Multiples Waveform Inversion

Dongliang Zhang and Gerard SchusterKing Abdullah University of Science and Technology

12/06/2013

Outline

Conclusions

MotivationMultiples contain more information

Numerical ExampleTest Marmousi model

TheoryAlgorithm of MWI and generation of multiples

Outline

Conclusions

TheoryAlgorithm of MWI and generation of multiples

Numerical ExampleTest Marmousi model

MotivationMultiples contain more information

Motivation

Multiples : wider coverage, denser illumination

primary

multiples

FWI MWI

Motivation Multiples waveform inversion vs full waveform inversion

Source wavefield Receiver wavefield

FWI Impulsive wavelet Recorded data

MWI Recorded data (P+M)

Multiples(M)

Impulsive wavelet

Recorded data (primary + multiples) multiplesRecorded data

Natural source

Outline

Conclusions

TheoryAlgorithm of MWI and generation of multiples

Numerical ExampleTest Marmousi model

MotivationMultiples contain more information

2 *

( )( )

Real[2 ( ) ( ) ( )]g s

gs

s F B

xxx x x

*1/ 2 ( , ) ( , )g s g sg s

M M

x x x x

2. Gradient of data residual

Theory

1. Misfit function

Algorithm of MWI

Multiples RTM

)()()( 1 xxx gss ii

3. Update velocity/slowness

( ) ( | ) ( , )g g gF G d dx x x x x

Forward propagation

Back propagation*( ) ( | ) ( , )g g gB G M d x x x x x

2 *

( )( )

Real[2 ( ) ( ) ( )]g s

gs

s F B

xxx x x

Algorithm of MWI

Number of iterations >N

MWI Workflow

No

Stop Yes

Update the velocity

Multiples RTM to get gradient of misfit function

Calculate multiples to get the multiples residual

Pd+Mddirect propagation

reflected propagation Mr

Line source(P +M)

Mr = (Pd+Md ) +Mr - (Pd+Md)

heterogeneous homogeneous

Generate Multiples

heterogeneous

Pd+Mddirect propagation

Line source(P +M) homogeneous

Step 1

Step 2

Step 3

Example

2

Z

(km

) 0

0 X (km) 4

5.5

T

(s)

0

(Pd+Md)+Mr

Virtual Source (P+M)

0 X (km) 4

(Pd+Md)

5.5

T

(s)

0

water homogeneous

0 X (km) 4

Mr (multiples)

Data residual

Impulsive wavelet

Multiples residual

Recorded data

Conventional migration

Multiples migration

Yike Liu (2011)

Gradient of MWI

Outline

Conclusions

TheoryAlgorithm of MWI and generation of multiples

Numerical ExampleTest Marmousi model

MotivationMultiples contain more information

2

Z

(km

)

0

1.5

k

m/s

5.5

True Velocity Model

Numerical Example2

Z (k

m)

0 1.

5

km

/s

5

.5

Initial Velocity Model

0 X (km) 4

Numerical Example

1.5

k

m/s

5.5

2

Z

(km

)

0

Tomogram of FWI

Tomogram of MWI

2

Z

(km

)

0

0 X (km) 4

1.5

km/s

5.5

Numerical Example

FWI FWI

MWIMWI

TrueTrue

RTM Image Using FWI Tomogram

Numerical Example2

Z

(km

)

0

0 X (km) 4

RTM Image Using MWI Tomogram

Numerical Example2

Z

(km

)

0

0 X (km) 4

Numerical Example

Common Image Gather Using FWI Tomogram

Numerical Example

Common Image Gather Using MWI Tomogram

Data Residual20

Res

(%)

10

0

FWI

MWI

Numerical ExampleConvergence of MWI is faster than that of FWI

1 Iterations 100

11

Res

(%)

14

Model Residual

FWI

MWI

MWI is more accurate than FWI

FWI Gradient for One Shot

Numerical Example

0 X (km) 4

MWI Gradient for One Shot

Outline

Conclusions

TheoryAlgorithm of MWI and generation of multiples

Numerical ExampleTest Marmousi model

MotivationMultiples contain more information

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

Future work: P+M FWI P+M MVA

vs

Thank you!