Instead of using just primaryInstead of using just primary

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

Seismic InterferometrySeismic Interferometry

Gerard SchusterGerard Schuster

University of UtahUniversity of Utah

Overview of Seismic Interferomtery Overview of Seismic Interferomtery Short CourseShort Course

Instead of using just primaryInstead of using just primary

arrivals, you also use the multiples for a wider visionarrivals, you also use the multiples for a wider vision

Small vs Huge IlluminationSmall vs Huge Illumination

Primary reflectionsPrimary reflections Multiple reflectionsMultiple reflections

Overview of Seismic Interferomtery Overview of Seismic Interferomtery Short CourseShort Course

Instead of using just primaryInstead of using just primary

arrivals, you also use the multiples for a arrivals, you also use the multiples for a wider wider visionvision

Redatum sources below overburdenRedatum sources below overburdenLocal VSP migrationLocal VSP migration

clearerclearer

Overview of Seismic Interferomtery Overview of Seismic Interferomtery Short CourseShort Course

Instead of using just primaryInstead of using just primary

arrivals, you also use the multiples for a arrivals, you also use the multiples for a wider wider visionvision

Data ExtrapolationData Extrapolation

clearerclearer

Overview of Seismic Interferomtery Overview of Seismic Interferomtery Short CourseShort Course

Instead of using just primaryInstead of using just primary

arrivals, you also use the multiples for a arrivals, you also use the multiples for a wider wider visionvision

clearerclearer

Monitoring 4DMonitoring 4D

Hydrofrac locationHydrofrac location

Goal:Goal: Learn Principles and Algorithms in Learn Principles and Algorithms in Seismic Interferometry Seismic Interferometry

Format MorningsFormat Mornings: Lecture 50 minutes, followed : Lecture 50 minutes, followed by exercise or MATLAB lab. by exercise or MATLAB lab.

Format AfternoonFormat Afternoon: MATLAB labs+discussion. : MATLAB labs+discussion.

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.

What is Seismic Interferometry?What is Seismic Interferometry?

Answer: Correlation and summation of trace pairs andAnswer: Correlation and summation of trace pairs and

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

= G(= G(BB||BB))

BB

xx

AG(A|B)

BB

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

with src at B and rec at B

Phase of Common Raypath CancelsPhase of Common Raypath Cancels

Assume a VSP experimentAssume a VSP experiment

direct reflection

iiee

xxBB+ + BBzz zzBBiiee

xxBB iiee

BBzz zzBB=

zz

VSP => SSPVSP => SSP

What is Seismic Interferometry?What is Seismic Interferometry?

Answer: Correlation and summation of trace pairs andAnswer: Correlation and summation of trace pairs and

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

= G(= G(BB||BB))

BB

xx

AG(A|B)

BB

**

direct reflection

iiee

xxBB+ + BBzz zzBBiiee

xxBB iiee

BBzz zzBB=

zz

VSP => SSPVSP => SSP

xx

Point Source Response

with src at A and rec at B

Phase of Common Raypath CancelsPhase of Common Raypath Cancels

-

x

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

What is Seismic Interferometry?What is Seismic Interferometry?

Answer: Correlation and summation of trace pairs andAnswer: Correlation and summation of trace pairs and

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

= G(= G(BB||BB))

BB

xx

AG(A|B)

BB

**

direct reflection

iiee

xxBB+ + BBzz zzBBiiee

xxBB iiee

BBzz zzBB=

zz

VSP => SSPVSP => SSP

xx

x

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

with src at A and rec at B

Do Not Need to Know Source Location!Do Not Need to Know Source Location!

No Need to know Source Initiation Time!No Need to know Source Initiation Time!

Phase of Common Raypath CancelsPhase of Common Raypath Cancels

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

Phase of Common Raypath CancelsPhase of Common Raypath Cancels

xx xx

AAAABB

VSPVSPVSPVSP SSPSSP

BB AA

Old Multiples Become

New Primaries!

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.

Instead of using just primaryInstead of using just primary

arrivals, you also use the multiples for a wider visionarrivals, you also use the multiples for a wider vision

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

Interferometry ApplicationsInterferometry Applications

1. VSP -> SSP : 1. VSP -> SSP :

2. VSP -> SWP : 2. VSP -> SWP :

Small vs Huge IlluminationSmall vs Huge Illumination

Redatum sources below overburdenRedatum sources below overburden

Local VSP migrationLocal VSP migration

Interferometry ApplicationsInterferometry Applications

3. SSP -> SSP : 3. SSP -> SSP :

4. OBS-> OBS : 4. OBS-> OBS :

InterpolationInterpolation

ExtrapolationExtrapolation

5. Source estimation5. Source estimation

Interferometry ApplicationsInterferometry Applications

6. Passive Imaging:6. Passive Imaging:

7. Source Location 7. Source Location

Monitoring 4DMonitoring 4D

Monitoring EORMonitoring EOR

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 VSPSeismic Interferomtery, deterministicSeismic Interferomtery, deterministic

2003-042003-04 Wapenaar Recip. Thm. Correlation TypeWapenaar Recip. Thm. Correlation TypeShell Virtual SourcesShell Virtual Sources

Snieder Stationary Phase RedatumingSnieder Stationary Phase Redatuming

Gestoft + others Surface Wave InterferometryGestoft + others Surface Wave Interferometry

x

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

19991999 Rickett+Claerbout V(z) HelioseismolgyRickett+Claerbout V(z) HelioseismolgyDaylight ImagingDaylight Imaging , passive, passive