Multisource Full Waveform Inversion of Marine Streamer Data
with Frequency Selection
Yunsong Huang and Gerard SchusterKAUST
• Goal of the study• Multisource
– Mismatch solution with marine data
• Low-discrepancy frequency coding• Numerical results • Conclusions
Outline
Standard optimization
for FWI
Goal of the Study
Multisource optimization for marine
FWI
Speed and quality
comparison
• Aim of the study• Multisource Migration
– Least Squares Multisource Migration
• Low-discrepancy frequency coding• Numerical results • Conclusions
Outline
Standard Migration vs Multisource Migration
Benefit: Reduced computation and memory
Liability: Crosstalk noise …
Given: d1 and d2
Find: m
Soln: m=L1 d1 + L2 d2T 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~~1
2J =arg min
m
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)
• Aim of the study• Multisource Migration
– Mismatch solution with marine data
• Low-discrepancy frequency coding• Numerical results • Conclusions
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
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
• Aim of the study• Multisource
– Mismatch solution with marine data• Low-discrepancy frequency coding• Numerical results • Conclusions
Outline
Low-discrepancy Frequency Encoding
Fre
qu
ency
ind
ex1
60
Source index1 60 Source index1 60
Low-discrepancyencodingencoding
Standard
Fre
qu
ency
ind
ex1
60
Fre
qu
ency
ind
ex1
60
• Aim of the study• Multisource
– Mismatch solution with marine data
• Low-discrepancy frequency coding• Numerical results • Conclusions
Outline
Frequency-selection FWI of 2D Marine Data
• Source freq: 8 Hz• Shots: 60• Receivers/shot: 84 • Cable length: 2.3 km
Z (
km
)0
1.5
0 6.8X (km)
4.5
1.5
(km/s)
FWI images
Starting modelActual model
Z (
km
)0
1.5
Standard FWI(69 iterations)
Z (
km
)0
1.5
0 X (km) 6.8
Multisource FWI(262 iterations)
0 X (km) 6.8
Convergence Rates
Waveform error
Log
nor
mal
ized
Log iteration number
10.
025
1 26269
by individual sources1 supergather, low-discrepancy 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 Rates
Velocity 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 iteration
number1 supergather, low-discrepancy encoding
Convergence Rates
Velocity error (normalized)
10.
75
iteration number1
10
standard encoding
Low-discrepancy encoding is
12% to 3x faster initially than
Standard encoding
• Frequency selection is implemented in FDTD– 2 x time steps per forward or backward
modeling
• Low-discrepancy frequency encoding – affects no asymptotic rate of convergence– helps to reduce model error in the beginning of
simulation
• 4x speedup for the multisource FWI on the synthetic marine model
Conclusions
ThanksSponsors of the CSIM (csim.kaust.edu.sa)
consortium at KAUST & KAUST HPC
Thank you!
• At lower (say 1/2) frequencies, the frequency selection strategy sees fewer frequency resources, but Computation cost:– (Nx x Nz) x Ns x Nt is reduced by 1/16,– since each factor is halved.
This part does not degrade the overall speedup much.
In the case of multiscale
Convergence Rates
Velocity error (normalized)
10.
75
iteration number1 10
by individual sources
1 supergather,
standard encoding
H
LSlew rate = H/L
1 supergather, low-discrepancy encoding