least-squares migration and full waveform inversion with multisource frequency selection
DESCRIPTION
Least-squares Migration and Full Waveform Inversion with Multisource Frequency Selection. Yunsong Huang. Sept . 5, 2013. Introduction Multisource Frequency Selection Least-squares migration (LSM) test on 2D and 3D synthetic data Full Waveform Inversion (FWI) - PowerPoint PPT PresentationTRANSCRIPT
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Least-squares Migration and Full Waveform Inversion with
Multisource Frequency Selection
Yunsong Huang
Sept. 5, 2013
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• Introduction• Multisource Frequency Selection
– Least-squares migration (LSM) test on 2D and 3D synthetic data
– Full Waveform Inversion (FWI) test on 2D synthetic and field GOM data
• Resolutions for Wave Equation Imaging • Summary
Outline
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Gulf of Mexico Seismic Survey
m
L m = d
L m = d1 1
L m = d2 2...N N
Time (s)
6 X (km)
4
0
1 d
Goal: Solve overdeterminedSystem of equations for m
Predicted data Observed data
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Details of Lm = d
Time (s)
6 X (km)
4
0
1 d
G(s|x)G(x|g)m(x)dx = d(g|s)
Reflectivityor velocity
model
Predicted data = Born approximationSolve wave eqn. to get G’s
m
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Standard Migration vs Multisource Migration
Benefit: Reduced computation and memory
Liability: Crosstalk noise …
Given: d1 and d2
Find: mSoln: m=L1 d1 + L2 d2
T T
Given: d1 + d2
Find: m
= L1 d1 + L2 d2T T
+ L1 d2 + L2 d1T T
Soln: m = (L1 + L2)(d1+d2)T
Romero, Ghiglia, Ober, & Morton, Geophysics, (2000)
Src. imaging cond. xtalk
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K=1K=10
Multisource LSM & FWI
Inverse problem:|| d – L m ||2
~~12
J =arg minm
Dd misfit
m(k+1) = m(k) + a L Dd~T
Iterative update:
+ L1 Dd2 + L2 Dd1T T
L1Dd1 + L2Dd2T T
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Brief Early History: Multisource
Phase Encoded Imaging
Romero, Ghiglia, Ober, & Morton, Geophysics, (2000)
Krebs, Anderson, Hinkley, Neelamani, Lee, Baumstein, Lacasse, SEG Zhan+GTS, (2009)
Virieux and Operto, EAGE, (2009)Dai, and GTS, SEG, (2009)
Migration
Waveform Inversion and Least Squares Migration
Biondi, SEG, (2009)
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Standard optimization
for LSM/FWI
Goal of the Study
Multisource optimization for marine LSM/FWI
Speed and quality
comparison
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• Introduction• Multisource Frequency Selection
– Least-squares migration (LSM) test on 2D and 3D synthetic data
– Full Waveform Inversion (FWI) test on 2D synthetic and field GOM data
• Resolutions for Wave Equation Imaging • Summary
Outline
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Land Multisource FWIFixed spread
Simulation geometry must be consistent with the acquisition geometry
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4 Hz 8 Hz
Marine Multisource FWI
Simulated land data
Observedmarine data
Mismatch solution with marine data
wrong misfit
Freq. encoding
8 Hz4 Hz
Blend
Decode & mutepurify
4 Hz 8 Hz
F.T.,freq. selec.
4 Hz 8 Hz
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• Introduction• Multisource Frequency Selection
– Least-squares migration (LSM) test on 2D and 3D synthetic data
– Full Waveform Inversion (FWI) test on 2D synthetic and field GOM data
• Resolutions for Wave Equation Imaging • Summary
Outline
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XYZ
kxky
w
Phase-shift Migration
Embarrassinglyparallel
domaindecomposition
DZ
Multisource freq. sel. initially implemented here.
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0 6.75X (km)
0Z
(km
)1.
48
a) Original b) Standard Migration
Migration Images (input SNR = 10dB)
0 6.75X (km)
c) Standard Migration with 1/8 subsampled shots
0Z
(km
)1.
48
0 6.75X (km)
d) 304 shots/gather26 iterations
304 shots in total an example shot and its aperture
38 76 152 304
9.48.06.65.4
1
Shots per supergather
Computational gain
Conventional migration:
SNR=30dB
Com
p. G
ain
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3D Migration Volume
6.7 km
True reflectivities
3.7 km
Conventional migration
13.4 km
256 shots/super-gather, 1
6 iterations
40 x gain in computational efficiency of OBS data
3.7 km
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• Introduction• Multisource Frequency Selection
– Least-squares migration (LSM) test on 2D and 3D synthetic data
– Full Waveform Inversion (FWI) test on 2D synthetic and field GOM data
• Resolutions for Wave Equation Imaging • Summary
Outline
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Transients Reduction
nt 2nt
causal
periodic periodic
steadytransient
t
t
8 Hz4 Hz
2nt
FDTD
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periodic
0-lagcorrelate
back-propagated residual wavefieldsteady transient
forward-propagatedsource wavefield
steady
2nt1tnt
transient
Computing FWI’s Gradient
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Multisource FWI Freq. Sel. Workflow
m(k+1) = m(k) + a L Dd~T
For k=1:K
end
Filter and blend observed data: dd
d d
Purify predicted data: dpreddpred
dpred dpred
Data residual: Dd=dpred-d
Select unique frequency for each src
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Quasi-Monte Carlo Mapping
Standard Random permutation
w index1 60
Sour
ce in
dex
160
Sour
ce in
dex
160
w index1 60
Q.M. w/repelling Coulomb force
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Quasi-Monte Carlo Mapping3
iter
atio
ns31
ite
ratio
ns
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• Introduction• Multisource Frequency Selection
– Least-squares migration (LSM) test on 2D and 3D synthetic data
– Full Waveform Inversion (FWI) test on 2D synthetic and field GOM data
• Resolutions for Wave Equation Imaging • Summary
Outline
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Frequency-selection FWI of 2D Marine Data
• Source freq: 8 Hz• Shots: 60• Receivers/shot: 84 • Cable length: 2.3 km
Z (k
m)
01.
5
0 6.8X (km)
4.5
1.5
(km/s)
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FWI imagesStarting modelActual model
Z (k
m)
01.
5
Standard FWI(69 iterations)
Z (k
m)
01.
5
0 X (km) 6.8
Multisource FWI(262 iterations)
0 X (km) 6.8
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Convergence RatesWaveform error
Log
nor
mal
ized
Log iteration number
10.
025
1 26269
by individual sources1 supergather, Quasi-Monte Carlo encoding
3.8 x
1 supergather,
standard encoding
Same asymptotic convergence rate of the red and white curves
Faster initial convergence rate of the white curve
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Convergence RatesVelocity error
Log
nor
mal
ized
Log iteration number
10.
35
1 26269
1 supergather,
standard encoding
by individual sources 3.8 x
Speedup60 / 2 / 2 / 3.8 = 4
Gain• 60: sourcesOverhead factors:• 2 x FDTD steps• 2 x domain size• 3.8 x iterations
1 supergather, Quasi-Monte Carlo encoding
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• Introduction• Multisource Frequency Selection
– Least-squares migration (LSM) test on 2D and 3D synthetic data
– Full Waveform Inversion (FWI) test on 2D synthetic and field GOM data
• Resolutions for Wave Equation Imaging • Summary
Outline
![Page 28: Least-squares Migration and Full Waveform Inversion with Multisource Frequency Selection](https://reader033.vdocument.in/reader033/viewer/2022061519/5681655e550346895dd7e170/html5/thumbnails/28.jpg)
Source wavelet estimation
3D to 2D conversion of the data
initial velocity model estimation
Run FWI in multiscales
Generate RTM, CIG & CSG images
Workflow: FWI on GOM dataset
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water surface -1 delay: Dt
s r
( ) ( )w t b t dt c
( ) ( )db t w tdt
Received direct wavecombined with ghost
Source wavelet
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Estimated w(t)
Bandpass filtered to [0, 25] Hz
Power spectrum of (b)
0.8 s
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Source wavelet estimation
3D to 2D conversion of the data
initial velocity model estimation
Run FWI in multiscales
Workflow: FWI on GOM dataset
data spectra /i w
( )d t t
Generate RTM, CIG & CSG images
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Source wavelet estimation
3D to 2D conversion of the data
initial velocity model estimation
Run FWI in multiscales
Workflow: FWI on GOM dataset
traveltime + semblance
Generate RTM, CIG & CSG images
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Generate RTM, CIG & CSG images
Source wavelet estimation
3D to 2D conversion of the data
initial velocity model estimation
Run FWI in multiscales
Workflow: FWI on GOM dataset
0—6 Hz, 51 x 3760—15 Hz, 101x 7520—25 Hz, 201x 1504
Multisource Freq. Sel.:# steps: method:
freq. band: grid size:
15
60
Gradient descent w/ line search.Stochastic gradient descent. Step size 1/ k
Mini-batch size: 2496 shots 8 supergathers
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Z (k
m)
Z (k
m)
Traveltime
FWIcost: 1
X (km)
Z (k
m)
FWIwMFScost: 1/8
Velocity models obtained from:
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FWIwMFS: VQ.M. – Vrandom permutation
Velocity difference due to encoding schemes: Q.M. vs standard
X (km)
Z (k
m)
• Model size: 18.8 x 2.5 km • Source freq: 0--25 Hz• Shots: 496 • Cable length: 6km• Receivers/shot: 480
Baldplate GOM Dataset
The freq. sel. scheme is resilient to specifics of encoding methods
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Source wavelet estimation
3D to 2D conversion of the data
initial velocity model estimation
Run FWI in multiscales
Workflow: FWI on GOM dataset
Generate RTM, CIG & CSG images
![Page 38: Least-squares Migration and Full Waveform Inversion with Multisource Frequency Selection](https://reader033.vdocument.in/reader033/viewer/2022061519/5681655e550346895dd7e170/html5/thumbnails/38.jpg)
X (km)
Z (k
m)
RTM image using traveltime tomogram
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Z (k
m)
X (km)
RTM image using FWI tomogram
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Z (k
m)
X (km)
RTM image using FWIwMFS tomogram
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Zoomed views of the RTM images
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Zoomed views of the RTM images
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Zoomed views of the RTM images
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CIGs for traveltime tomogram
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CIGs for FWI tomogram
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CIGs for FWIwMFS tomogram
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Observed CSG
7
Tim
e (s
)
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FWI predicted CSG
7
Tim
e (s
)
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FWIwMFS predicted CSG
7
Tim
e (s
)
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TRT predicted CSG
7
Tim
e (s
)
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• Introduction• Multisource Frequency Selection
– Least-squares migration (LSM) test on 2D and 3D synthetic data
– Full Waveform Inversion (FWI) test on 2D synthetic and field GOM data
• Resolutions for Wave Equation Imaging • Summary
Outline
![Page 52: Least-squares Migration and Full Waveform Inversion with Multisource Frequency Selection](https://reader033.vdocument.in/reader033/viewer/2022061519/5681655e550346895dd7e170/html5/thumbnails/52.jpg)
gs
p
L
W First Fresnel Zone: |ps| + |pg| = L + l/2
resolution W =
Wavepath Resolution (width)
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Wavepath Resolution
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• Introduction• Multisource Frequency Selection
– Least-squares migration (LSM) test on 2D and 3D synthetic data
– Full Waveform Inversion (FWI) test on 2D synthetic and field GOM data
• Resolutions for Wave Equation Imaging • Summary
Outline
![Page 56: Least-squares Migration and Full Waveform Inversion with Multisource Frequency Selection](https://reader033.vdocument.in/reader033/viewer/2022061519/5681655e550346895dd7e170/html5/thumbnails/56.jpg)
• The aperture mismatch problem that afflicts multisource inversion of marine data is overcome by frequency-selection encoding. 4 speedup for the multisource LSM and FWI
on the synthetic and field marine data robust with respect to the frequency-to-
source codebook same quality of the resulting images
compared to the standard approach• Interbed multiples help fill in
intermediate wavenumber gap.
Summary
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AcknowledgementsI thank
– my advisor, Dr. Gerard T. Schuster, for his guidance, support and encouragement;
– my committee members for the supervision over my dissertation;
– the sponsors of CSIM consortium for their financial support;
– my fellow graduate students for the collaborations and help over last 4 years.