goal: learn about potential, principles and

Goal:Goal: Learn about potential, principles andLearn about potential, principles and

FormatFormat: Lecture, sometimes : Lecture, sometimes followed by exercise. Course project. followed by exercise. Course project.

. .

TopicsTopics: Deterministic interferometry, stochastic : Deterministic interferometry, stochastic interferometry, 3x3 classification matrix, interferometry, 3x3 classification matrix, reciprocity theorems, applications to VSP, reciprocity theorems, applications to VSP, SSP, OBS, and Xwell data. SSP, OBS, and Xwell data.

Seismic Interferometry CourseSeismic Interferometry Course

(Schuster, Cambridge Press) (Schuster, Cambridge Press) algorithms of seismic interferometryalgorithms of seismic interferometry

Seismic Interferometry:Seismic Interferometry: Instead of using just primaryInstead of using just primary

arrivals, you also use the multiples for a wider viewarrivals, you also use the multiples for a wider view

Overview of Seismic Interferometry Overview of Seismic Interferometry and Applications in Explorationand Applications in Exploration

Gerard SchusterGerard Schuster

KAUST & University of UtahKAUST & University of Utah

OutlineOutline•What is Seismic Interferometry?What is Seismic Interferometry?

•ApplicationsApplications

•ConclusionsConclusions

•VSP->SSP (surface seismic profile)VSP->SSP (surface seismic profile)•VSP->SWP (single well profile)VSP->SWP (single well profile)•SSP->SSP SSP->SSP

SELECTIVE HISTORY SEISMIC INTERFEROMETRYSELECTIVE HISTORY SEISMIC INTERFEROMETRY

1968 1968 Claerbout V(z)+passiveClaerbout V(z)+passive

1980s1980s Cole+Claerbout V(x,y,z)+passive?Cole+Claerbout V(x,y,z)+passive?

1990s1990s Scherbaum earthquake V(z)+passiveScherbaum earthquake V(z)+passive

20012001 Utah: Stationary Phase Theory, SSP, and VSPUtah: Stationary Phase Theory, SSP, and VSP

Seismic Interferometric imaging, deterministicSeismic Interferometric imaging, deterministic

2002-042002-04 Wapenaar Recip. Thm. Correlation TypeWapenaar Recip. Thm. Correlation Type

Shell Virtual Sources:Calvert+BakulinShell Virtual Sources:Calvert+Bakulin

Snieder Stationary Phase RedatumingSnieder Stationary Phase Redatuming

Gerstoft + others Surface Wave InterferometryGerstoft + others Surface Wave Interferometry

19991999 Rickett+Claerbout V(z) HelioseismologyRickett+Claerbout V(z) HelioseismologyDaylight ImagingDaylight Imaging , passive, passive

1970s 1970s Berryhill model-based redatumBerryhill model-based redatum

redatum

http://images.google.com/imgres?imgurl=http://www.dailygalaxy.com/my_weblog/images/2007/11/19/sun_full_disk_soho_09_14_1997_2.jpg&imgrefurl=http://www.dailygalaxy.com/my_weblog/2007/11/&usg=__y0wA1MUQAAoGyODDbKltAM7r_XE=&h=262&w=300&sz=34&hl=en&start=13&tbnid=AOCLCo69H80bmM:&tbnh=101&tbnw=116&prev=/images?q=helioseismology+daylight+imaging&gbv=2&hl=en

SELECTIVE HISTORY SEISMIC INTERFEROMETRYSELECTIVE HISTORY SEISMIC INTERFEROMETRY

redatum

Surface wavesShapiro, Derode, Larose, Dong, Shapiro, Derode, Larose, Dong,

Xue, Halliday, Curtis,Xue, Halliday, Curtis,

Van Mannen, Robertsson,Van Mannen, Robertsson,

Gerstoft,Gerstoft, Sabra, Kepler, Roux, Sabra, Kepler, Roux,

He, Ritzwoller, Campillo etcHe, Ritzwoller, Campillo etcInterpolationSheng, Curry, Berkhout, Wang,Sheng, Curry, Berkhout, Wang,

Dong, Hanafy, Cao, etcDong, Hanafy, Cao, etc

Extrapolation

Dong, Hanafy, Cao, etcDong, Hanafy, Cao, etc

Theory: Acoustic, EM, Elastic, Potential

Fink, Wapenaar, Snieder, Papanicolaou, Blomgren,Fink, Wapenaar, Snieder, Papanicolaou, Blomgren,

Slob, Thorbeck, van der Neut etcSlob, Thorbeck, van der Neut etc

Refractions

Boise State Univ, DongBoise State Univ, Dong

Passive Reservoir

Shell, Draganov, Shell, Draganov,

Wapenaar, Snieder, Polleto Wapenaar, Snieder, Polleto

Miranda, etc Miranda, etc

Exploration

Curry, Guitton, Shragg, Yu,Curry, Guitton, Shragg, Yu,

ArtmanArtman

Yu, Calvert, Bakulin,Yu, Calvert, Bakulin, He, He,

Jiang, Hornby, Xiao, Willis, Lu,Jiang, Hornby, Xiao, Willis, Lu,

Toksoz, Campman etcToksoz, Campman etc

VSP

Model TankScales, Malcolm etcScales, Malcolm etc

Volcanoes+Coda

Snieder, Scales, Gret et alSnieder, Scales, Gret et al

Engineering Xwell

Minato, Onishi, Matsuoka etcMinato, Onishi, Matsuoka etc

Nowack, Sheng, Curtis etcNowack, Sheng, Curtis etc

Earthquakes

EMSlob, Wapenaar, SniederSlob, Wapenaar, Snieder

What is Seismic Interferometry?What is Seismic Interferometry?Answer: Redatums data byAnswer: Redatums data by correlationcorrelation of trace pairs andof trace pairs and

stacking the result for different shot positions stacking the result for different shot positions

A

G(G(BB||xx)) G(G(BB||xx))** = G(= G(BB||BB)) Point Source Response

with src at B and rec at B

Assume aAssume a

VSP experimentVSP experiment

directF.S. multiple

iiee

xxBB+ + BBzz zzB B iiee

xxBB iiee

BBzz zzBB=

VSP => SSPVSP => SSP

BB

zz zz

Phase of CommonPhase of Common

Raypath CancelsRaypath Cancels

virtual

primary

BB

xx

zz

virtual

source

correlationcorrelation

•No need to know src. locationNo need to know src. location

•No need to know src excitation timeNo need to know src excitation time

stackingstacking

•Redatum source closer to targetRedatum source closer to target

s

A

G(G(BB||xx)) G(G(BB||xx))** = G(= G(BB||BB)) Point Source Response

with src at B and rec at B

iiee

xxBB+ + BBzz zzB B iiee

xxBB iiee

BBzz zzBB=

zz zz

Phase of CommonPhase of Common

Raypath CancelsRaypath Cancelsxx

zz

x

xx

~~~~

•No need to know src. locationNo need to know src. location

•No need to know src excitation timeNo need to know src excitation time

•Redatum source closer to targetRedatum source closer to target

Answer: Redatums data byAnswer: Redatums data by correlationcorrelation of trace pairs andof trace pairs and

stacking the result for different shot positions stacking the result for different shot positions

correlationcorrelation

stackingstacking

What is Seismic Interferometry?What is Seismic Interferometry?

Reciprocity Correlation EquationReciprocity Correlation Equation2D Reflection Data2D Reflection Data

Phase of Common Raypath Cancels

xx xx

AAAABB

VSPVSPVSPVSP SSPSSP

BB AA

Old Multiples Become

New Primaries!

x

= G(= G(AA||BB)) G(G(x|x|BB)*)* G(G(x|x|AA)) k ~~~~

•No need to know VSP rec location at x

•No need to know receiver statics

Reciprocity Correlation EquationReciprocity Correlation Equation2D Reflection Data2D Reflection Data

x

= G(= G(AA||BB)) G(G(x|x|BB)*)* G(G(x|x|AA)) k

xx xx

AAAABB AABB

Old Multiples Become

New Primaries!

{ }{ }G(G(AA||xx))G(G(BB||xx)) G(G(BB||xx)) - G(- G(AA||xx)) d x

2= = G(G(AA||BB) - ) - G(G(BB||AA))n* * *

SS wellwell

(Wapenaar, 2004)(Wapenaar, 2004)

1-way+ far-field approx.1-way+ far-field approx.

Problems: FiniteProblems: Finite source aperturesource aperture

No attenuationNo attenuationDeghostfilt.,Deghostfilt., U & D separationU & D separation

Muting, Least squares or MDDMuting, Least squares or MDD

Atten. CompensationAtten. Compensation

Finite aperture leads to incomplete G(B|A)

Prediction Multiple by Convolution (SRME)Prediction Multiple by Convolution (SRME)

Prediction Primaries by CrosscorrelationPrediction Primaries by Crosscorrelation

(Crosscorrelation migration interferometry)(Crosscorrelation migration interferometry)

**

BB CCAA BB CC AA BB

50005000

130001300000 5600056000X (ft)X (ft)

De

pth

(ft)D

ep

th (ft)

VSP Multiple (12 receivers 13 kft @ VSP Multiple (12 receivers 13 kft @ 30 ft spacing; 500 shots) 30 ft spacing; 500 shots)

TLE, Jiang et al., 2005TLE, Jiang et al., 2005

50005000

130001300000 5600056000X (ft)X (ft)

De

pth

(ft)D

ep

th (ft)

Surface SeismicSurface Seismic


50005000

130001300000 5600056000X (ft)X (ft)

De

pth

(ft)D

ep

th (ft)

VSP Multiple (12 receivers 13 kft @ VSP Multiple (12 receivers 13 kft @ 30 ft spacing; 500 shots) 30 ft spacing; 500 shots)


Instead of using just primaryInstead of using just primary

arrivals, you also use the multiples for a wider/partialarrivals, you also use the multiples for a wider/partial visionvision

Small vs Huge IlluminationSmall vs Huge Illumination

Primary reflectionsPrimary reflections Multiple reflectionsMultiple reflections

Standard VSP ImagingStandard VSP Imaging Interferometric VSP ImagingInterferometric VSP Imaging

Standard VSP vs Interferometric VSP ImagingStandard VSP vs Interferometric VSP Imaging

Stellar InterferometryStellar InterferometryAn astronomical interferometer is an array of telescopes or mirror An astronomical interferometer is an array of telescopes or mirror

segments acting together to probe structures with higher resolution. segments acting together to probe structures with higher resolution.

stellar interferometry, a team of French astronomers has captured one of the sharpest color images ever made. They observed the star T Leporis stellar interferometry, a team of French astronomers has captured one of the sharpest color images ever made. They observed the star T Leporis

with the European Southern Observatory's with the European Southern Observatory's Very Large Telescope Interferometer (VLTI; Cerro Paranal, Chile), which emulates a virtual telescope (VLTI; Cerro Paranal, Chile), which emulates a virtual telescope

about 100 meters across, and which revealed a spherical molecular shell around the aged star. about 100 meters across, and which revealed a spherical molecular shell around the aged star.

http://www.laserfocusworld.com/articles/article_display.cfm?ARTICLE_ID=340445

3x3 Classification Matrix3x3 Classification Matrix

SSPSSP VSPVSP SWPSWP

VSPVSP

SSPSSP

SWPSWP

SSPSSP SSPSSP SSPSSP SSPSSPVSPVSP SWPSWP

VSPVSP VSPVSP VSPVSP

SWPSWP SWPSWP SWPSWP

VSPVSP

SWPSWP

SWPSWP

VSPVSP

SSPSSP

SSPSSP

inout

SummarySummary•Seismic InterferometrySeismic Interferometry: :

x Im[G(Im[G(AA||BB)])] G(G(x|x|BB)*)* G(G(x|x|AA)) ~~~~

AA BB

x

G(G(AA||xx)) G(G(BB||xx))

imaginary

k

AA BB

x

G(G(AA||BB))

•Merits:Merits: Eliminates need for src location, excitation time, some statics. Eliminates need for src location, excitation time, some statics. Moves rec./srcs closer to target , no velocity model needed (unlike Moves rec./srcs closer to target , no velocity model needed (unlike Berryhill).Berryhill).

•Challenges:Challenges: Finite aperture and noise, attenuation, acoustic & farfield Finite aperture and noise, attenuation, acoustic & farfield approximations , amplitude fidelityapproximations , amplitude fidelity

•Killer Apps in Earthquake:Killer Apps in Earthquake: Surface wave interferometry Surface wave interferometry

•Killer Apps in Exploration:Killer Apps in Exploration: Passive reservoir monitoring? OBS? EM? VSP Passive reservoir monitoring? OBS? EM? VSP

OutlineOutline

•What is Seismic Interferometry?What is Seismic Interferometry?

•Reciprocity Equation Correlation TypeReciprocity Equation Correlation Type

•Classification MatrixClassification Matrix



•Background for Non-geo typesBackground for Non-geo types

Reciprocity Eqn. of Correlation TypeReciprocity Eqn. of Correlation Type1. Helmholtz Eqns: 1. Helmholtz Eqns:

2+ k

2[ ] G(A|x) =- (x-A);

2+ k

2[ ] P(B|x) =- (x-B) **

**

2 2+ k[ ] G(A|x) =- (x-A) P(B|x) P(B|x)

2 2+ k[ ] P(B|x) =- (x-B) G(A|x) G(A|x)

** **

G(A|x)P(B|x) P(B|x) - G(A|x)2

= (B-x)G(A|x) - (A-x)P(B|x) 2

**** **

2. Multiply by 2. Multiply by G(A|x)G(A|x) and and P(B|x)P(B|x) and subtract and subtract**

G(A|x)

A A B B

Free surface

P(B|x)

xx

G(A|x) = G(A|x) = P(B|x) P(B|x)P(B|x) G(A|x)G(A|x)2

{ } - - P(B|P(B|xx)) G(A|x)G(A|x)****** [ ]

P(B|P(B|xx)) = = G(A|x) G(A|x) G(A|x) P(BP(B|x|x))2

- G(A|x) - G(A|x) P(BP(B|x|x))[[ ]] ****** [ ]

Reciprocity Eqn. of Correlation TypeReciprocity Eqn. of Correlation Type1. Helmholtz Eqns: 1. Helmholtz Eqns:

2+ k

2[ ] G(A|x) =- (x-A);

2+ k

2[ ] P(B|x) =- (x-B) **

**

2 2+ k[ ] G(A|x) =- (x-A) P(B|x) P(B|x)

2 2+ k[ ] P(B|x) =- (x-B) G(A|x) G(A|x)

** **

G(A|x)P(B|x) P(B|x) - G(A|x)2

= (B-x)G(A|x) - (A-x)P(B|x) 2

**** **

2. Multiply by 2. Multiply by G(A|x)G(A|x) and and P(B|x)P(B|x) and subtract and subtract**

G(A|x) = G(A|x) = P(B|x) P(B|x)P(B|x) G(A|x)G(A|x)2

{ } - - P(B|P(B|xx)) G(A|x)G(A|x)******

P(B|P(B|xx)) = = G(A|x) G(A|x) G(A|x) P(BP(B|x|x))2

- G(A|x) - G(A|x) P(BP(B|x|x))[[ ]] ******

G(A|x)P(B|x) P(B|x) - G(A|x){ { } } = (B-x)G(A|x) - (A-x)P(B|x) ******

G(A|x)

A A B B

Free surface

P(B|x)

xx

Reciprocity Eqn. of Correlation TypeReciprocity Eqn. of Correlation Type3. Integrate over a volume3. Integrate over a volume

4. Gauss’s Theorem4. Gauss’s Theorem

Source lineSource line

G(A|x)P(B|x) P(B|x) - G(A|x) d x3

= G(A|B) - P(B|A){ }{ } ******


= G(A|B) - P(B|A){ }{ } n** ** **

G(A|B) G(A|B)

Integration at infinity vanishesIntegration at infinity vanishesA A B B

Free surface

xx

Reciprocity Eqn. of Correlation TypeReciprocity Eqn. of Correlation Type3. Integrate over a volume3. Integrate over a volume

4. Gauss’s Theorem4. Gauss’s Theorem



= G(A|B) - P(B|A){ }{ } ******

G(A|x)G(B|x) G(B|x) - G(A|x) d x2

= G(A|B) - G(B|A){ }{ }

n** ** **

G(A|B) G(A|B)

Integration at infinity vanishesIntegration at infinity vanishesA A B B

Free surface

xx

Relationship between reciprocal Green’s functionsRelationship between reciprocal Green’s functions

Reciprocity Eqn. of Correlation TypeReciprocity Eqn. of Correlation Type


G(A|x)G(B|x) G(B|x) - G(A|x) d x2

= G(A|B) - G(B|A){ }{ }

n** ** **= 2i Im[G(A|B)]= 2i Im[G(A|B)]

Recall Recall G(A|x ) =G(A|x ) =

|r||r|

iwr/ciwr/ceeiw/ciw/c

nn nn rr

G(BG(B|x|x )* )* = =|r||r|

-iwr/c-iwr/cee-iw/c-iw/c

nn nn rr

(1)(1)

(2a)(2a)

(2b)(2b)

Plug (2a) and (2b) into (1)Plug (2a) and (2b) into (1)

G(A|x )G(A|x )ikik

G(B|G(B|xx ) )**-ik-ik


G(A|x)G(B|x) d x2

= G(A|B) - G(B|A)r** **= 2i Im[G(A|B)]= 2i Im[G(A|B)] (3)(3)n2ik2ik

Neglect 1/rNeglect 1/r22

A XX

B


G(A|x)G(B|x) d x2



xx

B AB A

G(B|x)*G(B|x)*

xx

B AB A

G(A|x)G(A|x)

xx

B AB A

G(A|B)G(A|B)

Source redatumed from x to BSource redatumed from x to B

Virtual sourceVirtual source

ImplementationImplementation

x

= Im[G(= Im[G(AA||BB)])] G(G(AA||xx)*)* G(G(BB||xx))kk

AA

xx

BBAA

xx

BB AA

xx

BB

VSP VSP SSPVSP VSP SSP

1. FK Filter up and downgoing waves1. FK Filter up and downgoing waves

2. Correlation: 2. Correlation: (A,B,x) = (A,B,x) = G(G(AA||xx)*)* G(G(BB||xx))

3. Summation: 3. Summation: x

= Im[G(= Im[G(AA||BB)])] kk (A,B,x) (A,B,x)

4. Migration:4. Migration: M(x) = M(x) = Mig(Mig(G(G(AA|B|B))))

Challenge: Finite Receiver Aperture = Partial ReconstructionChallenge: Finite Receiver Aperture = Partial Reconstruction

3D SEG Salt Model Test3D SEG Salt Model Test

(He, 2006)(He, 2006)

VSP Multiples MigrationVSP Multiples Migration

( CourtesyCourtesy of P/GSI: ~¼ million traces, ~3 GB memory, ~4 hours on a PC )

Stack of 6 receiver gathersStack of 6 receiver gathers

(He, 2006)(He, 2006)

Marine 3D VSP Field Data Marine 3D VSP Field Data ApplicationApplication

BP 3D VSP Survey Geometry (36 recs)BP 3D VSP Survey Geometry (36 recs)~ 11 km~ 11 km

3 km3 km

1.6 km1.6 km

4.0 km4.0 km

(He et al., 2007)(He et al., 2007)

VSP->SSP SummaryVSP->SSP Summary

Key Point #1: Every Bounce Pt on Surface Acts a New Virtual SourceKey Point #1: Every Bounce Pt on Surface Acts a New Virtual Source

Key Point #2: Kills Receiver StaticsKey Point #2: Kills Receiver Statics

Key Point #3: Redatuming = Huge Increase Illumination areaKey Point #3: Redatuming = Huge Increase Illumination area

x

= Im[G(= Im[G(AA||BB)])] G(G(AA||xx)*)* G(G(BB||xx))kk

AA

xx

BBAA

xx

BB AA

xx

BB

VSP VSP SSPVSP VSP SSP

Key Point #4: Liabilities: Finite Aperture noise, attenuation, loss amplitudes fidelityKey Point #4: Liabilities: Finite Aperture noise, attenuation, loss amplitudes fidelity

Problem:Problem: Overburden+statics defocus VSP migration Overburden+statics defocus VSP migration

Redatum sources below overburdenRedatum sources below overburden

Local VSP migrationLocal VSP migration

Solution:Solution: VSP -> SWP Transform (Calvert, Bakulin) VSP -> SWP Transform (Calvert, Bakulin)

MotivationMotivation

VSPVSPVSPVSP SWPSWP

VSP GeometryVSP Geometry

Offset (m)Offset (m)00 10001000

DepthDepth (m)(m)

15001500

35003500Time (s)Time (s)

00

33

Reflection Reflection wavefieldwavefield

(He , 2006)(He , 2006)

VSP GeometryVSP Geometry

Offset (m)Offset (m)00 10001000

DepthDepth (m)(m)

15001500

35003500

(He , 2006)(He , 2006)

Time (s)Time (s)

00

33

Reflection Reflection wavefieldwavefield

superresolutionsuperresolution

China

VSP Salt Flank Imaging VSP Salt Flank Imaging (Hornby & Yu, 2006)(Hornby & Yu, 2006)

? 98 geophones

120 shots

Overburden

Poor image of flank by standard migrationPoor image of flank by standard migration

0 2000 ft 0 2000 ft

Interferometric Migration Interferometric Migration ResultResult

VSP->SWP SummaryVSP->SWP Summary

3. Kills Source Statics and no need to know src location or excitation time3. Kills Source Statics and no need to know src location or excitation time

1. Redatum sources below overburden1. Redatum sources below overburden

2. Local VSP migration2. Local VSP migration

4. Super-resolution4. Super-resolution

5. Instead of redatuming receivers to surface, we5. Instead of redatuming receivers to surface, we

redatum sources to depth.redatum sources to depth.

xx BBAA

Surface Wave InterferometrySurface Wave Interferometry

G(G(AA||xx)*)* G(G(BB||xx))

xx BBAA

G(G(BB||AA))

AA


G(G(AA||xx)* G()* G(BB||xx) = G() = G(BB||AA))

BB

xx

Shear velocityShear velocity

AA


G(G(AA||xx)* G()* G(BB||xx) = G() = G(BB||AA))

BB

xx

x

Yao (2009)Yao (2009)

S-velocity distribution, surface wave predic.+eliminationS-velocity distribution, surface wave predic.+elimination

3x3 Classification Matrix3x3 Classification Matrix

SSPSSP VSPVSP SWPSWP

VSPVSP

SSPSSP

SWPSWP

SSPSSP SSPSSP SSPSSP SSPSSPVSPVSP SWPSWP

VSPVSP VSPVSP VSPVSP

SWPSWP SWPSWP SWPSWP

VSPVSP

SWPSWP

SWPSWP

VSPVSP

SSPSSP

SSPSSP

inout

SummarySummary•Seismic InterferometrySeismic Interferometry: :

x Im[G(Im[G(AA||BB)])] G(G(x|x|BB)*)* G(G(x|x|AA)) ~~~~

k

AA BB

x

G(G(AA||BB))AA BB

x

G(G(AA||xx)) G(G(BB||xx))•Merits:Merits: Eliminates need for src location, excitation time, some statics. Eliminates need for src location, excitation time, some statics. Moves rec./srcs closer to target , no velocity model needed (unlike Moves rec./srcs closer to target , no velocity model needed (unlike Berryhill).Berryhill).

•Challenges:Challenges: Finite aperture and noise, attenuation, acoustic & farfield Finite aperture and noise, attenuation, acoustic & farfield approximations , amplitude fidelityapproximations , amplitude fidelity

•Killer Apps in Earthquake:Killer Apps in Earthquake: Surface wave interferometry Surface wave interferometry

•Killer Apps in Exploration:Killer Apps in Exploration: Passive reservoir monitoring? OBS? EM? VSP Passive reservoir monitoring? OBS? EM? VSP

ThanksThanks

•UTAM sponsorsUTAM sponsors

•Min Zhou, Chaiwoot Boonyasiriwat, Ge ZhanMin Zhou, Chaiwoot Boonyasiriwat, Ge Zhan

OutlineOutline







Saudi Land SurveySaudi Land Survey

overburden

shale

sandstoneshale

sandstone


primaryprimary

multiplemultiple


SSP=Surface Seismic

Survey

12.5 m12.5 m

SSP=Surface Seismic

Survey

Marine SSP SurveyMarine SSP Survey

Vertical Seismic Profile Survey Vertical Seismic Profile Survey

Survey Goal: GetSurvey Goal: Get d d fromfrom dd Geologist Goal: GetGeologist Goal: Get mm fromfrom d d

d(g,t)d(g,t)

gg

tt

m(x,z)m(x,z)

LLmm==dd m m = [L L] L = [L L] L d ~ d ~ LL d dTT TT TT-1-1

Model basedModel based

Data basedData based


G(A|x)G(B|x) d x2



Source redatumed from x to BSource redatumed from x to B

xx

B AB A

G(B|x)*G(B|x)*

xx

B AB A

G(A|x)G(A|x)

xx

B AB A

G(A|B)G(A|B)Recovering the Green’s function

OutlineOutline







goal: learn about potential, principles and

Documents

stochastic interferometry

deterministic interferometry

vsp experimentvsp

redatums data

correlation of trace

src location

xwell data

virtual telescope