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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)
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
x x x x* 2ˆ ˆ( , , ) ( , , )}B i A iG G n d x x x x x
Dipole at x
x
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
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
High-frequencyapproximation
Far-field approximation(Fraunhofer)
* 22 ˆ ˆ( , , ) ( , , )B ASG G d
c
x x x x x
Ax Bx
High-frequencyapproximation
Far-field approximation(Fraunhofer)
( , , ) ( , , )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
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
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
High-frequencyapproximation
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
Far-field approximation(Fraunhofer)
Ax Bx
Free surface
1S
0SHigh-frequencyapproximation
Far-field approximation(Fraunhofer)
( , , ) ( , , )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
Real data application:
Draganov et al.Seismic interferometry on background-noise field data
Tomorrow, 8:30 AM, session CH 4, room 278
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
x x x x* 2ˆ ˆ( , , ) ( , , )}B i A iG G n d x x x x x
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
x x x x* 2ˆ ˆ( , , ) ( , , )}B i A iG G n d x x x x x
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
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
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
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
zV xV zV x
Seismic interferometry for multicomponent exploration data
From 3-component data to 3x3 component data
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
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
Snieder, Wapenaar and Larner, 2006