Goal: Learn about potential, principles and Format : Lecture, sometimes followed by exercise. Course project.. Topics : Deterministic interferometry, stochastic interferometry, 3x3 classification matrix, reciprocity theorems, applications to VSP, SSP, OBS, and Xwell data. Seismic Interferometry Course (Schuster, Cambridge Press) algorithms of seismic interferometry

Seismic Interferometry: Instead of using just primary arrivals, you also use the multiples for a wider view

Overview of Seismic Interferometry and Applications in Exploration Gerard Schuster KAUST & University of Utah

Outline 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->SSPSSP->SSP

SELECTIVE HISTORY SEISMIC INTERFEROMETRY 1968 Claerbout V(z)+passive 1980s Cole+Claerbout V(x,y,z)+passive? 1990s Scherbaum earthquake V(z)+passive 2001 Utah: Stationary Phase Theory, SSP, and VSP Seismic Interferometric imaging, deterministic Wapenaar Recip. Thm. Correlation Type Shell Virtual Sources:Calvert+Bakulin Snieder Stationary Phase Redatuming Gerstoft + others Surface Wave Interferometry Gerstoft + others Surface Wave Interferometry ! 1999 Rickett+Claerbout V(z) Helioseismology Daylight Imaging, passive 1970s Berryhill model-based redatum redatum

SELECTIVE HISTORY SEISMIC INTERFEROMETRY ! redatum Surface waves Shapiro, Derode, Larose, Dong, Xue, Halliday, Curtis, Van Mannen, Robertsson, Gerstoft, Sabra, Kepler, Roux, Gerstoft, Sabra, Kepler, Roux, He, Ritzwoller, Campillo etc Interpolation Sheng, Curry, Berkhout, Wang, Dong, Hanafy, Cao, etc Extrapolation Dong, Hanafy, Cao, etc Theory: Acoustic, EM, Elastic, Potential Fink, Wapenaar, Snieder, Papanicolaou, Blomgren, Slob, Thorbeck, van der Neut etc Refractions Boise State Univ, Dong Passive Reservoir Shell, Draganov, Wapenaar, Snieder, Polleto Miranda, etc Exploration Curry, Guitton, Shragg, Yu, Artman Yu, Calvert, Bakulin, He, Jiang, Hornby, Xiao, Willis, Lu, Toksoz, Campman etc VSP Model Tank Scales, Malcolm etc Volcanoes+Coda Snieder, Scales, Gret et al Engineering Xwell Minato, Onishi, Matsuoka etc Nowack, Sheng, Curtis etc Earthquakes EM Slob, Wapenaar, Snieder

What is Seismic Interferometry? Answer: Redatums data by correlation of trace pairs and stacking the result for different shot positions stacking the result for different shot positions A G(B|x) * = G(B|B) Point Source Response with src at B and rec at B Assume a VSP experiment VSP experiment direct F.S. multiple i  e xBxBxBxB +  BzBzBzBz zBzBzBzB i  e xBxBxBxB i  e  BzBzBzBz zBzBzBzB = VSP => SSP B z z Phase of Common Raypath Cancels Raypath Cancels virtual primary B x z virtual sourcecorrelation No need to know src. location No need to know src. location No need to know src excitation time No need to know src excitation time stacking Redatum source closer to target Redatum source closer to target s

A G(B|x) * = G(B|B) Point Source Response with src at B and rec at B i  e xBxBxBxB +  BzBzBzBz zBzBzBzB i  e xBxBxBxB i  e  BzBzBzBz zBzBzBzB = z z Phase of Common Raypath Cancels Raypath Cancels x z x x ~~ No need to know src. location No need to know src. location No need to know src excitation time No need to know src excitation time Redatum source closer to target Redatum source closer to target Answer: Redatums data by correlation of trace pairs and stacking the result for different shot positions stacking the result for different shot positions correlation stacking What is Seismic Interferometry?

Reciprocity Correlation Equation 2D Reflection Data Phase of Common Raypath Cancels x x A A B VSP VSP SSP BA Old Multiples Become New Primaries! x = G(A|B) G(x|B)* G(x|A) k ~~ No need to know VSP rec location at x No need to know receiver statics

Reciprocity Correlation Equation 2D Reflection Data x = G(A|B) G(x|B)* G(x|A) k xx A A B AB Old Multiples Become New Primaries! { } G(A|x) G(B|x) G(B|x) G(B|x) - G(A|x) d x 2 = G(A|B) - G(B|A) n * * * S well (Wapenaar, 2004) 1-way+ far-field approx. 1-way+ far-field approx. Problems: Finite source aperture No attenuation Deghostfilt., U & D separation Muting, Least squares or MDD Atten. Compensation Finite aperture leads to incomplete G(B|A)

 Prediction Multiple by Convolution (SRME)  Prediction Primaries by Crosscorrelation (Crosscorrelation migration interferometry) * BCABCAB

X (ft) Depth (ft) VSP Multiple (12 receivers ft spacing; 500 shots) TLE, Jiang et al., 2005

X (ft) Depth (ft) Surface Seismic TLE, Jiang et al., 2005

X (ft) Depth (ft) VSP Multiple (12 receivers ft spacing; 500 shots) TLE, Jiang et al., 2005

Instead of using just primary arrivals, you also use the multiples for a wider/partial vision Small vs Huge Illumination Primary reflections Multiple reflections Standard VSP Imaging Interferometric VSP Imaging Standard VSP vs Interferometric VSP Imaging

Stellar Interferometry An astronomical interferometer is an array of telescopes or mirror 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 with the European Southern Observatory's Very Large Telescope Interferometer (VLTI; Cerro Paranal, Chile), which emulates a virtual telescope Very Large Telescope InterferometerVery Large Telescope Interferometer 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.

3x3 Classification Matrix SSPVSPSWP VSP SSP SWP SSPSSPSSPSSPVSPSWP VSPVSPVSP SWPSWPSWP VSP SWP SWP VSP SSP SSP in out

Summary Seismic Interferometry:Seismic Interferometry: x Im[G(A|B)] Im[G(A|B)] G(x|B)* G(x|A) ~ ~ A B x G(A|x) G(B|x) imaginary k A B x G(A|B) Merits: Eliminates need for src location, excitation time, some statics. Moves rec./srcs closer to target, no velocity model needed (unlike Berryhill).Merits: Eliminates need for src location, excitation time, some statics. Moves rec./srcs closer to target, no velocity model needed (unlike Berryhill). Challenges: Finite aperture and noise, attenuation, acoustic & farfield approximations, amplitude fidelityChallenges: Finite aperture and noise, attenuation, acoustic & farfield approximations, amplitude fidelity Killer Apps in Earthquake: Surface wave interferometryKiller Apps in Earthquake: Surface wave interferometry Killer Apps in Exploration: Passive reservoir monitoring? OBS? EM? VSPKiller Apps in Exploration: Passive reservoir monitoring? OBS? EM? VSP

Outline What is Seismic Interferometry?What is Seismic Interferometry? Reciprocity Equation Correlation TypeReciprocity Equation Correlation Type Classification MatrixClassification Matrix ApplicationsApplications ConclusionsConclusions Background for Non-geo typesBackground for Non-geo types

Reciprocity Eqn. of Correlation Type 0. Define Problem Given:Find:A G(A|B) Free surface B G(A|x)AB G(B|x) x

Reciprocity Eqn. of Correlation Type 1. Helmholtz Eqns: 2 + k 2 []G(A|x) =- (x-A); 2 + k 2 []P(B|x) =- (x-B) * * 22 + k []G(A|x) =- (x-A)P(B|x) 22 + k []P(B|x) =- (x-B)G(A|x) * * P(B|x) - G(A|x) 2 = (B-x)G(A|x) - (A-x)P(B|x) 2 ** * * 2. Multiply by G(A|x) and P(B|x) and subtract * G(A|x) AB Free surface P(B|x) x G(A|x) = P(B|x) P(B|x) P(B|x) G(A|x) G(A|x) 2 { } - P(B|x) - P(B|x) G(A|x) G(A|x) *** [ ] P(B|x) = G(A|x) G(A|x) G(A|x) P(B|x) P(B|x) 2 - G(A|x) - G(A|x) P(B|x) P(B|x) [ ]*** [ ]

Reciprocity Eqn. of Correlation Type 1. Helmholtz Eqns: 2 + k 2 []G(A|x) =- (x-A); 2 + k 2 []P(B|x) =- (x-B) * * 22 + k []G(A|x) =- (x-A)P(B|x) 22 + k []P(B|x) =- (x-B)G(A|x) * * P(B|x) - G(A|x) 2 = (B-x)G(A|x) - (A-x)P(B|x) 2 ** * * 2. Multiply by G(A|x) and P(B|x) and subtract * G(A|x) = P(B|x) P(B|x) P(B|x) G(A|x) G(A|x) 2 { } - P(B|x) - P(B|x) G(A|x) G(A|x) *** P(B|x) = G(A|x) G(A|x) G(A|x) P(B|x) P(B|x) 2 - G(A|x) - G(A|x) P(B|x) P(B|x) [ ]*** G(A|x)P(B|x) - G(A|x) { } = (B-x)G(A|x) - (A-x)P(B|x) * * * G(A|x) AB Free surface P(B|x) x [

Reciprocity Eqn. of Correlation Type 3. Integrate over a volume 4. Gauss’s Theorem Source line G(A|x)P(B|x) - G(A|x)d x 3 = G(A|B) - P(B|A) { } *** G(A|x)P(B|x) - G(A|x)d x 2 = G(A|B) - P(B|A) { } n * * * G(A|B) Integration at infinity vanishes AB Free surface x

Reciprocity Eqn. of Correlation Type 3. Integrate over a volume 4. Gauss’s Theorem Source line G(A|x)P(B|x) - G(A|x)d x 3 = G(A|B) - P(B|A) { } *** G(A|x)G(B|x) - G(A|x) d x 2 = G(A|B) - G(B|A) { } n* * *G(A|B) Integration at infinity vanishes AB Free surface x Relationship between reciprocal Green’s functions

Reciprocity Eqn. of Correlation Type Source line G(A|x)G(B|x) - G(A|x) d x 2 = G(A|B) - G(B|A) { } n** * = 2i Im[G(A|B)] Recall G(A|x ) = |r| iwr/c e iw/cnnr G(B|x )* = |r| -iwr/c e -iw/c nnr(1)(2a)(2b) Plug (2a) and (2b) into (1) G(A|x ) ik G(B|x ) *-ik Source line G(A|x)G(B|x) d x 2 = G(A|B) - G(B|A) r * * = 2i Im[G(A|B)] (3) n 2ik Neglect 1/r 2 A X B

Far-Field Reciprocity Eqn. of Correlation Type G(A|B) AB Free surface x nr~~ 1 Source line G(A|x)G(B|x) d x 2 = G(A|B) - G(B|A) r * * = Im[G(A|B)] = 2i Im[G(A|B)](3) n k Source line G(A|x)G(B|x) d x 2 = G(A|B) - G(B|A) r * * = Im[G(A|B)] = 2i Im[G(A|B)](4) nk A n r^^

Far-Field Reciprocity Eqn. of Correlation Type nr~~ 1 Source line G(A|x)G(B|x) d x 2 = G(A|B) - G(B|A) r * * = Im[G(A|B)] = 2i Im[G(A|B)](3) n k Source line G(A|x)G(B|x) d x 2 = G(A|B) - G(B|A) r * * = Im[G(A|B)] = 2i Im[G(A|B)](4) nk G(A|B)AB Free surface x

Source line G(A|x)G(B|x) d x 2 = G(A|B) - G(B|A) r * * = Im[G(A|B)] = 2i Im[G(A|B)](4) nk Far-Field Reciprocity Eqn. of Correlation Type x B A G(B|x)* x G(A|x)x G(A|B) Source redatumed from x to B Virtual source

Outline 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->SSPSSP->SSP

Implementation x = Im[G(A|B)] G(A|x)* G(B|x) k A x B A x B A x B VSP VSP SSP 1. FK Filter up and downgoing waves 2. Correlation:  (A,B,x) = G(A|x)* G(B|x) 3. Summation: x = Im[G(A|B)] k  (A,B,x) 4. Migration: M(x) = Mig(G(A|B)) Challenge: Finite Receiver Aperture = Partial Reconstruction

3D SEG Salt Model Test (He, 2006)

VSP Multiples Migration Courtesy ( Courtesy of P/GSI: ~¼ million traces, ~3 GB memory, ~4 hours on a PC ) Stack of 6 receiver gathers (He, 2006)

Marine 3D VSP Field Data Application

BP 3D VSP Survey Geometry (36 recs) ~ 11 km 3 km 1.6 km 4.0 km (He et al., 2007)

VSP->SSP Summary ! Key Point #1: Every Bounce Pt on Surface Acts a New Virtual Source Key Point #2: Kills Receiver Statics Key Point #3: Redatuming = Huge Increase Illumination area x = Im[G(A|B)] G(A|x)* G(B|x) k A x B A x B A x B VSP VSP SSP Key Point #4: Liabilities: Finite Aperture noise, attenuation, loss amplitudes fidelity

Outline 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->SSPSSP->SSP

Problem: Overburden+statics defocus VSP migration Redatum sources below overburden Local VSP migration Solution: VSP -> SWP Transform (Calvert, Bakulin) MotivationVSPVSPSWP

VSP Geometry Offset (m) Depth (m) (m) Time (s) 0 3 Reflectionwavefield (He, 2006)

VSP Geometry Offset (m) Depth (m) (m) (He, 2006) Time (s) 0 3 Reflectionwavefield superresolution China

VSP Salt Flank Imaging (Hornby & Yu, 2006) ? 98 geophones 120 shots Overburden Poor image of flank by standard migration

ft Interferometric Migration Result

VSP->SWP Summary ! 3. Kills Source Statics and no need to know src location or excitation time 1. Redatum sources below overburden 2. Local VSP migration 4. Super-resolution 5. Instead of redatuming receivers to surface, we redatum sources to depth. redatum sources to depth.

Outline 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->SSPSSP->SSP

x BA Surface Wave Interferometry G(A|x)* G(B|x) x B A G(B|A)

A Surface Wave Interferometry G(A|x)* G(B|x) = G(B|A) B x

Shear velocity A Surface Wave Interferometry G(A|x)* G(B|x) = G(B|A) B x x Yao (2009) S-velocity distribution, surface wave predic.+elimination

3x3 Classification Matrix SSPVSPSWP VSP SSP SWP SSPSSPSSPSSPVSPSWP VSPVSPVSP SWPSWPSWP VSP SWP SWP VSP SSP SSP in out

Summary Seismic Interferometry:Seismic Interferometry: x Im[G(A|B)] Im[G(A|B)] G(x|B)* G(x|A) ~ ~ k A B x G(A|B) A B x G(A|x) G(B|x) Merits: Eliminates need for src location, excitation time, some statics. Moves rec./srcs closer to target, no velocity model needed (unlike Berryhill).Merits: Eliminates need for src location, excitation time, some statics. Moves rec./srcs closer to target, no velocity model needed (unlike Berryhill). Challenges: Finite aperture and noise, attenuation, acoustic & farfield approximations, amplitude fidelityChallenges: Finite aperture and noise, attenuation, acoustic & farfield approximations, amplitude fidelity Killer Apps in Earthquake: Surface wave interferometryKiller Apps in Earthquake: Surface wave interferometry Killer Apps in Exploration: Passive reservoir monitoring? OBS? EM? VSPKiller Apps in Exploration: Passive reservoir monitoring? OBS? EM? VSP

Thanks UTAM sponsorsUTAM sponsors Min Zhou, Chaiwoot Boonyasiriwat, Ge ZhanMin Zhou, Chaiwoot Boonyasiriwat, Ge Zhan

Outline What is Seismic Interferometry?What is Seismic Interferometry? Reciprocity Equation Correlation TypeReciprocity Equation Correlation Type Classification MatrixClassification Matrix ApplicationsApplications ConclusionsConclusions Background for Non-geo typesBackground for Non-geo types

Saudi Land Survey overburden shale sandstone shale sandstone

Saudi Land Survey primary multiple

-3.6 Offset (km) 0 2 Time (s) Saudi Land Survey SSP=Surface Seismic Survey

12.5 m SSP=Surface Seismic Survey Marine SSP Survey

Vertical Seismic Profile Survey

Survey Goal: Get d from d Geologist Goal: Get m from d Geologist Goal: Get m from d d(g,t) g t m(x,z) Lm=dLm=dLm=dLm=d m = [L L] L d ~ L d TTT Model based Data based

Source line G(A|x)G(B|x) d x 2 = G(A|B) - G(B|A) r * * = Im[G(A|B)] = 2i Im[G(A|B)](4) nk Far-Field Reciprocity Eqn. of Correlation Type Source redatumed from x to B x B A G(B|x)* x G(A|x) x G(A|B) Recovering the Green’s function

Outline What is Seismic Interferometry?What is Seismic Interferometry? Reciprocity Equation Correlation TypeReciprocity Equation Correlation Type Classification MatrixClassification Matrix ApplicationsApplications ConclusionsConclusions Background for Non-geo typesBackground for Non-geo types