Transcript Extended Diffraction-Slice Theorem for Wavepath Traveltime

Least-squares Migration and
Full Waveform Inversion with
Multisource Frequency Selection
Yunsong Huang
Sept. 5, 2013
Outline
• 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
Gulf of Mexico Seismic Survey
Predicted data
4
d
Time (s)
L 1 m = d1
L 2 m. = d2
..
Observed data
Goal: Solve overdetermined
System of equations for m
L N m = dN
0
6
X (km)
m
Details of Lm = d
4
d
Time (s)
0
6
X (km)
Reflectivity
or velocity
model
G(s|x)G(x|g)m(x)dx = d(g|s)
Predicted data = Born approximation
Solve wave eqn. to get G’s
m
Standard Migration
vs
Multisource Migration
Romero, Ghiglia, Ober, & Morton, Geophysics, (2000)
Given: d1 and d2
Find: m
T
T
Soln: m=L1 d1 + L2 d2
Given: d1 + d2
Find: m
T
Soln: m = (L1 + L2)(d1+d2)
Benefit: Reduced computation and memory
Liability: Crosstalk noise …
Src. imaging cond. xtalk
T
T
= L1 d1 + L2 d2
T
T
+ L1 d2 + L2 d1
Multisource LSM & FWI
Inverse problem:
arg min J =
m
1
2
~ ~
|| d – L m ||2
misfit
Dd
Iterative update:
~
T
(k+1)
(k)
m
= m + a L Dd
L1Dd1 + L2Dd2
T
T
+ L1 Dd2 + L2 Dd1
T
K=10
K=1
T
Brief Early History: Multisource
Phase Encoded Imaging
Migration
Romero, Ghiglia, Ober, & Morton, Geophysics, (2000)
Waveform Inversion and Least Squares Migration
Krebs, Anderson, Hinkley, Neelamani, Lee, Baumstein,
Lacasse, SEG Zhan+GTS, (2009)
Virieux and Operto, EAGE, (2009)
Dai, and GTS, SEG, (2009)
Biondi, SEG, (2009)
Goal of the Study
Standard
optimization
for LSM/FWI
Speed and quality
comparison
Multisource
optimization
for marine
LSM/FWI
Outline
• 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
Land Multisource FWI
Fixed spread
Simulation geometry must be consistent with
the acquisition geometry
Marine Multisource FWI
Mismatch solution with marine data
Observed
marine data
Simulated
land data
purify
Freq. encoding
Decode & mute
4 Hz
8 Hz
F.T.,
freq. selec.
wrong
misfit
Blend
4 Hz
8 Hz
Outline
• 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
Phase-shift Migration
 Multisource freq. sel. initially implemented here.
domain
decomposition
w
DZ
ky
kx
Z
Y
X
Embarrassingly
parallel
Migration Images (input SNR = 10dB)
an example shot and its aperture
0
304 shots in total
b) Standard Migration
0 1.48
Z (km)
a) Original
X (km)
Computational
gain
c) Standard
Migration with
9.4
1/8 subsampled shots
0
6.75
d) 304 shots/gather
26 iterations
1.48
Z (km)
8.0
6.6
5.4
Conventional migration:
1
0 38
76 X (km) 152
Shots per supergather
3046.75 0
X (km)
6.75
3D Migration Volume
6.7 km
3.7 km
3.7 km
13.4 km
40 x gain in computational
efficiency of OBS data
Outline
• 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
Transients Reduction
4 Hz
8 Hz FDTD
nt
2nt
2nt
transient steady
causal
t
t
periodic
periodic
Computing FWI’s Gradient
periodic
nt
1
transient
2nt
steady
0-lag
correlate
steady
transient
t
forward-propagated
source wavefield
back-propagated
residual wavefield
Multisource FWI Freq. Sel. Workflow
For k=1:K
Select unique frequency for each src
d
d

Filter and blend observed data: dd
dpred
Purify predicted data: dpreddpred
Data residual: Dd=dpred-d
m(k+1)
end
=
m(k)
~T
+ a L Dd
dpred

Quasi-Monte Carlo Mapping
Standard
Random permutation
60
60
Source index
Source index
1
1
Q.M. w/
repelling Coulomb force
1
w index
60
1
w index
60
31 iterations
3 iterations
Quasi-Monte Carlo Mapping
Outline
• 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
Frequency-selection FWI of 2D
Marine Data
• Shots: 60
• Receivers/shot: 84
• Source freq: 8 Hz
• Cable length: 2.3 km
Z (km)
0
4.5
(km/s)
1.5
1.5
0
X (km)
6.8
0
FWI images
Starting model
Standard FWI
(69 iterations)
Multisource FWI
(262 iterations)
1.5
Z (km)
0
1.5
Z (km)
Actual model
0
X (km)
6.8 0
X (km)
6.8
Convergence Rates
Waveform error
0.025
Log normalized
1
Faster initial
convergence rate of
the white curve
Same asymptotic
convergence rate of
the red and white
curves
3.8 x
69
Log iteration number
262
Convergence Rates
Speedup
60 / 2 / 2 / 3.8 = 4
1
Velocity error
0.35
Log normalized
Gain
• 60: sources
Overhead factors:
• 2 x FDTD steps
• 2 x domain size
• 3.8 x iterations
3.8 x
69
Log iteration number
262
Outline
• 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
Workflow: FWI on GOM dataset
Source wavelet estimation
3D to 2D conversion of the data
initial velocity model estimation
Run FWI in multiscales
Generate RTM, CIG & CSG
images
water surface
-1
s
delay: Dt
r
Received direct wave
combined with ghost
Source wavelet
d
b(t )  w(t )
dt
 w(t )   b(t )dt  c
Estimated w(t)
0.8 s
Bandpass filtered to [0, 25] Hz
Power spectrum of (b)
Workflow: FWI on GOM dataset
Source wavelet estimation
data spectra  i / w
3D to 2D conversion of the data
initial velocity model estimation
Run FWI in multiscales
Generate RTM, CIG & CSG
images
d (t )  t
Workflow: FWI on GOM dataset
Source wavelet estimation
3D to 2D conversion of the data
initial velocity model estimation
Run FWI in multiscales
Generate RTM, CIG & CSG
images
traveltime +
semblance
Workflow: FWI on GOM dataset
freq. band: grid size:
Source wavelet estimation
0—6 Hz, 51 x 376
0—15 Hz, 101x 752
0—25 Hz, 201x 1504
3D to 2D conversion of the data
Multisource Freq. Sel.:
initial velocity model estimation
Run FWI in multiscales
Generate RTM, CIG & CSG
images
# steps:
method:
15 Gradient descent w/ line
search.
60 Stochastic gradient descent.
Step size  1/ k
Mini-batch size: 2
496 shots  8 supergathers
Velocity models obtained from:
Z (km)
Traveltime
FWI
Z (km)
cost: 1
Z (km)
cost: 1/8
X (km)
FWIwMFS
Baldplate GOM Dataset
• Model size: 18.8 x 2.5 km
• Shots: 496
• Receivers/shot: 480
• Source freq: 0--25 Hz
• Cable length: 6km
Velocity difference
due to encoding schemes: Q.M. vs standard
Z (km)
FWIwMFS: VQ.M. – Vrandom permutation
X (km)
The freq. sel. scheme is resilient to
specifics of encoding methods
Workflow: FWI on GOM dataset
Source wavelet estimation
3D to 2D conversion of the data
initial velocity model estimation
Run FWI in multiscales
Generate RTM, CIG & CSG
images
Z (km)
RTM image using traveltime tomogram
X (km)
Z (km)
RTM image using FWI tomogram
X (km)
Z (km)
RTM image using FWIwMFS tomogram
X (km)
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
Time (s)
Observed CSG
7
Time (s)
FWI predicted CSG
7
Time (s)
FWIwMFS predicted CSG
7
Time (s)
TRT predicted CSG
7
Outline
• 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
Wavepath Resolution (width)
p
W
s
L
First Fresnel Zone:
|ps| + |pg| = L + l/2
g
⟹ resolution W = 𝜆𝐿
Wavepath Resolution
Outline
• 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
Summary
• 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-tosource codebook
 same quality of the resulting images
compared to the standard approach
• Interbed multiples help fill in
intermediate wavenumber gap.
Acknowledgements
I 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.