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Seismic interferometry: Who needs a seismic source?. Roel Snieder Center for Wave Phenomena Colorado School of Mines email rsnieder@mines.edu http://www.mines.edu/~rsnieder download publications from: http://www.mines.edu/~rsnieder/Publications.html. F. (Einstein, 1905).

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seismic interferometry who needs a seismic source
Seismic interferometry:Who needs a seismic source?

Roel Snieder

Center for Wave Phenomena

Colorado School of Mines

email rsnieder@mines.edu

http://www.mines.edu/~rsnieder

download publications from:

http://www.mines.edu/~rsnieder/Publications.html

fluctuation dissipation theorem

F

(Einstein, 1905)

Fluctuation-dissipation theorem

(Kubo, Rep. Prog. Phys., 29, 255-284, 1966)

very long baseline interferometry
Very Long Baseline Interferometry

http://www.lupus.gsfc.nasa.gov/brochure/bintro.html

distance between usa and germany
Distance between USA and Germany

http://www.lupus.gsfc.nasa.gov/brochure/btoday2.html

pseudo random source
Pseudo-random source

Piezo-electric

vibrator from CGG

coda wave interferometry
Coda wave interferometry

45°C

50°C

(Snieder et al., Science, 295, 2253-2255, 2002)

cross correlation
Cross-correlation
  • sum of causal and acausal response
  • uncorrelated left- and rightgoing waves
need to extend this to include
Need to extend this to include:
  • heterogeneous media
  • - more space dimensions
derivation based on normal modes
Derivation based on normal-modes

(Lobkis and Weaver, JASA, 110, 3011-3017, 2001)

displacement response
Displacement response

Heaviside function

correlation1
Correlation

Green’s function

correlation2
Correlation

Green’s function

correlation3
Correlation

Green’s function

correlation and 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
Dealing with with acausal Green’s function
  • truncate correlation for t<0
  • average correlation for t<0 and t>0
displacement instead of velocity
Displacement instead of velocity

Conclusion: time derivative may appear

acoustic waves
Acoustic waves

Green’s function:

time reversal
Time-reversal

When is a solution.

then is a solution as well

N.B. this does not hold in the presence

of attenuation

left hand side
Left hand side

reciprocity

for spherical surface far away
For spherical surface far away

Radiation condition:

virtual sources
Virtual-sources

(Wapenaar, Fokkema, and Snieder, JASA, 118, 2783-2786 2005

heuristic derivation: Derode et al., JASA, 113, 2973-2976, 2003)

computing synthetic seismograms
Computing synthetic seismograms

(Van Manen et al., Phys. Rev. Lett., 94, 164301,2005)

field example of virtual sources
Field example of virtual sources

complicated overburden

reservoir

(Bakulin and Calvert, SEG expanded abstracts, 2477-2480, 2004)

slide42

Peace River 4D VSP

Component used,

along-the-well (450)

virtual sources1
Virtual-sources

(Wapenaar, Fokkema, and Snieder, JASA, 118, 2783-2786 2005

heuristic derivation: Derode et al., JASA, 113, 2973-2976, 2003)

excitation by uncorrelated sources on surface
Excitation by uncorrelated sources on surface
  • Uncorrelated sources can be:
  • sequential shots
  • uncorrelated noise
green s function from uncorrelated sources
Green’s function from uncorrelated sources

(For elastic waves: Wapenaar, Phys. Rev. Lett, 93, 254301, 2004)

raindrop model
Raindrop model
  • Sources can be:
  • real sources
  • secondary sources (scatterers)
double sum over sources
Double sum over sources

diagonal terms

cross-terms

cross terms
Cross-terms
  • vanish on average
  • in a single realization:

(Snieder, Phys. Rev. E, 69, 046610, 2004)

for dense scatterers
For dense scatterers

n = scatterer density

stationary phase regions
Stationary phase regions

“anti-Fresnel zones”

stationary phase integration
Stationary phase integration

(Snieder, Phys. Rev. E, 69, 046610, 2004,

for reflected waves see:

Snieder, Wapenaar, and Larner, Geophysics, in press, 2005)

yet another type of illumination
Yet another type of illumination

(Weaver and Lobkis, JASA, 116, 2731-2734)

ultrasound experiment

54 mm

source

135 mm

receivers

Ultrasound experiment

(Malcolm et al., Phys. Rev. E, 70, 015601, 2004)

surface waves
Surface waves

(Campillo and Paul, Science, 299, 547-549, 2003)

slide68

correlation

Green’s tensor

Z/Z

Z/R

Z/T

slide69

correlation

Green’s tensor

Z/Z

Z/R

Z/T

R/Z

R/R

R/T

T/Z

T/R

T/T

surface wave green s function
Surface wave Green’s function

(Snieder, Phys. Rev. E, 69, 046610, 2004)

slide71

Surface wave

dispersion

from noise

(Shapiro and Campillo,

Geophys. Res. Lett.,

31, L07614, 2004)

slide75

normal modes

traveling waves

slide80

+

+

t deconvolved 4 5 to 15 sec1
T – Deconvolved (4.5 to 15 sec)

β

=100 m/s

β

=150 m/s

β

=250 m/s

β

=200 m/s

β

=550 m/s

depth (m)

time (sec)

z deconvolved 1 to 15 sec1
Z – Deconvolved (1 to 15 sec)

α

=1500 m/s

α

=1250 m/s

α

=1350 m/s

α

=1600 m/s

depth (m)

α

=2200 m/s

time (sec)

r deconvolved 4 5 to 15 sec1
R – Deconvolved (4.5 to 15 sec)

β

=100 m/s

β

=150 m/s

β

=250 m/s

β

=200 m/s

β

=550 m/s

depth (m)

time (sec)

r deconvolved 1 to 4 5 sec1
R – Deconvolved (1 to 4.5 sec)

β

=100 m/s

β

=150 m/s

β

=250 m/s

β

=200 m/s

β

=550 m/s

depth (m)

time (sec)

receiver function
Receiver Function

depth (m)

time (sec)

receiver function1
Receiver Function

depth (m)

time (sec)

seismic interferometry in millikan library1
Seismic interferometry in Millikan Library

(Snieder and Safak, Bull. Seismol. Soc. Am., in press, 2005)

advantage 4 use other type of data
Advantage (4), use other type of data

earthquake

correlation

(1 year)

correlation

(1 month)

(Shapiro et al., Science, 307, 1615-1618, 2005)

slide118

0.01

0.01

0.1

1

10

Frequency (Hz)

slide119

5-10

sec.

0.01

0.01

0.1

1

10

Frequency (Hz)