Seismic Interferometry Course Schuster Cambridge Press Goal Learn

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

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

SELECTIVE HISTORY SEISMIC INTERFEROMETRY 1968 ! Claerbout V(z)+passive redatum 1970 s Berryhill model-based redatum 1980 s Cole+Claerbout V(x, y, z)+passive? 1990 s Scherbaum earthquake V(z)+passive 1999 Rickett+Claerbout V(z) Helioseismology Daylight Imaging, passive Utah: Stationary Phase Theory, SSP, and VSP Seismic Interferometric imaging, deterministic 2002 -04 Wapenaar Recip. Thm. Correlation Type Gerstoft + others Surface Wave Interferometry Snieder Stationary Phase Redatuming Shell Virtual Sources: Calvert+Bakulin 2001

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

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

What is Seismic Interferometry? Answer: Redatums data by correlation of trace pairs and stacking the result for different shot positions stacking t ) iwtx. B iw(t x. B+ t. B+ z z. B x e G(B|x)* e G(B|x) z x x Phase of Common Raypath Cancels ~ = ~ z iw( t. B+z tz. B ) = e G(B|B) Point Source Response with src at B and rec at B z A • No need to know src. location • No need to know src excitation time • Redatum source closer to target

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

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

ØPrediction Multiple by Convolution (SRME) * ØPrediction Primaries by Crosscorrelation (Crosscorrelation migration interferometry) A B C A B B C

VSP Multiple (12 receivers 13 kft @ 30 ft spacing; 500 shots) 5000 Depth (ft) 13000 0 X (ft) 56000 TLE, Jiang et al. , 2005

Surface Seismic 5000 Depth (ft) 13000 0 X (ft) 56000 TLE, Jiang et al. , 2005

VSP Multiple (12 receivers 13 kft @ 30 ft spacing; 500 shots) 5000 Depth (ft) 13000 0 X (ft) 56000 TLE, Jiang et al. , 2005

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

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 about 100 meters across, and which revealed a spherical molecular shell around the aged star. Stellar Interferometry An astronomical interferometer is an array of telescopes or mirror segments acting together to probe structures with higher resolution.

3 x 3 Classification Matrix out in SSP VSP SWP SSP SSP VSP SWP VSP SSP VSP VSP SWP SWP SSP SWP VSP SWP

Summary • Seismic Interferometry: imaginary x G(x|B)* G(x|A) ~ ~ Im[G(A|B)] x x A G(A|x) B G(B|x) k A B 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). • Challenges: Finite aperture and noise, attenuation, acoustic & farfield approximations , amplitude fidelity • Killer Apps in Earthquake: Surface wave interferometry • Killer Apps in Exploration: Passive reservoir monitoring? OBS? EM? VSP

Outline • Background for Non-geo types • What is Seismic Interferometry? • Reciprocity Equation Correlation Type • Classification Matrix • Applications • Conclusions

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

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

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

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

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

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

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

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

Outline • What is Seismic Interferometry? • Applications • VSP->SSP (surface seismic profile) • VSP->SWP (single well profile) • SSP->SSP • Conclusions

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

3 D SEG Salt Model Test (He, 2006)

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

Marine 3 D VSP Field Data Application

BP 3 D VSP Survey Geometry (36 recs) ~ 11 km 1. 6 km 4. 0 km 3 km (He et al. , 2007)

VSP->SSP Summary VSP k VSP SSP ! x G(A|x)* G(B|x) = A B Im[G(A|B)] A B x x 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 Key Point #4: Liabilities: Finite Aperture noise, attenuation, loss amplitudes fidelity

Outline • What is Seismic Interferometry? • Applications • VSP->SSP (surface seismic profile) • VSP->SWP (single well profile) • SSP->SSP • Conclusions

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

VSP Geometry 1500 Reflection wavefield Depth (m) 0 3500 0 Offset (m) Time (s) 1000 (He , 2006) 3

VSP Geometry 1500 Reflection wavefield Depth (m) superresolution 0 3500 0 China Offset (m) Time (s) 1000 (He , 2006) 3

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

Interferometric Migration Result 0 2000 ft

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

Outline • What is Seismic Interferometry? • Applications • VSP->SSP (surface seismic profile) • VSP->SWP (single well profile) • SSP->SSP • Conclusions

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

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

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

3 x 3 Classification Matrix out in SSP VSP SWP SSP SSP VSP SWP VSP SSP VSP VSP SWP SWP SSP SWP VSP SWP

Summary • Seismic Interferometry: x x G(x|B)* G(x|A) ~ ~ Im[G(A|B)] x k A B G(B|x) G(A|B) G(A|x) • 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 fidelity • Killer Apps in Earthquake: Surface wave interferometry • Killer Apps in Exploration: Passive reservoir monitoring? OBS? EM? VSP

Thanks • UTAM sponsors • Min Zhou, Chaiwoot Boonyasiriwat, Ge Zhan

Outline • Background for Non-geo types • What is Seismic Interferometry? • Reciprocity Equation Correlation Type • Classification Matrix • Applications • Conclusions

Saudi Land Survey overburden sandstone shale

Saudi Land Survey multiple primary

Saudi Land Survey SSP=Surface Seismic Survey

Marine SSP Survey SSP=Surface Seismic Survey 12. 5 m

Vertical Seismic Profile Survey

Survey Goal: Get m d from Geologist from dd d(g, t) t g Model based L m= d T -1 T T m = [L L] L d ~ L d Data based m(x, z)

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

Outline • Background for Non-geo types • What is Seismic Interferometry? • Reciprocity Equation Correlation Type • Classification Matrix • Applications • Conclusions