multiples waveform inversion dongliang zhang and gerard schuster king abdullah university of science...
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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
xx
x 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
xx
x 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+Md
direct propagation
reflected propagation Mr
Line source(P +M)
Mr = (Pd+Md ) +Mr - (Pd+Md)
heterogeneous homogeneous
Generate Multiples
heterogeneous
Pd+Md
direct propagationLine source
(P +M)homogeneous
Step 1
Step 2
Step 3
Example
2
Z
(k
m)
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
(k
m)
0
1.5
k
m/s
5.5
True Velocity Model
Numerical Example
2
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
(k
m)
0
Tomogram of FWI
Tomogram of MWI
2
Z
(k
m)
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
(%
)
100
FWI
MWI
Numerical Example
Convergence 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!