Seismic interferometry: Who needs a seismic source? Roel Snieder Center for Wave Phenomena Colorado School of Mines download publications from:

Fluctuation-dissipation theorem F (Einstein, 1905) (Kubo, Rep. Prog. Phys., 29, , 1966)

Very Long Baseline Interferometry

Distance between USA and Germany

Pseudo-random source Piezo-electric vibrator from CGG

45°C 50°C Coda wave interferometry (Snieder et al., Science, 295, , 2002)

1D example

Cross-correlation sum of causal and acausal response uncorrelated left- and rightgoing waves

Right-going wave only

DC-component must vanish

Need to extend this to include: - heterogeneous media - more space dimensions

Derivation based on normal-modes (Lobkis and Weaver, JASA, 110, , 2001)

Displacement response Heaviside function

Velocity response

Uncorrelated excitation

Correlation

Correlation as sum over modes

For uncorrelated modes

Correlation Green’s function

Correlation Green’s function

Correlation Green’s function

Correlation and Green’s function - sum of causal and acausal Green’s function - holds for arbitrary heterogeneity

Dealing with with acausal Green’s function - truncate correlation for t<0 - average correlation for t 0

Displacement instead of velocity Conclusion: time derivative may appear

(Weaver and Lobkis, Ultrasonics, 40, , 2002)

Representation theorem

Acoustic waves Green’s function:

Time reversal = complex conjugation Time-reversed solution

Time-reversal When is a solution. then is a solution as well N.B. this does not hold in the presence of attenuation

Representation theorem replace:

Left hand side reciprocity

Right hand side

For spherical surface far away Radiation condition:

Virtual-sources (Wapenaar, Fokkema, and Snieder, JASA, 118, heuristic derivation: Derode et al., JASA, 113, , 2003)

Computing synthetic seismograms (Van Manen et al., Phys. Rev. Lett., 94, ,2005)

Field example of virtual sources (Bakulin and Calvert, SEG expanded abstracts, , 2004) reservoir complicated overburden

Peace River 4D VSP Component used, along-the-well (45 0 )

Image from virtual sources top bottom

Virtual sourceSurface

Virtual-sources (Wapenaar, Fokkema, and Snieder, JASA, 118, heuristic derivation: Derode et al., JASA, 113, , 2003)

Excitation by uncorrelated sources on surface Uncorrelated sources can be: - sequential shots - uncorrelated noise

Response to uncorrelated noise

Green’s function from uncorrelated sources (For elastic waves: Wapenaar, Phys. Rev. Lett, 93, , 2004)

Raindrop model Sources can be: - real sources - secondary sources (scatterers)

Response to random sources

Correlation:

Double sum over sources diagonal termscross-terms

Cross-terms - vanish on average - in a single realization: (Snieder, Phys. Rev. E, 69, , 2004)

For dense scatterers n = scatterer density

Correlation as volume integral

Stationary phase contribution x y z

Stationary phase regions “anti-Fresnel zones”

Stationary phase integration (Snieder, Phys. Rev. E, 69, , 2004, for reflected waves see: Snieder, Wapenaar, and Larner, Geophysics, in press, 2005)

Yet another type of illumination (Weaver and Lobkis, JASA, 116, )

Four types of averaging

Ultrasound experiment source receivers 54 mm 135 mm (Malcolm et al., Phys. Rev. E, 70, , 2004)

Surface waves (Campillo and Paul, Science, 299, , 2003)

correlation Green’s tensor Z/Z Z/R Z/T

correlation Green’s tensor Z/Z Z/T R/Z R/R R/T T/Z T/R T/T Z/R

Surface wave Green’s function (Snieder, Phys. Rev. E, 69, , 2004)

Surface wave dispersion from noise (Shapiro and Campillo, Geophys. Res. Lett., 31, L07614, 2004)

Seismic interferometry in Millikan Library

Deconvolution with top floor

Deconvolution with bottom floor

traveling waves normal modes

Deconvolution with bottom floor

+ +

Sheiman-interpretation

Fundamental mode: - +

Borehole data from Treasure Island

T – Deconvolved (4.5 to 15 sec) time (sec) depth (m)

T – Deconvolved (4.5 to 15 sec) time (sec) depth (m) β β β β β =100 m/s =150 m/s =200 m/s =250 m/s =550 m/s

Z – Deconvolved (1 to 15 sec) time (sec) depth (m)

Z – Deconvolved (1 to 15 sec) time (sec) depth (m) α α α α α =1500 m/s =1250 m/s =1600 m/s =1350 m/s =2200 m/s

R – Deconvolved (4.5 to 15 sec) time (sec) depth (m)

time (sec) depth (m) β β β β β =100 m/s =150 m/s =200 m/s =250 m/s =550 m/s R – Deconvolved (4.5 to 15 sec)

Borehole data from Treasure Island

R – Deconvolved (1 to 4.5 sec) time (sec) depth (m)

R – Deconvolved (1 to 4.5 sec) time (sec) depth (m) β β β β β =100 m/s =150 m/s =200 m/s =250 m/s =550 m/s

Receiver Function time (sec) depth (m)

Receiver Function time (sec) depth (m)

Advantage (1), virtual sources at new locations reservoir salt

Advantage (1), virtual sources at new locations

Advantage (2), virtual sources at “all” times

Seismic interferometry in Millikan Library (Snieder and Safak, Bull. Seismol. Soc. Am., in press, 2005)

Deconvolution with top floor

Advantage (3), get better illumination

Use surface bounce

“Schuster trick”

Advantage (4), use other type of data (Shapiro et al., Science, 307, , 2005) earthquake correlation (1 year) correlation (1 month)

Frequency (Hz)

5-10 sec Frequency (Hz)