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