1. Angle-domain parameters computed via weighted slant-stack Claudio GuerraSEP-131

2. Motivation Post migration processes in the reflection-angle domain –migration-velocity analysis –residual multiple attenuation –AVA –regularization of the least-squares inverse imaging Compensate for illumination problems in ADCIGs

3. Outline Introduction Weighted OFF2ANG Results Conclusions

4. Introduction SEP125 - Valenciano and Biondi –Compute the Hessian in the angle domain by chaining operators T *, H and T. S(m) = ½||Lm h – d obs || 2 = ½||LTm  – d obs || 2  2 S(m)/  m 2 = T * L * LT H(x,  ; x ’,  ’ ) = T * ( ,h) H ( x, h ; x ’, h ’ ) T( ,h) H(x,  ; x ’,  ’ ) – angle-domain Hessian H ( x, h ; x ’, h ’) – offset-domain Hessian m  – ADCIGm h – SODCIG T( ,h) – angle-to-offset transformation T * ( ,h) – offset-to-angle transformation L – modeling operatorL * - migration

5. angle -10 60 Introduction SEP125 - Valenciano and Biondi –“The Hessian... in the angle dimension lacks of resolution to be able to interpret which angles get more illumination.” offset -1200 1200 depth offset -1200 1200 angle -10 60 depth

6. Weighted OFF2ANG Assymptotic approximation of Kirchhoff Migration –Main contribution comes from the vicinity of the stationary point Bleistein(1987) and Tygel et.al(1993) –migration with two different weights –division of the migrated images t z M(x,z) x –  * N(  *,t)

7. Weighted OFF2ANG – phase behavior Slant – stack Q – ADCIGP – SODCIG  – stacking line f (z) – wavelet z r – reflector A – amplitude h – subsurface offset  – reflection angle – rho filter

8. Weighted OFF2ANG – phase behavior Slant – stack Q – ADCIG  – phase function f (z) – wavelet A – amplitude h * – stationary offset  – reflection angle

9. Weighted OFF2ANG Weighted Slant – stack – ADCIG  – phase function f (z) – wavelet A – amplitude h * – stationary offset  – reflection angle

10. Results Sigsbee2b depth cmp

11. Results – Input data offset -1200 1200 depth offset -1200 1200 SODCIGDiagonal of the Hessian

12. Results –ADCIGs angle -10 60 angle -10 60 angle -10 60 depth angle -10 60 angle -10 60 angle -10 60 depth angle -10 60 angle -10 60 angle -10 60 Main diagonal

13. Results – Angle sections 15 o 30 o 40 o depth cmp depth cmp depth cmp depth cmp depth cmp depth cmp Main diagonal

14. Results – Amplitude correction angle -10 60 angle -10 60 angle -10 60 depth angle -10 60 angle -10 60 angle -10 60 depth Main diagonal

15. Results – Amplitude correction 15 º angle section depth cmp depth cmp 30 º angle section depth cmp 45 º angle section Main diagonal

16. Results – Amplitude correction depth cmp Angle stack

17. Main diagonal5 th off-diagonal Results – 0 o Off-diagonals depth cmp 15 th off-diagonal

18. Main diagonal5 th off-diagonal Results – 15º Off-diagonals depth cmp 15 th off-diagonal

19. Conclusions Alternative approach to transform the Hessian to the angle domain Well balanced ADCIGs –Better angle-stack Off-diagonal terms –Still no direct application