1. Data modeling using Cagniard-de Hoop method
Jingfeng Zhang and Arthur B. Weglein
M-OSRP annual meeting
University of Houston
May 10th –12th, 2006

2. Outline Background and Motivation Theory: Numerical tests Conclusions
Data generation using Cagniard-de Hoop method
Numerical tests
Conclusions

3. Background and Motivation
Data modeling is important for:
Evaluation of new algorithms
Forward model matching methods
Conventional data processing techniques:
Arrival time; Amplitude

4. Background and Motivation
(Recently) developed new algorithms:
Deghosting
ISS free surface multiple removal method
ISS internal multiple attenuation and elimination
Imaging without the velocity
Nonlinear inversion

5. Background and Motivation
Reasons to choose Cagniard-de Hoop method for deghosting:
1.5D medium data will suffice for initial tests
“Perfect” data: regular integrand on a finite integral range
Quality control each processing step: deghosting performed in two steps

6. Background and Motivation
Primary and S-G
Primary and S-G
Receiver
deghosting +
Source deghosting
Primary
R-G and S-R-G

7. Theory The 2D acoustic constant density wave equation:
The corresponding Green’s function equation:
Relationship:

8. Theory Fourier Transform over and (layered medium): where
Just need to solving 1D wave equation and matching boundaries
for layered medium.

9. Theory
Even for the direct wave in homogeneous medium:

10. Caniard-de Hoop
Fourier Transform over and Laplace transform over :

11. Strategy: Manipulate the integral
( )
Aki & Richards (2nd Edition)

12. Theory
Direct wave:
Primary:
Pre-critical
Pos-critical

13. Theory
(1) Evaluation of the integration (direct wave):

14. Theory
(2) Sign of :

15. Numerical Tests

16. Numerical Tests

17. Numerical Tests
Correct data

18. Incorrect data

19. Deghosting result
using correct data

20. Deghosting result
using incorrect data

21. Deghosting results
Red Solid: Exact results; Blue Dash: Calculated results

22. FSMR results
Red Solid: Before FSMR; Blue Dash: After FSMR

23. Conclusions and Acknowledgments
Very high quality of data can be generated using Cagniard-de Hoop method.
It is demonstrated that using the generated data deghosting and FSMR algorithms produce very good results.
We appreciate the help from Adrian de Hoop.
The support of M-OSRP sponsors is much appreciated.