ps, ssp, pspi, ffd

PS, SSP, PSPI, FFDPS, SSP, PSPI, FFDSSPSSP

FFDFFD

KMKM

PSPIPSPI

k

k z

x

k = k 1 – k z

2

k 2x ~ k (1 – k + ..)

2x

k 22

P(x,z,) = P(x,0 ,) e zik(x) z

PS, SSP, PSPI, FFDPS, SSP, PSPI, FFDk = k 1 – k z

2

k 2x

-1 1.2

1

k z ~ k(1 – k ) 2x

k 22

k z ~ k (1 – .43 ) 2

21 -.5

= k 2x

k 2

P(x,z,) = P(x,0 ,) e zik(x)z

k

k

x

z

SSP MigrationSSP Migration

k = k(x) 1 – k z

2

k(x)2x = k 1 – k

2

k 2x - k

0

0

Thin lens

P(x,z,) = P(x,0 ,) e zik(x)z

FFD MigrationFFD Migration

k = k(x) 1 – k z

2

k(x)2x = k 1 – k

2

k 2x - k

0

0

Thin lens

P(x,z,) = P(x,0 ,) e zik(x)z

k = k(x) 1 – k z

2

k(x)2x = k 1 – k

2

k 2x - k

0

0

Thin lens

FFD MigrationFFD MigrationP(x,z,) = P(x,0 ,) e zik(x)z

FFD MigrationFFD MigrationP(x,z,) = P(x,0 ,) e zik(x)z

FFD MigrationFFD Migrationother term

P(x,z,) = P(x,0 ,) e zik(x)z

FFD MigrationFFD Migration

PDE associated withother term

other term

Rearrange PDE

P(x,z,) = P(x,0 ,) e zik(x)z

FFD MigrationFFD Migration

Substitute FD approximations into above

P(x,z,) = P(x,0 ,) e zik(x)z

FFD MigrationFFD Migration

Substitute FD approximations into above

P(x,z,) = P(x,0 ,) e zik(x)z

FFD MigrationFFD Migration

k = k(x) 1 – k z

2

k(x)2x = k 1 – k

2

k 2x - k

0

0

Thin lens

P(x,z,) = P(x,0 ,) e zik(x)z

PS, SSP, PSPI, FFDPS, SSP, PSPI, FFD

PS, SSP, PSPI, FFDPS, SSP, PSPI, FFD

SummarySummaryCost:Cost:

Accuracy:Accuracy: KMKM SSPSSP

PSPIPSPI FFDFFD

Course SummaryCourse Summary

m(x)= (g,s,x) G(g|x)d(g|x)G(x|s)dgdsg,s,

G(g|x) = G(g|x) + G(g|x) d(g|x) = d(g|x) + d(x|g)

G(g|x) = G(g|x) d(g|x) = d(g|x)

Filter

RTM

Asymptotic G

KM Phase Shift Beam

1-way G Asymptotic G+ Fresnel Zone

1980

Multisource SeismicMultisource SeismicImagingImaging

vs

copper

VLIW

Superscalar

RISC

1970 1990 2010

1

100

100000

10

1000

10000

Aluminum

Year

202020001980

CPU Speed vs Year

OUTLINEOUTLINE

Theory ITheory I

Theory IITheory II

Numerical ResultsNumerical Results

RTM Problem & Possible Soln.RTM Problem & Possible Soln.

• Problem:Problem: RTM computationally costly RTM computationally costly

• Solution:Solution: Multisource LSM RTM Multisource LSM RTM

1919

Preconditioning speeds up by factor 2-3Preconditioning speeds up by factor 2-3

LSM reduces crosstalkLSM reduces crosstalk

5

Multisource Migration:Multisource Migration: mmmigmig=L=LTTdd

Forward Model:Forward Model:

Multisource Least Squares Migration Multisource Least Squares Migration

d +d +dd =[ =[L +L +LL ]m ]m11 222211

LL{dd{

=[=[L +L +LL ]( ](dd + + dd ) ) 11 222211

TT TT

= = L d +L d +L dL d + + 11 222211

TT TT

LL dd + +L L dd22 112211

Crosstalk noiseCrosstalk noiseStandard migrationStandard migration

TT TT

Multisource Least Squares Phase-encoded Multisource Least Squares Phase-encoded Migration Migration

=[=[NN L +L +N LN L ](N ](N dd + + NN dd ) ) 11 222211 22 221111

mmmigmig

==N*NN*N L d +L d +N*N L dN*N L d + N* + N*NN L L dd + + N*N*NN L L dd 11 2211 22 221111 11 11 11 22 1122 22 22 22

TT TT

TT TT TT TT

** **

= = L d +L d + L d L d11 11 22 22

Standard migrationStandard migration

If <N N > = If <N N > = (i-j)(i-j)i j

Crosstalk noiseCrosstalk noise

Orthogonal phase encoding s.t. <Orthogonal phase encoding s.t. <N* N* N >=0N >=01 1 22

Key AssumptionKey Assumption

d(t) =d(t) =

Zero-mean white noise: <N(t)>=0; <N(t) N(t’) >=0

++ M= Stack Number

Am

plit

ude

k=1k=1

MM

N(t )N(t )(k)(k)

<N(t)> ~<N(t)> ~

k=1k=1

MM

[ S(t) ][ S(t) ]22

M1

SNR SNR

M

M vs M

k=1k=1

MM

[ N(t) ][ N(t) ]22

~

(k)(k)

(k)(k)

[ S(t) ][ S(t) ]22

k=1k=1

MM

[ N(t) ][ N(t) ]22 22

~(k)(k)

MM22

[ S(t) ][ S(t) ]22

~MM

22

M M

k=1k=1

MM

[S(t) +N(t) ][S(t) +N(t) ]

Multisource S/N RatioMultisource S/N Ratio

# geophones/CSG# geophones/CSG

# CSGs# CSGs

L [d + d +.. ]1 221

d +d T d , d 2211

L [d + d + … ]1 2

T , …. +….

Multisrc. Migration vs Standard Migration

# iterations# iterations

Iterative Multisrc. Migration vs Standard Migration

vs

vs

MSMSS-1

M~~

# geophones/CSG# geophones/CSG # CSGs# CSGs

MSMI

SummarySummary

Time Statics

Time+Amplitude Statics

QM Statics

1. Multisource crosstalk term analyzed analytically1. Multisource crosstalk term analyzed analytically

2. Crosstalk decreases with increasing 2. Crosstalk decreases with increasing , randomness, , randomness, dimension, iteration #, and decreasing depthdimension, iteration #, and decreasing depth

3. Crosstalk decrease can now be tuned3. Crosstalk decrease can now be tuned

4. Some detailed analysis and testing needed to refine 4. Some detailed analysis and testing needed to refine predictions.predictions.

LL dd + +L L dd22 112211

TT TT

OUTLINEOUTLINE

Theory ITheory I

Theory IITheory II

Numerical ResultsNumerical Results

0Z

k(m

)3

0 X (km) 16

The Marmousi2 Model

The area in the white box is used for S/N calculation.

0 X (km) 16

0Z

k(m

)3

0Z

(k

m)

3

0 X (km) 16

Conventional Source: KM vs LSM (50 iterations)

0 X (km) 16

0Z

k(m

)3

0Z

(k

m)

3

0 X (km) 16

200-source Supergather: KM vs LSM (300 its.)

S/N

0

1 Number of Iterations 300

S/N =7

The S/N of MLSM image grows as the square root of the number of iterations.

I

• Fast Multisource Least Squares Fast Multisource Least Squares Phase Shift.Phase Shift.

• Multisource Waveform Inversion (Ge Zhan)Multisource Waveform Inversion (Ge Zhan)

• Theory of Crosstalk Noise (Schuster)Theory of Crosstalk Noise (Schuster)

8

Multisource TechnologyMultisource Technology

The True Model

• use constant velocity model with c = 2.67 km/s

• center frequency of source wavelet f = 20 Hz

X (km)

Z (

km)

Reflectivity, SEG/EAGE Salt Model

0 1 2 3 4 5

0

0.2

0.4

0.6

0.8

1

1.2

Multi-source PSLSM

X (km)

Z (k

m)

Reflectivity, Ten 10-source supergathers

0 1 2 3 4 5

0

0.2

0.4

0.6

0.8

1

1.2

• 645 receivers and 100 sources, equally spaced 10 sets of sources, staggered; each set constitutes a supergather

• 50 iterations of steepest descent

Single-source PSLSM

• 645 receivers and 100 sources, equally spaced 100 individual shots

• 50 iterations of steepest descent

X (km)

Z (k

m)

Reflectivity, 100 single source gathers

0 1 2 3 4 5

0

0.2

0.4

0.6

0.8

1

1.2

Multi-Source Waveform Inversion StrategyMulti-Source Waveform Inversion Strategy(Ge Zhan) (Ge Zhan)

Generate multisource field data with known time shift

Generate synthetic multisource data with known time shift from estimated

velocity model

Multisource deblurring filter

Using multiscale, multisource CG to update the velocity model with

regularization

Initial velocity model

144 shot gathers144 shot gathers

3D SEG Overthrust Model(1089 CSGs)

15 km

3.5 km

15 km

3.5 km

Dynamic QMC TomogramDynamic QMC Tomogram (99 CSGs/supergather)(99 CSGs/supergather)

Static QMC TomogramStatic QMC Tomogram(99 CSGs/supergather)(99 CSGs/supergather)

15 km

Dynamic Polarity TomogramDynamic Polarity Tomogram(1089 CSGs/supergather)(1089 CSGs/supergather)

Numerical ResultsNumerical Results

OUTLINEOUTLINE

Theory ITheory I

Theory IITheory II

Numerical ResultsNumerical Results

Multisource Least Squares Migration Multisource Least Squares Migration Crosstalk term

Time Statics

Time+Amplitude Statics

QM Statics

36

SummarySummaryCrosstalk term

Time Statics

Time+Amplitude Statics

QM Statics

1. Multisource crosstalk term analyzed analytically1. Multisource crosstalk term analyzed analytically

2. Crosstalk decreases with increasing 2. Crosstalk decreases with increasing , randomness, , randomness, dimension, and decreasing depthdimension, and decreasing depth

3. Crosstalk decrease can now be tuned3. Crosstalk decrease can now be tuned

4. Some detailed analysis and testing needed to refine 4. Some detailed analysis and testing needed to refine predictions.predictions.

37

Multisource Migration:Multisource Migration: mmmigmig=L=LTTdd

Forward Model:Forward Model:

Multisource Least Squares Migration Multisource Least Squares Migration

d +d =[d +d =[L +L ]mL +L ]m11 222211

LL{dd{Standard migration

Crosstalk term

Phase encodingPhase encoding

Kirchhoff kernelKirchhoff kernel

34

Multisource Least Squares Migration Multisource Least Squares Migration Crosstalk term

35

Multisource Least Squares Migration Multisource Least Squares Migration Crosstalk term

Time Statics

Time+Amplitude Statics

QM Statics

36

Crosstalk TermCrosstalk Term

Time Statics

Time+Amplitude Statics

QM Statics

LL dd + +L L dd22 112211

TT TT

SummarySummaryCrosstalk term

Time Statics

Time+Amplitude Statics

QM Statics

1. Multisource crosstalk term analyzed analytically1. Multisource crosstalk term analyzed analytically

2. Crosstalk decreases with increasing 2. Crosstalk decreases with increasing , randomness, , randomness, dimension, and decreasing depthdimension, and decreasing depth

3. Crosstalk decrease can now be tuned3. Crosstalk decrease can now be tuned

4. Some detailed analysis and testing needed to refine 4. Some detailed analysis and testing needed to refine predictions.predictions.

37

Multisource FWI SummaryMultisource FWI Summary(We need faster migration algorithms & better velocity models)(We need faster migration algorithms & better velocity models)

IO 1 vs 1/20

Cost 1 vs 1/20 or better

Resolution dx 1 vs 1

Sig/MultsSig ?

Stnd. FWI Multsrc. FWIStnd. FWI Multsrc. FWI

Key AssumptionKey Assumption

<d(t)>= <S(t)> + <N(t)><d(t)>= <S(t)> + <N(t)>

Zero-mean white noise: <N>=0; <N N >=0i j

++ n= Stack Number

Am

plit

ude

<N(t)> ~ <N(t)> ~ 22 n <S(t)> ~ <S(t)> ~

22 n 22

k=1k=1

nn

N(t )N(t )(k)(k)

<N(t)> ~<N(t)> ~1/n

<N(t) > ~<N(t) > ~ 22

k=1k=1

nn

[ N(t ) ][ N(t ) ](k)(k) 22

1/n

<N(t) > ~<N(t) > ~ 22

k=1k=1

nn

[ N(t ) ][ N(t ) ](k)(k) 22

1/n