Deghosting of towed streamer
and OBC data
Jingfeng Zhang, Arthur B. Weglein
M-OSRP Annual Meeting,
University of Houston
March 31 – April 1, 2004
1
March 31st–April 1st, 2004
Outline
• Motivation
• Theory overview
• Towed streamer deghosting
– Theory and strategy
– Numerical tests
• Ocean bottom deghosting
• Conclusions and plans
• Acknowledgements
2
March 31st–April 1st, 2004
Motivation
• Towed streamer deghosting
– Conventional methods
– New techniques
• Ocean Bottom deghosting
– Conventional methods
– New techniques
3
March 31st–April 1st, 2004
M-OSRP projects
•
•
•
•
•
•
4
Wavelet estimation
Deghosting
Interpolation and extrapolation
3-D multiple attenuation
Inverse scattering sub series for imaging
Inverse scattering sub series for inversion
March 3rd, 2004
Theory Overview
Weglein et al. (2002)
deg hosted  
P
( r , rs ,  )
' 
  '
 ' 
G0 ( r , r ,  )
P ( r , rs ,  )   '
  '
 P ( r , rs ,  )
ds
 G0 ( r , r ,  )
'
'

n
n

M .S. 
F.S.

rs

r
M.S.
earth
5
March 31st–April 1st, 2004
Note (1)
' 
' 
' 
2
 P ( r , rs ,  )  2  ' P ( r , rs ,  )  A( ) ( r  rs )
c (r )
'2
2
2

'

1


(
r
)

c 2 ( r ' ) c02

 '2 ' 
' 
'  2 ' 
 2 ' 
 P ( r , rs ,  )  2 P ( r , rs ,  )  A( ) ( r  rs )   ( r ) 2 P ( r , rs ,  )
c0
c0


2
 ' 2G ( r ' , r ,  )   G ( r ' , r ,  )   ( r '  r )
0
0

c02
 
 
 

P
(
r
,
r
,

)

G
(
r
,
r
,

)

G
(
r
, r ,  )

'2
'
s
'
0
'
0
'2

 

P ( r ' , rs ,  ) dr '
V

 '
' 
'  '
' 
' 
'  2 ' 
  P ( r , rs ,  ) ( r  r )dr   G0 ( r , r ,  ) A( ) ( r  rs )   ( r ) 2 P ( r , rs ,  ) dr
c0


V
V
6
March 31st–April 1st, 2004
Note (2)
Green’s Second Identity
 

' 
' 
' 
' 
'
'2
'2
P ( r , rs ,  ) G0 ( r , r ,  )  G0 ( r , r ,  ) P ( r , rs ,  ) dr
V
 


'
' 
' 
' 
' 
'
'
P ( r , rs ,  ) G0 ( r , r ,  )  G0 ( r , r ,  ) P ( r , rs ,  )  dS
S
 

'
' 
' 
' 
' 
'
'
P ( r , rs ,  ) G0 ( r , r ,  )  G0 ( r , r ,  ) P ( r , rs ,  )  dS
S

 '
' 
'  '
' 
' 
'  2 ' 
  P ( r , rs ,  ) ( r  r )dr   G0 ( r , r ,  ) A( ) ( r  rs )   ( r ) 2 P ( r , rs ,  ) dr
c0


V
V
7
(*)
March 31st–April 1st, 2004
Note (3)

rs
F.S.
Deghosting formula Eq. (1)
M.S.
Weglein et al. (2002)
V

r
earth
 
 
 
 

P
(
r
,
r
,

)

G
(
r
,
r
,

)

G
(
r
,
r
,

)

P
(
r
, r ,  ) dS

'
'
s
'
0
'
0
'
'
'
s
S

 
' 
'  '
' 
' 
'  2 ' 
  P ( r , rs ,  ) ( r  r )dr   G0 ( r , r ,  ) A( ) ( r  rs )   ( r ) 2 P ( r , rs ,  ) dr '
c0


V
V
(*)
'
' 
' 
' 
' 
' 
'  2 ' 
'
'
'
P
(
r
,
r
,

)

G
(
r
,
r
,

)

G
(
r
,
r
,

)

P
(
r
,
r
,

)

d
S


G
(
r
,
r
,

)

(
r
)
P
(
r
,
r
,

)
d
r
s
0
0
s
0
s


c02
M .S .
V


' 
'  2 ' 

   G0 ( r , r ,  ) earth( r ) 2 P ( r , rs ,  )dr '
c0
V
' 
  ' 

 ' 
 '
 ' 
deg hosted  
P
(
r
,
r
,

)
G
(
r
,
r
,

)

G
(
r
,
r
,

)
P
(
r
,
r
,

)
dS

P
( r , rs ,  )
s
0
0
s
'
'




z

z

M .S . 
8
(1)
March 31st–April 1st, 2004
Note (4)

rs
F.S.
Field prediction Eq. (2)
V
H. Tan (1992) and A.Osen et al. (1998)
M.S.

r
Scattered field prediction Eq. (3)
earth
H. Tan (1999), Weglein et al. (2000)
 
 
 
 

P
(
r
,
r
,

)

G
(
r
,
r
,

)

G
(
r
,
r
,

)

P
(
r
, r ,  ) dS

'
'
s
'
0
'
'
'
'
0
s
S

 
' 
'  '
' 
' 
'  2 ' 
  P ( r , rs ,  ) ( r  r )dr   G0 ( r , r ,  ) A( ) ( r  rs )   ( r ) 2 P ( r , rs ,  ) dr '
c0


V
V
 
(*)

'
' 
' 
' 
' 
 
 
'
'
P ( r , rs ,  ) G0 ( r , r ,  )  G0 ( r , r ,  ) P ( r , rs ,  )  dS  P ( r , rs ,  )  A( )G0 ( r , rs ,  )
S
 
DD  
P ( r , rs ,  )  A( )G0 ( r , rs ,  ) 
 

'
' 
' DD  ' 
P ( r , rs ,  ) G0 ( r , r ,  )  dS
( 2)
M .S .
 

'
' 
' 
 
 
 
' D ' 
D ' 
'
P ( r , rs ,  ) G 0 ( r , r ,  )  G 0 ( r , r ,  ) P ( r , rs ,  )  dS  P ( r , rs ,  )  A( )G 0D ( r , rs ,  )  Ps ( r , rs ,  )
( 3)
M .S .
9
March 31st–April 1st, 2004
Note (5)
Wavelet estimation Eq. (4)
F.S.
Weglein and Secrest, (1990)
M.S.
V

rs
earth

r
 
 
 
 

P
(
r
,
r
,

)

G
(
r
,
r
,

)

G
(
r
,
r
,

)

P
(
r
, r ,  ) dS

'
'
s
'
0
'
0
'
'
'
s
S

 
' 
'  '
' 
' 
'  2 ' 
  P ( r , rs ,  ) ( r  r )dr   G0 ( r , r ,  ) A( ) ( r  rs )   ( r ) 2 P ( r , rs ,  ) dr '
c0


V
V
 
(*)

'
' 
' 
' 
' 
 
'
'
P ( r , rs ,  ) G0 ( r , r ,  )  G0 ( r , r ,  ) P ( r , rs ,  )  dS   A( )G0 ( r , rs ,  )
S
 

'
' 
' 
 
' D ' 
D ' 
'
P ( r , rs ,  ) G 0 ( r , r ,  )  G 0 ( r , r ,  ) P ( r , rs ,  )  dS   A( )G 0D ( r , rs ,  )
(4)
M .S .
10
March 31st–April 1st, 2004
Notes conclusion
 

'
' 
' 
' 
' 
'
'
P ( r , rs ,  ) G0 ( r , r ,  )  G0 ( r , r ,  ) P ( r , rs ,  )  dS
S

 
' 
'  '
' 
' 
'  2 ' 
  P ( r , rs ,  ) ( r  r )dr   G0 ( r , r ,  ) A( ) ( r  rs )   ( r ) 2 P ( r , rs ,  ) dr '
c0


V
V
' 
  ' 

 ' 
 '
 ' 
P
(
r
,
r
,

)
G
(
r
,
r
,

)

G
(
r
,
r
,

)
P
(
r
,
r
,

)
dS
s
0
0
s
'
'



z
z

M .S. 
 
P deg hosted ( r , rs ,  ) 
(1)
 
DD  
P ( r , rs ,  )  A( )G0 ( r , rs ,  ) 
 
Ps ( r , rs ,  ) 
(*)
 
M .S .
 

'
' 
' DD  ' 
P ( r , rs ,  ) G0 ( r , r ,  )  dS
( 2)

( 3)
'
' 
' 
' D ' 
D ' 
'
P ( r , rs ,  ) G 0 ( r , r ,  )  G 0 ( r , r ,  ) P ( r , rs ,  )  dS
M .S .
 
A( )G 0 ( r , rs ,  )  
D
 

'
' 
' 
' D ' 
D ' 
'
P ( r , rs ,  ) G 0 ( r , r ,  )  G 0 ( r , r ,  ) P ( r , rs ,  )  dS
(4)
M .S.
11
March 31st–April 1st, 2004
Towed streamer deghosting
(Theory)
Weglein et al. (2002)
deg hosted  
P
( r , rs ,  ) 
 
' 
 ' 


G0 ( r , r ' ,  )

P
(
r
, rs ,  )  '

'

dS
 G0 ( r , r ,  )
'
'

 P ( r , rs ,  )
n
n

M .S . 
F.S.

rs

r
Pseudo-M.S.
M.S.
deg hosted  
P
( r , rs ,  ) 
12
"
 P ( r )
P ( r " ),  "
 ' n
P (r )
 
" 
 " 


G0 ( r , r " ,  )

P
(
r
, rs ,  )  "

"

dS
 G0 ( r , r ,  )
"
"

 P ( r , rs ,  )
n
n

P.M .S . 
March 31st–April 1st, 2004
Towed streamer deghosting
(Theory)
H. Tan (1992) and A.Osen et al. (1998)
' "
" 
' 
G ( r , r ,  ) '
DD  " 
P ( r , rs ,  )  A( )G0 ( r , rs ,  )   P ( r , rs ,  )
dS
'
n
M .S .
 
 
 
' 
P ( r " , rs ,  )
G0DD ( r " , rs ,  )
 2G0DD ( r ' , r " ,  ) '
 A( )
  P ( r , rs ,  )
dS
"
"
' "
n
n
n n
M .S .
DD
0
H. Tan (1999), Weglein et al. (2002)
" 
P ( r , rs ,  )
 
' 
G0DD ( r ' , r " ,  ) '
  P ( r , rs ,  )
dS
'

n
M .S .
" 
2 DD  '  "



G0 ( r , r ,  ) '
P ( r , rs ,  ) 
'
P
(
r
,
r
,

)
dS
' "
s

"
n n
M .S.
n
13
March 31st–April 1st, 2004
Towed streamer deghosting
(Theory)
K=0.3 (f~72Hz)
Pseudo-M.S.
14
March 31st–April 1st, 2004
Towed streamer deghosting
(Theory)
 
 
 
' 
P ( r " , rs ,  )
G0DD ( r " , rs ,  )
 2G0DD ( r ' , r " ,  ) '
 A( )
  P ( r , rs ,  )
dS
"
"
' "
n
n
n n
M .S .
15
March 31st–April 1st, 2004
Towed streamer deghosting
(Theory)
" 
DD  " 
P ( r , rs ,  )  A( )G0 ( r , rs ,  ) 
DD  " 
 A( )G0 ( r , rs ,  ) 
 
M .S .
 
 A( )G0DD ( r " , rs ,  )  A( )
DD  '  "





G
D
'
'
0 (r , r ,  )
A( )G0 ( r , rs ,  )  Ps ( r , rs ,  )
dS '
'
n

DD  '  "
DD  '  "





G
(
r
,
r
,

)

G
D
'
'
'
0
0 (r , r ,  )
G
(
r
,
r
,

)
dS

P
(
r
,
r
,

)
dS '

'
0
s
s
s
'


n
n
M .S .
M .S .
(2)
16
 
' 
G0DD ( r ' , r " ,  ) '
P ( r , rs ,  )
dS
'

n
M .S .
(3)
March 31st–April 1st, 2004
Towed streamer deghosting
(Theory)
Offset x (m)
17
Exact A()=1.0
March 31st–April 1st, 2004
Towed streamer deghosting
(Numerical tests)
F.S.
(0,2)
6.0m
M.S.
300m
c1=1500m/s
c2=2250m/s
18
March 31st–April 1st, 2004
Ricker wavelet
19
March 31st–April 1st, 2004
Total data received
At (0,6.0)
20
At (1500,6.0)
March 31st–April 1st, 2004
Wavelet approximation
21
March 31st–April 1st, 2004
22
March 31st–April 1st, 2004
23
March 31st–April 1st, 2004
24
March 31st–April 1st, 2004
25
March 31st–April 1st, 2004
Wavelet approximation
26
March 31st–April 1st, 2004
27
March 31st–April 1st, 2004
28
March 31st–April 1st, 2004
29
March 31st–April 1st, 2004
30
March 31st–April 1st, 2004
Depth sensitivity
K=0.3 (f~72Hz)
A1(w)=(2,3),A2=0.04*A1,A3=0.03*A1,A4=0.3*A1
Pseudo-M.S.
31
March 31st–April 1st, 2004
Red solid: Exact Up-going P (5.8m)
Blue dash: Predicted Up-going P (6.3m) (using wrong depth 6.5m)
32
March 31st–April 1st, 2004
Red solid: Exact Up-going P (5.8m)
Blue dash: Predicted Up-going P (6.3m) (using wrong depth 6.5m)
33
March 31st–April 1st, 2004
Red solid: Exact Up-going P (5.8m)
Blue dash: Predicted Up-going P (6.3m) (using wrong depth 6.5m)
34
March 31st–April 1st, 2004
Red solid: Exact Up-going P (5.8m)
Blue dash: Predicted Up-going P (6.3m) (using wrong depth 6.5m)
35
March 31st–April 1st, 2004
Ocean bottom data deghosting
(Theory)
Weglein et al. (2002)
 
P deg hosted ( r , rs ,  )
 
' 
 ' 


G0 ( r , r ' ,  )

P
(
r
, rs ,  )   '

'

ds
 G0 ( r , r ,  )
'
'

 P ( r , rs ,  )
n
n

M .S. 
• Both P and P ' (particle velocity) are measured.
– Noise on geophone
– Coupling issue and scale factor : actually measured
are P and  P '
36
March 31st–April 1st, 2004
Ocean bottom data deghosting
(Theory)
Troublesome and historic
impediment measurement
(P ' )
Triangle relationship
Two stable measurements
( A( ), P )
Wavelet estimation
Weglein and Secrest, (1990)
 

'
' 
' 
' D ' 
D ' 
'
D  
P ( r , rs ,  ) G 0 ( r , r ,  )  G 0 ( r , r ,  ) P ( r , rs ,  )  dS   A( )G 0 ( r , rs ,  )
M .S .
ik
d
A
(

)
e
P k x , z' , x s , z s ,   
dz'
37
x xs
e
 ikz z s


 e ikz z s  ikz P k x , z' , x s , z s ,   e  ikz z '  e ikz z '
e  ikz z '  e ikz z '

March 31st–April 1st, 2004
Ocean bottom data deghosting
(Theory)
• In this procedure:
– Using P and A() to calculate P '
{P  A( )}  P '
– Deghosting
38
March 31st–April 1st, 2004
Conclusions for towed streamer
deghosting
• If source wavelet is available, the deghosting
algorithm performs well, as expected.
• With an approximate wavelet, the algorithm
still works well. If the rough duration of the
source wavelet is known, very good deghosting
result can be obtained.
• Field data test is planned for 2004.
39
March 31st–April 1st, 2004
Plans and Acknowledgements
• Numerical tests on the proposed procedure
for ocean bottom deghosting using both
synthetic and ocean bottom cable field data.
• We thank M-OSRP sponsors for supporting
this project.
• Special thanks to Nizar Chemingui and Jon
Sheiman for their interests. We thank A. deHoop for providing references and Hing Tan
for valuable discussions.
40
March 31st–April 1st, 2004