1. Raanan Dafni,  PhD in Geophysics (Tel-Aviv University)  Paradigm R&D (2009-2014)  Post-Doc (Rice University) Current Interest: “Wave-equation based imaging/inversion methods in the angle-domain”

2. Angle Decomposition via Subsurface Offset Extended RTM Raanan Dafni Annual Report Meeting TRIP 2016

3. Outline 3  Subsurface offset extended wave-equation migration  Subsurface offset relations with the angle-domain  Angle decomposition (scattering, dip, multi-angle)  Examples  Future implications

4. Subsurface Offset Extension 4 X Y S R M M hh Common Image Gathers (CIGs) are calculated by prestack depth migration methods. Reflectivity is ‘extended’ by a characteristic prestack parameter: acquisition offset / scattering-angle / subsurface offset (horizontal)

5. Subsurface Offset Extension 5 X Y S R M hh Subsurface offset extended migration operator (Stolk et al., 2009):

6. HOCIG Image Section (h=0) 110%V90%V 100%V Subsurface Offset Extension 6 Synthetic example: -5º dipping reflector

7. Extended Impulse Response: Subsurface Offset Extension 110%V90%V 100%V HOCIG 7

8. Subsurface Offset to Angle Domain M h h s r ν γ ν γ M s r ν γ γ h=0 Common Reflection Point (CRP) h!=0 Split Reflection Point (SRP) 8 Geometry of Reflection:

9. 2D 3D dip angle (ν) scattering angle (γ) scattering angle and azimuth (γ 1, γ 2 ) dip angle and azimuth (ν 1, ν 2 ) I[z, x, h] I[z, x, y, h x, h y ] (Sava and Fomel, 2003) (Dafni and Symes, 2016) Subsurface Offset to Angle Domain 9 Radon Transform Relations:

10. Subsurface Offset to Angle Domain x’ h x z h z z z h q p p q ADCIGγ ADCIGν ADCIGνγ HOCIG 10

11. Angle Domain Decomposition z(m) -40 γ (º) 0 20 2000 0 z(m) -40 ν (º) 0 40 2000 0 -2040-2020 40 0 2000 4000 0 0 z(m) γ (º) ν (º) -50500-40 ν (º) -50 50 HOCIG Image Section (h=0) ADCIGγ ADCIGνγ ADCIGν Synthetic example: -5º dipping reflector

12. Extended Impulse Response – Angle Variant: Scattering-Angle Domain (ADCIGγ) 110%V 90%V 100%V Parametric RT ADCIGγ 12

13. Dip-Angle Domain (ADCIGν) 110%V 90%V Parametric RT z(m) -40 ν (º) 0 40 2000 0 -40 ν (º) 0 40 2000 0 -40 ν (º) 0 40 2000 0 100%V Extended Impulse Response – Angle Variant: 13

14. Dip-Angle Decomposition (reflections) z(m) -40 ν (º) 0 40 2000 0 z(m) -40 ν (º) 0 40 2000 0 -2020 -2020 ADCIG ν ADCIG ν Kirchhoff  The same specular dip information is provided.  The “tails” of the response are annihilated. 14 The dip-angle response of reflections Q: Where have the response “tails” gone?

15. Dip-Angle Decomposition (reflections) The tails are distractively canceled while imaging in the subsurface offset domain, before the angles are decomposed. A: It is a property of imaging methods in the subsurface offset domain. 15 The dip-angle response of reflections Q: Where have the response “tails” gone?

16. Dip-Angle Decomposition (reflections) ADCIGν A: It is not a property of the imaging method. HOCIG Image Section (h=0) 16 The dip-angle response of reflections Q: Where have the response “tails” gone? Subsurface offset extended Kirchhoff migration:

17. Conflicting Dips HOCIG Image Section (h=0) ADCIGγ ADCIGν -20º 15º -20º 15º 17

18. Conflicting Dips 18 -20º 15º Image Section (h=0) ADCIGνγ -20º15º -20º 15º

19. Seismic Diffractions 19 HOCIG Image Section (h=0) ADCIGγ ADCIGν -10º 5º

20. Seismic Diffractions 20 -10º 5º ADCIGνγ (depth slices) Above Diffractor To the right of Diffractor Image Section (h=0)

21. Field Data Example 2D line, Offshore east Mediterranean Sea. Image Section (h=0) HOCIG 21

22. Field Data Example 2D line, Offshore east Mediterranean Sea. 22 ADCIGγ ADCIGνγ (depth slices) ADCIGν

23. Future Implications Specular Enhancement Diffraction Imaging Amplitude Variation with Angle (AVA) Reflection Tomography Migration Velocity Analysis FWI HOCIG ADCIGν ADCIGγ Velocity Model Optimization Image Interpretation Amplitude Analysis 23 ADCIGνγ Angle-Domain Technology, based on Wave-Equation Methods.

24.  The Rice University Inversion Project (TRIP) members and sponsors.  Shell International Exploration and Production Inc. for their sponsorship.  The Israeli Ministry of National Resources for partial financial support. Thank you! Acknowledgments: 24