Data modeling using Cagniard-de Hoop method

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Presentation transcript:

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

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

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

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

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

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

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

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

Theory Even for the direct wave in homogeneous medium:

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

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

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

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

Theory (2) Sign of :

Numerical Tests

Numerical Tests

Numerical Tests Correct data

Incorrect data

Deghosting result using correct data

Deghosting result using incorrect data

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

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

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.