Least-squares Migration and Full Waveform Inversion with Multisource Frequency Selection

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.