Jingfeng Zhang and Arthur B. Weglein Application of Extinction Theorem Deghosting method on Ocean Bottom Data 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 Acknowledgments

Background and Motivation Most of conventional multiple, imaging and inversion algorithms: Robust and low expectation Inverse scattering series related (ISS) algorithms: ISS free surface multiple removal ISS internal multiple attenuation and elimination Imaging without the velocity Nonlinear inversion (1) Chain; (2) Amplitude and arrival time

Background and Motivation Benefits of Deghosting Prerequisite for ISS FSMR Eliminate angle-dependent ghost effect Large angle AVO Nonlinear inversion Imaging without the velocity Restoring amplitude spectrum, low frequency component: Ghost notch

Background and Motivation Advantage of Extinction Theorem deghosting: Stable No low frequency assumption

Review: Theory Weglein et al. (2002) F.S. Pseudo-M.S. M.S. Earth

Review: Deghosting H. Tan (1992) and A.Osen et al. (1998)

Review: Towed streamer deghosting (Numerical tests: Model) F.S. (0,2) 6.0m M.S. 300m c1=1500m/s c2=2250m/s

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

Review: FSMR results Red Solid: Before FSMR; Blue Dash: After FSMR Using the 1st term in the ISS FSMR series

Ocean bottom data deghosting (Theory) Weglein et al. (2002): Using measured P and its derivative Disadvantages: Noise on geophone Coupling issue and scale factor : actually measured are and

Ocean bottom data deghosting (Theory) Two stable measurements troublesome and historic impediment measurement Triangle relationship Wavelet estimation (Weglein and Secrest, 1990)

Advantages and Disadvantages Avoid noise on geophone Avoid coupling issue and scale factor : actually measured are and Disadvantages: Unstable spectral division

Ocean bottom data deghosting (Theory) Assume there is no direct wave, then (1) only calculate “good” points; (2) interpolate others is the receiver depth

Interpolation at unstable points

Interpolation at unstable points

Ocean bottom data deghosting (Theory) Direct wave; (b) Primary; (c) Receiver ghost of primary; (d) 1st order FSM; (e) Source-Receiver ghost of Primary (f) Source ghost of the 1st order FSM

A note on FSMR Primary Primary*Primary FSM Weglein et al. (1997, 2003)

Procedure Receiver side deghosting Source side deghosting Calculate using spectral division Source side deghosting

Receiver ghost and Source-Receiver ghost Primary and its source ghost Before deghosting Receiver ghost and Source-Receiver ghost

After deghosting

Another procedure Receiver side deghosting Source side deghosting Calculate using spectral division Source side deghosting Calculate using prediction in space domain

Deghosting (Theory) H. Tan (1992) and A.Osen et al. (1998)

New procedure

Former procedure

Applying taper at k_z=0 end

Conclusions The provided OBC deghosting procedure has certain advantages and disadvantages. In predicting the derivative of the field, avoid using spectral division gives better result. Further effort is needed in order to remove all of the artifacts.

Requirements for the field data Tower streamer data REAL point receiver 3D survey Good estimation of source wavelet radiation pattern Ocean bottom data REAL 3D survey More work to remove artifacts

Acknowledgments Kris Innanen and Ken Matson (BP) is thanked for helpful discussions. The support of M-OSRP sponsors is much appreciated.