Seismic interferometry for passive and exploration data: reconstruction of internal multiples Kees...

Seismic interferometry forpassive and exploration data:

reconstruction of internal multiples

Kees Wapenaar

76th SEG meeting, New OrleansOctober 3, 2006

Seismic interferometry :obtaining new seismic responses by X-correlation

• Claerbout, 1968 (1-D version)• Schuster, 2001, 2004 (interferometric imaging)• Weaver and Lobkis, 2001 (diffuse wave fields)• Wapenaar, Draganov et al., 2002, 2004 (reciprocity)• Derode et al., 2003 (time-reversal)• Campillo and Paul, 2003 (surface waves)• Berkhout and Verschuur, 2003 (primaries from multiples)• Snieder, 2004 (stationary phase)• Bakulin and Calvert, 2004 (virtual source)• Gerstoft, Sabra et al., 2004 (surface wave tomography)• Van Manen, Robertsson & Curtis, 2005 (modeling)

AxBx

S

AxBx

1S

0S

Modification for passive data

AxBx

0S

1S

Modification for exploration data

Ax Bx

ˆ2 { ( , , )}B AG x x*1 ˆ ˆ{ ( , , ) ( , , )i B AS

G Gj

x x x x* 2ˆ ˆ( , , ) ( , , )}B i A iG G n d x x x x x

Monopole at x

x

Ax Bx

ˆ2 { ( , , )}B AG x x*1 ˆ ˆ{ ( , , ) ( , , )i B AS

G Gj


Dipole at x

x

Ax Bx

ˆ2 { ( , , )}B AG x x*1 ˆ ˆ{ ( , , ) ( , , )i B AS

G Gj


x

Ax Bx

ˆ2 { ( , , )}B AG x x

High-frequencyapproximation

* 22 ˆ ˆ{ ( , , ) ( , , )}i B ASG G d

j

x x x x x

Ax Bx

ˆ2 { ( , , )}B AG x x


Far-field approximation(Fraunhofer)

* 22 ˆ ˆ( , , ) ( , , )B ASG G d

c

x x x x x

Ax Bx



( , , ) ( , , )B A B AG t G t x x x x22

( , , ) ( , , )B ASG t G t d

c x x x x x

Ax Bx

( , , ) ( , , )B A B AG t G t x x x x22

( , , ) ( , , )B ASG t G t d

c x x x x x

0

Ax Bx

( , , ) ( , , )B A B AG t G t x x x x22

( , , ) ( , , )B ASG t G t d

c x x x x x

2

( , )

( , , ) ( , )

A

AS

p t

G t N t d

x

x x x x

2

( , )

( , ', ) ( ', ) '

B

BS

p t

G t N t d

x

x x x x

Uncorrelated noise sources:

Ax Bx

( , , ) ( , , )B A B AG t G t x x x x

2

( , )

( , , ) ( , )

A

AS

p t

G t N t d

x

x x x x

2

( , )

( , ', ) ( ', ) '

B

BS

p t

G t N t d

x

x x x x

( , ) ( , )B Ap t p t x x

Uncorrelated noise sources:

Ax Bx

( , ) ( , )B Ap t p t x x

( , , ) ( , , )B A B AG t G t x x x x

AxBx

S

AxBx

1S

0S

Modification for passive data

Ax Bx

Free surface

1S

0S

ˆ2 { ( , , )}B AG x x

1

*1 ˆ ˆ{ ( , , ) ( , , )i B ASG G

j

x x x x

* 2ˆ ˆ( , , ) ( , , )}B i A iG G n d x x x x x

Ax Bx

Free surface

1S

0S

ˆ2 { ( , , )}B AG x x

1

* 22 ˆ ˆ{ ( , , ) ( , , )}i B ASG G d

j

x x x x x


Ax Bx

Free surface

1S

0SHigh-frequencyapproximation

ˆ2 { ( , , )}B AG x x

1

* 22 ˆ ˆ( , , ) ( , , )B ASG G d

c

x x x x x


Ax Bx

Free surface

1S

0SHigh-frequencyapproximation


( , , ) ( , , )B A B AG t G t x x x x

1

22( , , ) ( , , )B ASG t G t d

c x x x x x

Ax Bx

Free surface

1S

0S

( , , ) ( , , )B A B AG t G t x x x x

1

22( , , ) ( , , )B ASG t G t d

c x x x x x

Ax Bx

Free surface

1S

0SUncorrelated noise sources

( , , ) ( , , ) ( , ) ( , )B A B A B AG t G t p t p t x x x x x x

1

2( , ) ( , , ) ( , )A ASp t G t N t d x x x x x

1

2( , ) ( , , ) ( , )B BSp t G t N t d x x x x x

Draganov and Wapenaar, SEG 2005

Real data application:

Draganov et al.Seismic interferometry on background-noise field data

Tomorrow, 8:30 AM, session CH 4, room 278

AxBx

S

AxBx

0S

1S

Modification for exploration data

100Az m

300Bz m

( / )Pc m s

0 0z m

100Az m

300Bz m

0 0z m

100Az m

300Bz m

0 0z m(s)t0 2 4 6 10

0( , , )AG z z t

100Az m

300Bz m

0 0z m(s)t

(s)t0 2 4 6 10

0 2 4 6 10

0( , , )AG z z t

0( , , )BG z z t

100Az m

300Bz m

0 0z m(s)t

(s)t0 2 4 6 10

0 2 4 6 10

(s)t

0 0( , , ) ( , , )A BG z z t G z z t

0( , , )AG z z t

0( , , )BG z z t

-4 -2 0 4

100Az m

300Bz m

0 0z m(s)t

(s)t0 2 4 6 10

0 2 4 6 10

(s)t

0 0( , , ) ( , , )A BG z z t G z z t

0( , , )AG z z t

0( , , )BG z z t

-4 -2 0 4

-4 -2 0 4 (s)t

( , , ) ( , , )B A B AG z z t G z z t

AxBx

0S

1S

ˆ2 { ( , , )}B AG x x

*1 ˆ ˆ{ ( , , ) ( , , )i B ASG G

j


r

Analysis of integral over for 1S r ˆ ( , , ) : (1/ )AG O rx x

* 2ˆ ˆ : (1/ )iG G O r2

1 : ( )S O r

1

2 : (1)S

d O x

x

Hence, integral over alone is not sufficient0S

AxBx

1S

ˆ2 { ( , , )}B AG x x

*1 ˆ ˆ{ ( , , ) ( , , )i B ASG G

j


r

Analysis of integral over for 1S r ˆ ( , , ) : ( ( ) / ); ( ) 0AG O T r r T r x x

* 2 2ˆ ˆ : ( ( ) / )iG G O T r r2

1 : ( )S O r

1

2 2: ( ( )) 0S

d O T r x

‘Sufficiently inhomogeneous’

0S

x

Hence, integral over alone is sufficient !0S

100Az m

300Bz m

( / )Pc m s

0 0z m

( / )Pc m s

25 layers

( / )Pc m s

250 layers

3000

2000

10000 1000 2000 3000 5000

(m/s)Pc

(m)z

(m)r

0

1

2

3

5

(s)t

(m)r

0 1000 2000 3000 5000

0 1000 2000 3000 5000

1.0

0.60.40.20.0

2 ( )T r

1500

(a)

(b)

(c)

3000

2000

10000 1000 2000 3000 5000

(m/s)Pc

(m)z

(m)r

0

1

2

3

5

(s)t

(m)r

0 1000 2000 3000 5000

0 1000 2000 3000 5000

1.0

0.60.40.20.0

21 ( )T r

1500

(a)

(b)

(c)

(s)t

(s)t0 2 4 6 10

0 2 4 6 10

(s)t

0 0( , , ) ( , , )A BG z z t G z z t

0( , , )AG z z t

0( , , )BG z z t

-4 -2 0 4

-4 -2 0 4 (s)t

( , , ) ( , , )B A B AG z z t G z z t

(a)

(b)

(c)

(d)

25 layers

(s)t

(s)t0 2 4 6 10

0 2 4 6 10

(s)t

0 0( , , ) ( , , )A BG z z t G z z t

0( , , )AG z z t

0( , , )BG z z t

-4 -2 0 4

-4 -2 0 4 (s)t

( , , ) ( , , )B A B AG z z t G z z t

(a)

(b)

(c)

(d)

250 layers

Observations:• Exact reconstruction possible from sources on alone• The full coda contributes to the reconstruction of early arrivals: Hence, (much) longer registrations required

To be investigated:• Stability (Snieder and Scales)• More realistic configurations• Comparison with virtual source (Bakulin and Calvert)• Comparison with primaries from multiples (Berkhout and Verschuur)• Effect of anelastic losses• Elastodynamic extension

0S

zV xV zV x

Seismic interferometry for multicomponent exploration data

From 3-component data to 3x3 component data

Conclusions• Exact representation requires sources on closed surface

AxBx

S

AxBx

1S

0S

Conclusions• Exact representation requires sources on closed surface• For passive data: sources in subsurface suffice

AxBx

0S

Conclusions• Exact representation requires sources on closed surface• For passive data: sources in subsurface suffice• For exploration data: sources at surface suffice if medium is sufficient inhomogeneous

Conclusions• Exact representation requires sources on closed surface• For passive data: sources in subsurface suffice• For exploration data: sources at surface suffice if medium is sufficient inhomogeneous• The full coda contributes to the reconstruction of early arrivals Hence, (much) longer registrations required

Conclusions• Exact representation requires sources on closed surface• For passive data: sources in subsurface suffice• For exploration data: sources at surface suffice if medium is sufficient inhomogeneous• The full coda contributes to the reconstruction of early arrivals Hence, (much) longer registrations required• Extension to multicomponent data

zV xV zV x

Ax

Bx

0S

Snieder, Wapenaar and Larner, 2006

0

0.5

1.0

-1.0

-0.5

t

0

-1.0

-0.5

0.5

t

x-3000 -1500 0 1500 3000

1 1

3 3

2 2

44

1.0


R)(RG


R)(RG

1R2R

)( 21 RRrG


R)(RG

1R2R

)( 21 RRrG

1R2R

)( 21* RRrG


R)(RG

1R2R

)( 21 RRrG

1R2R

)( 21* RRrG

R)(*2 RGr


0

0.5

1.0

-1.0

-0.5

t

0

-1.0

-0.5

0.5

t

x-3000 -1500 0 1500 3000

1 1

3 3

2 2

44

1.0


Seismic interferometry for passive and exploration data: reconstruction of internal multiples Kees...

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