Center for Wave Phenomena

Department of GeophysicsColorado School of Mines

Golden, Colorado

CWP FacultyIlya Tsvankin

“We are committed to quality education.”

Roel SniederDave Hale

Ilya Tsvankin

Paul SavaNorm Bleistein

Ken Larner

What do we offer?• Full financial support

• Diverse and enthusiastic faculty

• State-of-the-art research

• Industry contacts and internships

Need more Information?Prof. Ilya Tsvankinilya@dix.mines.edu

Prof. Roel Snieder rsnieder@mines.edu

www.cwp.mines.edu

Center for Wave PhenomenaColorado School of Mines

Golden, CO 80401

Seismic interferometry:Who needs a seismic source?

Roel Sniederemail rsnieder@mines.edu

Problem with sub-salt imaging

reservoir

salt

What if we had virtual sources below the salt?

reservoir

salt

Response to random sources

Ar Br

Response to random sources

Ar Br

dttptpC B

T

AAB ),(),()(0

rrCorrelation:

Very Long Baseline Interferometry

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

Distance between USA and Germany

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

1D example

)/()/(),( cxtLcxtRtxu

cxtR / cxtL /

0x Hx

Cross-correlation

)/()/()()0( cHtCcHtCHxuxu LR

t

cH / cH /

• sum of causal and acausal response• uncorrelated left- and rightgoing waves

Need to extend this to include:

- heterogeneous media

- more space dimensions

Derivation based on normal-modes

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

Displacement response

m

mmmmm

m tbtautu

cossin)(),( rr

)(sin)'()(),',( tHtuutGm

mm

mm

rrrr

Heaviside function

Velocity response

m

mmmmm tbtautv sincos)(),( rr

)(cos)'()(),',()( tHtuutGm

mmmv rrrr

Uncorrelated excitation

m

mmmmm tbtautv sincos)(),( rr

0

2

2

mn

nmmn

nmmn

ba

Fbb

Faa

Correlation

),(),()()( tvtvC BAvAB rr

m

mmmmBAmBA tbtautv sincos)(),( ,, rr

Correlation as sum over modes

ttbb

ttab

ttba

ttaa

uuC

mnmn

mnmn

mnmn

mnmn

mnBmAn

vAB

sinsin

cossin

sincos

coscos

)()()(,

)( rr

For uncorrelated modes

ttbb

ttab

ttba

ttaa

uuC

mnmn

mnmn

mnmn

mnmn

mnBmAn

vAB

sinsin

cossin

sincos

coscos

)()()(,

)( rr

nmF 2

For uncorrelated modes

ttbb

ttab

ttba

ttaa

uuC

mnmn

mnmn

mnmn

mnmn

mnBmAn

vAB

sinsin

cossin

sincos

coscos

)()()(,

)( rr

nmF 2

mcos

Correlation

m

mBmAmvAB uuFC cos)()()( 2)( rr

Green’s function

)(cos)()(),,()( HuuGm

mBmAmBAv rrrr

Correlation and Green’s function

),,(),,()( )()(2)( tGtGFtC BAv

BAvv

AB rrrr

- sum of causal and acausal Green’s function

- holds for arbitrary heterogeneity

(Weaver and Lobkis, Ultrasonics, 40, 435-439, 2002)

20 30 40 50 60 70 80 90 100 110-4500

-4000-3500-3000-2500

-2000-1500-1000

-500

0500

100015002000

-0.5-0.4-0.3-0.2-0.10.00.10.20.30.40.50.60.70.80.91.01.1

time (microseconds)

Pulse/echo

noiseautocorrelation

(Weaver and Lobkis, Ultrasonics, 40, 435-439, 2002)

Raindrop model

Sources can be:

- real sources

- secondary sources (scatterers)

Extract response by correlation

Ar Br

Sr

dttptpC B

T

AAB ),(),()(0

rrCorrelation:

Non-stationary source point

Ar Br

Non-stationary source point

Ar Br

Stationary source point

Ar Br

Stationary source point

Ar Br

Stationary phase regions

“anti-Fresnel zones”

Stationary phase integration

R

ikReR

ikReCAB

44)(

)()()( * RGRGCAB

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

Four types of averaging

Computing synthetic seismograms

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

Field example of virtual sources

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

reservoir

complicated overburden

Peace River 4D VSP

1 0.5 00.5

1x

10.50

0.51y

1 0.50

0.51

z

1 0.5 00.5

1x

10.50

0.51y

Component used,along-the-well (450)

Image from virtual sources

topbottom

Virtual source Surface

Surface waves

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

correlation Green’s tensor

Z/Z

Z/R

Z/T

Surface wave Green’s function

iG

iGC klkl

kl )(

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

Seismic interferometry in Millikan Library

(Snieder and Safak, Bull. Seismol. Soc. Am., 96, 586-598, 2006)

Deconvolution with top floor

Deconvolution with bottom floor

traveling waves normal modes

Four new wave states

(Snieder, Sheiman, and Calvert, Phys. Rev. E., 73, 066620, 2006)

building borehole

Advantage (1), virtual sources atnew locations

reservoir

salt

Advantage (1), virtual sources atnew locations

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

Advantage (3), use other type of data

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

earthquake

correlation(1 year)

correlation(1 month)

5-10sec.

1010.10.010.01Frequency (Hz)

More information

www.mines.edu/~rsnieder

email rsnieder@mines.edu

www.mines.edu/~rsnieder/SPICE06_Snieder.ppt