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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 Presentation
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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) test on 2D synthetic and field GOM data
• Resolutions for Wave Equation Imaging • Summary
Outline
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
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
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
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
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)
Standard optimization
for LSM/FWI
Goal of the Study
Multisource optimization for marine LSM/FWI
Speed and quality
comparison
• 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
Land Multisource FWIFixed spread
Simulation geometry must be consistent with the acquisition geometry
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
• 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
XYZ
kxky
w
Phase-shift Migration
Embarrassinglyparallel
domaindecomposition
DZ
Multisource freq. sel. initially implemented here.
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
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
• 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
Transients Reduction
nt 2nt
causal
periodic periodic
steadytransient
t
t
8 Hz4 Hz
2nt
FDTD
periodic
0-lagcorrelate
back-propagated residual wavefieldsteady transient
forward-propagatedsource wavefield
steady
2nt1tnt
transient
Computing FWI’s Gradient
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
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
Quasi-Monte Carlo Mapping3
iter
atio
ns31
ite
ratio
ns
• 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
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)
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
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
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
• 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
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
water surface -1 delay: Dt
s r
( ) ( )w t b t dt c
( ) ( )db t w tdt
Received direct wavecombined with ghost
Source wavelet
Estimated w(t)
Bandpass filtered to [0, 25] Hz
Power spectrum of (b)
0.8 s
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
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
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
Z (k
m)
Z (k
m)
Traveltime
FWIcost: 1
X (km)
Z (k
m)
FWIwMFScost: 1/8
Velocity models obtained from:
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
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
X (km)
Z (k
m)
RTM image using traveltime tomogram
Z (k
m)
X (km)
RTM image using FWI tomogram
Z (k
m)
X (km)
RTM image using FWIwMFS tomogram
Zoomed views of the RTM images
Zoomed views of the RTM images
Zoomed views of the RTM images
CIGs for traveltime tomogram
CIGs for FWI tomogram
CIGs for FWIwMFS tomogram
Observed CSG
7
Tim
e (s
)
FWI predicted CSG
7
Tim
e (s
)
FWIwMFS predicted CSG
7
Tim
e (s
)
TRT predicted CSG
7
Tim
e (s
)
• 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
gs
p
L
W First Fresnel Zone: |ps| + |pg| = L + l/2
resolution W =
Wavepath Resolution (width)
Wavepath Resolution
• 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
• 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
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.