.5 2.0 2.5 3.0 Time [s] CMP location

• approx. 13km

3 2 4a 4b 5 1

NMO/DMO/stack Optimized CRS stack Data courtesy of

and

.

Real data example: conventional NMO/DMO/stack

0.5 1.0 1.5 2.0 2.5 3.0 Time [s] CMP location

• approx. 13km

3 2 4a 4b 5 1

Data courtesy of

and

.

Real data example: optimized CRS stack

0.5 1.0 1.5 2.0 2.5 3.0 Time [s] CMP location

• approx. 13km

3 2 4a 4b 5 1

Data courtesy of

and

.

Real data example: post-stack depth migrated sections

1 2 3 4 5 Depth [km] CMP location 1 2 4 3 13km 1 2 3 4 5 Depth [km] CMP location 1 2 4 3 13km

NMO/DMO/stack Optimized CRS stack Data courtesy of

and

.

Real data example: post-stack depth migrated NMO/DMO/stack

1 2 3 4 5 Depth [km] CMP location 1 2 4 3 13km

Data courtesy of

and

.

Real data example: post-stack depth migrated CRS stack

1 2 3 4 5 Depth [km] CMP location 1 2 4 3 13km

Data courtesy of

and

.

Conclusions The CRS stack is a model independent seismic imaging method and thereby can be performed without any ray trac- ing and macro velocity model estimation. Only the knowledge

• f 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.