Weighted Stacking of 3-D Converted-wave Data for Birefringent Media Richard Bale

Introduction Shear-wave splitting (birefringence) is a “litmus test” for azimuthal anisotropy Used to characterize fractured media Can degrade image if uncorrected  Causes acquisition footprint for 3-D 

Radial and Transverse DMO Stacks ms In-lines Cross Lines Cross Lines

Background Estimation of principal axes –e.g. using transverse polarity from 3-D data Layer stripping to remove anisotropy –needs estimates of S1-S2 transmission 2-D: rotation after stack 3-D: must rotate before stack –…but is that all?

Converted Wave Splitting Legend: P SV S1 S2 Azimuthally Anisotropic Layer Fracture Direction Radial Direction X Y Shot Receiver Conversion Point

Surface Geometry X Y S1 S2 Radial   U PS Receiver Shot

The 3-D Splitting Equation where:is a rotation matrix, Radial converted wave Projection onto S1 & S2 S1 & S2 propagation Recording on X and Y and:

Multi-azimuth CCP Binning X CCP Bin Receivers Shots 11 22 33 NN …. Þ Acquisition- dependent amplitudes

Least Squares Stacking for S1 and S2 We have two (decoupled) least squares problems, for U PS1 and U PS2 Weighted stacking equations: S1 Effective Fold S2 Effective Fold

Orthogonal Acquisition Y (meters) X (meters) Shot Lines Receiver Lines

Isotropic ACCP Fold Cross-line Number In-line Number

S1 Effective ACCP Fold:  =0° Cross-line Number In-line Number

S1 Effective ACCP Fold:  =45° Cross-line Number In-line Number

Gryphon: Acquisition Geometry In-lines 950 Cross lines CCP Stacking Fold Cables Shot Lines 400m

Effective Fold Maps In-lines 950 Cross lines S1 Norm:  cos 2 (  i -  ) S2 Norm:  sin 2 (  i -  ) In-lines 950 Cross lines

TransverseRadial Radial and Transverse DMO Stacks Cross line 895 Cross line

S2S1 Least-squares S1 and S2 DMO Stacks Cross line 895 Cross line

Least-squares S1 and S2 DMO Stacks ms In-lines Cross Lines Cross Lines

Radial and Transverse DMO Stacks ms In-lines Cross Lines Cross Lines

Offset Dependence Converted wave amplitudes strongly depend on angle of incidence For small angles (<20°): for ray-parameter p, local compressional velocity V P, angle of incidence , and local shear velocity V S (Stewart, Zhang, and Guthoff; 1995)

Angle Gathers: Alba Radial Component Maximum Amplitude in Window Linear Sampling Sin(  ) Sampling Time (sec.)

Offset Dependent Least Squares Stacking for S1 and S2 Updated weighted stacking equations: S2 Effective Fold S1 Effective Fold t 0 = 2-way zero-offset time r i = offset t(r i ) = 2-way time

S1 Effective ACCP Fold:  =45° Cross-line Number In-line Number

Offset weighted S1 Eff. ACCP Fold:  =45° Cross-line Number In-line Number

Conclusions Preliminary work done on a method for 3-D S1 and S2 imaging Offset dependence can be included Effective fold maps include azimuth and offset effects for S1 and S2 Initial results show increased resolution, and less acquisition footprint

Future Work Test method on synthetic and field data Fractured reservoir imaging: consider conversions within birefringent medium Long offset issues: –Orthogonality –2-term AVO fit: I S, (I S1, I S2 ?),  parameterization Multiple birefringent layers PS1-PS2 Migration?

Acknowledgements Kerr-McGee North Sea (UK) Ltd., and the Gryphon partners Chevron and the Alba partners WesternGeco –In particular Tony Probert and Gabriela Dumitru The CREWES sponsors