Multiples Waveform Inversion Dongliang Zhang and Gerard Schuster King Abdullah University of Science and Technology 12/06/2013

Outline Motivation Theory Numerical Example Conclusions Multiples contain more information Theory Algorithm of MWI and generation of multiples Numerical Example Test Marmousi model Conclusions

Outline Motivation Theory Numerical Example Conclusions Multiples contain more information Theory Algorithm of MWI and generation of multiples Numerical Example Test Marmousi model Conclusions

Motivation Multiples : wider coverage, denser illumination multiples primary Multiples : wider coverage, denser illumination FWI MWI

Recorded data (primary + multiples) Motivation Multiples waveform inversion vs full waveform inversion Source wavefield Receiver wavefield FWI Impulsive wavelet Recorded data MWI Recorded data (P+M) Multiples (M) Recorded data (primary + multiples) Impulsive wavelet Recorded data multiples Natural source

Outline Motivation Theory Numerical Example Conclusions Multiples contain more information Theory Algorithm of MWI and generation of multiples Numerical Example Test Marmousi model Conclusions

Theory Algorithm of MWI 1. Misfit function 2. Gradient of data residual Multiples RTM

Algorithm of MWI Forward propagation Back propagation 3. Update velocity/slowness

MWI Workflow Calculate multiples to get the multiples residual Multiples RTM to get gradient of misfit function Update the velocity Number of iterations >N No Yes Stop

Generate Multiples Mr = (Pd+Md ) +Mr - (Pd+Md) Step 1 Pd+Md Mr Step 2 direct propagation Pd+Md Line source (P +M) heterogeneous Mr reflected propagation Step 2 direct propagation homogeneous Line source (P +M) Pd+Md heterogeneous homogeneous Step 3 Mr = (Pd+Md ) +Mr - (Pd+Md)

Example water homogeneous (Pd+Md)+Mr (Pd+Md) Mr (multiples) Virtual Source (P+M) Example 5.5 T (s) 0 2 Z (km) 0 water homogeneous 0 X (km) 4 5.5 T (s) 0 (Pd+Md)+Mr 0 X (km) 4 (Pd+Md) 0 X (km) 4 Mr (multiples)

Conventional migration Gradient of MWI Multiples residual Recorded data Impulsive wavelet Data residual Multiples migration Conventional migration Yike Liu (2011)

Outline Motivation Theory Numerical Example Conclusions Multiples contain more information Theory Algorithm of MWI and generation of multiples Numerical Example Test Marmousi model Conclusions

Numerical Example True Velocity Model Initial Velocity Model 1.5 km/s 5.5 2 Z (km) 0 2 Z (km) 0 1.5 km/s 5.5 Initial Velocity Model 0 X (km) 4

Numerical Example Tomogram of FWI Tomogram of MWI 2 Z (km) 0 1.5 km/s 5.5 2 Z (km) 0 Tomogram of MWI 2 Z (km) 0 0 X (km) 4 1.5 km/s 5.5

Numerical Example True True FWI FWI MWI MWI

Numerical Example RTM Image Using FWI Tomogram 2 Z (km) 0 0 X (km) 4

Numerical Example RTM Image Using MWI Tomogram 2 Z (km) 0 0 X (km) 4

Numerical Example Common Image Gather Using FWI Tomogram

Numerical Example Common Image Gather Using MWI Tomogram

Numerical Example FWI MWI FWI MWI Data Residual 20 Res (%) 100 Convergence of MWI is faster than that of FWI FWI MWI 1 Iterations 100 11 Res (%) 14 Model Residual FWI MWI MWI is more accurate than FWI

Numerical Example FWI Gradient for One Shot MWI Gradient for One Shot 0 X (km) 4 MWI Gradient for One Shot

Outline Motivation Theory Numerical Example Conclusions Multiples contain more information Theory Algorithm of MWI and generation of multiples Numerical Example Test Marmousi model Conclusions

Conclusions Source wavelet is not required Illuminations are denser MWI converge faster than FWI in test on Marmousi model Tomogram of MWI is better than that of FWI in test on Marmousi model FWI MWI FWI MWI

Limitations: Dip angle vs Future work: P+M FWI P+M MVA

Thank you!