Elastic Green's theorem preprocessing

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Presentation transcript:

Elastic Green's theorem preprocessing for on-shore internal multiple attenuation: theory and initial synthetic data tests Jing Wu* and Arthur B. Weglein May 28th, 2014 Austin, TX 1 1

( Bahareh Boustani et al. 2013 ) Problem ( Bahareh Boustani et al. 2013 ) Ground Roll (Rayleigh Wave)

( Bahareh Boustani et al. 2013 ) Problem Reference wave Green’s theorem Ground Roll (Rayleigh Wave) ( Bahareh Boustani et al. 2013 )

( Bahareh Boustani et al. 2013 ) Problem Elastic Green’s theorem Reference wave Ground Roll (Rayleigh Wave) ( Bahareh Boustani et al. 2013 )

Elastic Green’s theorem reference wave prediction Theory of Elastic Green’s theorem reference wave prediction

Actual medium Experiment Reference medium Perturbation Active source ( “Passive source” ) “Source”

Off-shore: reference medium Air Water ( Acoustic ) F. S.

Off-shore: reference medium M. S. F. S. Air Water ( Acoustic )

Off-shore: reference medium + “source” Earth M. S. F. S. Air Water ( Acoustic )

Off-shore: reference wave M. S. F. S. Earth Air Water ( Acoustic ) ( Weglein and Secrest 90; Weglein 02; J. Zhang 05, 06, 07; Mayhan 12, 13; L. Tang 13 )

Off-shore: reference wave M. S. F. S. Earth Air Water ( Acoustic ) ( Weglein and Secrest 90; Weglein 02; J. Zhang 05, 06, 07; Mayhan 12, 13; L. Tang 13 )

On-shore: reference medium Elastic F. S. Air

On-shore: reference medium M. S. F. S. Elastic Air

On-shore: reference medium + “source” Elastic M. S. F. S. Air Earth

On-shore: reference wave M. S. F. S. Elastic Air Earth

On-shore: reference wave M. S. F. S. Elastic Air Earth

On-shore: reference wave M. S. F. S. Elastic Air Earth

On-shore: reference wave prediction in (x,)

On-shore: reference wave prediction in (x,) ( Stolt & Weglein 1992, 2012 )

On-shore: reference wave prediction in (x,) ( Stolt & Weglein 1992, 2012 )

M. S. F. S. Elastic Air

F. S. Elastic Air M. S.

F. S. Elastic Air M. S.

F. S. Elastic Air M. S.

F. S. Elastic Air M. S.

F. S. Elastic Air M. S.

F. S. Elastic Air M. S.

On-shore: reference wave prediction in (kx,) Assuming M.S. is horizontal

On-shore: reference wave prediction in (kx,) M. S. F. S. Elastic Air Earth

Wavelet Estimation or

Numerical Evaluation

Water (acoustic) /elastic model --- OBC Zs = -10 m O. B. 0m M.S. 1 m Elastic Water Layer P Velocity (m/s) S Velocity (m/s) Density (kg/m3) 1 1500 1000 2 1700 700 2000

Water (acoustic) /elastic model --- OBC Zs = -10 m O. B. 0m M.S. 1 m Elastic Water Layer P Velocity (m/s) S Velocity (m/s) Density (kg/m3) 1 1500 1000 2 1700 700 2000

Reference wave prediction in water/earth: P wave component Scholte wave Input data P Predicted Reference wave P0 P-P0

Actual wavelet

Estimated wavelet from P0

Reference wave prediction in water/earth: S wave component Input data S Predicted Reference wave S0 S-S0 Scholte wave

Actual wavelet

Estimated wavelet from S0

Air/elastic model --- On shore Zs = 0 m F. S. 0m M.S. 1 m Elastic Layer P Velocity (m/s) S Velocity (m/s) Density (kg/m3) 1 340 3 2 2200 1200 2000

Reference wave prediction in air/earth: P wave component Input data P Predicted Reference wave P0 P-P0 Rayleigh wave

Reference wave prediction in air/earth: S wave component Input data S Predicted Reference wave S0 S-S0 Rayleigh wave

The elastic Green’s theorem method Summary The elastic Green’s theorem method Predicts reference wave Estimates the wavelet Removes the ground roll without damaging the reflection data

Discussion & Future research Data requirements ( Weglein & Secrest 1990; Weglein, Keho & Secrest 1990; Corrigan, Weglein & Thompson 1991 )

Discussion & Future research Back out near surface properties (L. Tang et al.)

Discussion & Future research Extend to near surface with lateral variance

Thank you Comments/Questions?

Appendix

For isotropic homogeneous medium

(ux,uz) space to (P,S) space For isotropic homogenous medium (Weglein and Stolt 1992, Zhang 2006)

For actual medium (inhomogeneous)

For actual medium (inhomogeneous)

Green’s Function Reference medium Air Boundary Elastic

Air Boundary Elastic P S

P Air Boundary Elastic S

Elastic Air Boundary S P

Boundary condition At two sides of the boundary (z=0) (Aki & Richards, 2002) Air Boundary Elastic

The constitutive relation

The constitutive relation

The constitutive relation

Air Boundary at depth 0 Elastic P S

When z0, by using the boundary condition, The coefficients can be confirmed. air elastic

Air Boundary at depth 0 Elastic P S

With boundary condition at z=0 air elastic

Air Boundary at depth 0 Elastic S P

With boundary condition at z=0 air elastic

If both source and receiver are below the boundary

Green’s theorem reference wavefield prediction derivation

Air Earth m.s. v e.s.

Green’s Second Identity

Green’s Second Identity

Reference wave prediction in (x, )

Reference wave prediction in (kx, )

Reference wave prediction in (kx, )

Reciprocity of Green’s function

Even, only real part left

Odd, only image part left

Appendix

Boundary condition (acoustic/elastic) Displacement X: viscid is low along the boundary, can be discontinuous; Z: no cavitation in the earth along the boundary, continuous. Traction Same magnitudes and opposite directions;

At two side of the boundary (z=0) Boundary condition Air Boundary Elastic At two side of the boundary (z=0)