Transcript PPT file - UTAM

Wave-Equation Migration in
Anisotropic Media
Jianhua Yu
University of Utah
Contents
Motivation
Anisotropic Wave-Equation Migration
Numerical Examples:
Cusp model
2-D SEG/EAGE model
3-D SEG/EAGE model
Conclusions
Contents
Motivation
Anisotropic Wave-Equation Migration
Numerical Examples:
Cusp model
2-D SEG/EAGE model
3-D SEG/EAGE model
Conclusions
What Blurs Seismic Images?
Irregular acquisition geometry
Bandwidth source wavelet
Velocity errors
Higher order phenomenon:
Anisotropy
Anisotropic Imaging
Ray-based anisotropic migration:
Anisotropic velocity model
Anisotropic wave-equation migration:
---Ristow et al, 1998
---Han et al. 2003
Objective:
Develop 3-D anisotropic wave-equation
migration method in orthorhombic
model
o
>78 wave propagator
High efficiency
Improve image accuracy
Contents
Motivation
Anisotropy Wave-Equation Migration
Numerical Examples:
Cusp model
2-D SEG/EAGE model
3-D SEG/EAGE model
Conclusions
General Wave Equation
Wave equation in displacement
 ui
2

 t
2
Ui :
Cijkl


x j
(Cijkl
uk
xl
)  Fi
displacement component
:
4th-order stiffness tensor
3
3
 ij   cijklekl ,
k
l
i , j  1, 2 , 3
Eigensystem Equation
 11  V

12
13


2
 21
22  V
23 


2





V
31
32
33


2
 U1 
 
U 2   0
U 
 3
Polarization components of P-P, SV,
and SH waves
Orthorhombic Anisotropic
Γ11  c n  c n  c n
2
11 1
2
66 2
2
55 3
Γ 22  c n  c n  c n
2
66 1
2
22 2
2
44 3
Γ 33  c n  c n  c n
2
55 1
2
44 2
Γ12  (c11  c66 )n1n2
Γ13  (c13  c55 )n1n3
2
33 3
Orthorhombic Anisotropic
Γ 21  (c21  c66 )n1n2
Γ 23  (c23  c44 )n2n3
Γ 32  (c32  c44 )n2n3
Γ 31  (c31  c55 )n1n3
Decoupled P plane Wave Motion
Equations in (x,z) and (y,z) planes
 c11K x2  c55K z2   2
( c13  c55 ) K x K z U1 

   0

2
2
2 
 (c  c ) K K
U
c55K x  c33K z    2 
55
x
z
 13
and
 c22 K x2  c44 K z2   2
( c23  c44 ) K x K z U 2 

   0

2
2
2 
 (c  c ) K K
U
c44 K x  c33K z    3 
44
x
z
 23
Decoupled P plane Wave Motion
Equations in (x,z) and (y,z) planes
 c11K x2  c55K z2   2
( c13  c55 ) K x K z U1 
   0
det 

2
2
2 
 (c  c ) K K
U
c55K x  c33K z    2 
55
x
z
 13
and
 c22 K x2  c44 K z2   2
( c23  c44 ) K x K z U 2 
det 
   0

2
2
2 
 (c  c ) K K
U
c44 K x  c33K z    3 
44
x
z
 23
Dispersion Equations
    (1   ) K
4
K 
2
z
K 
2
   2(
2
2
(1)
(1)

(1)
    (1  
4
2
z
2
2
   2(
2
2
2
(2)

) K
4
( 2)
( 2)
2
x
)K
2
y
) K
4
Thomsen’s Parameters
2
x
(x,z) plane
(y,z) plane
2
y
Thomsen’s Parameters
c33


(2)



(1)

c22  c33
2c33
c11  c33
2c33
( c23  c44 )  ( c33  c44 )
2

(1)

2c33 (c33  c44 )
(c13  c55 )  (c33  c55 )
2

( 2)

2
2c33 (c33  c55 )
2
c44  c55
VTI:
K 


(1)

( 2)
( 2)


   0 (1  2 0 ) K
4
2
z

(1)
2
2
x
2
x
   2( 0   0 ) K
2


2
0
4
0
( m  A0 ) K
A
2
2
x
 0 [1  ( B  B0 )] K
2
x
 (
1


1
0
FFD
algorithm
)
FFD Anisotropy Migration
A0  a (1  2
A  a(1  2
(1)
0
(1)
)
)
B0  b  2(a  2b)
(1)
0
 2(a  b)
(1)
0
B  b  2(a  2b)
(1)
 2(a  b)
(1)
How to Set Velocity and
Anisotropy Parameters
Velocity:
Anisotropy:
a &b:
  0  d

(1)


(1)

(1)
0
(1)
0
 d
(1)
 d
(1)
Optimization coefficients of
Pade approximation for FD
Pade Approximation Comparison
Error %
5
0
0
Angle
90
Pade Approximation Comparison
0.05
Beyond 78 within 0.02 %
Error
%
0
0
Angle
78
Contents
Motivation
Anisotropy Wave-Equation Migration
Numerical Examples:
Cusp model
2-D SEG/EAGE model
3-D SEG/EAGE model
Conclusions
0.6
Weak Anisotropy
Strong Anisotropy
Exact
** Approximation
Exact
** Approximation
0  0
 0  0.1
0  0
  0.0015
  0.5
  0.4
Kz
  0.05
 0  0.2
0
-0.3
Kx
0.3
-0.3
Kx
0.3
Dispersion Equation Approximation
Kz
0.3
Strong anisotropy
0
-0.3
Kx
0.3
V/V0=3
iso
V/V0=3
iso
Standard
Depth (km)
New
0
2.0
 0  0.1
Depth (km)
0
2.0
 0  0.2   0.5
V/V0=3
0  0
V/V0=3
  0.4
Strong Aniso
0  0
  0.05
  0.0015
Weak Aniso
Contents
Motivation
Anisotropy Wave-Equation Migration
Numerical Examples:
Cusp model
2-D SEG/EAGE model
3-D SEG/EAGE model
Conclusions
0
X (km)
Depth (km)
0
1
Velocity (2.0-3.0 km/s)
1.5
X (km)
1.5
1
0
0
 0  0.04
1.5
 0  0.1   0
  0
Time (s)
Time (s)
0
0
X (km)
Isotropic data
(SUSYNLY)
Velocity
(2.0-3.0
km/s)
1.2 Anisotropic data (SUSYNLVFTI)
X (km)
0
1.5 0
1.5
0
Depth (km)
0
1
Isotropic data
Isotropic mig (su)
Anisotropic data
Isotropic mig
Anisotropic data
Anisotropic mig
1.5
Contents
Motivation
Anisotropy Wave-Equation Migration
Numerical Examples:
Cusp model
2-D SEG/EAGE model
3-D SEG/EAGE model
Conclusions
X (km)
0
 0  0.045
 0  0.1
  0
Depth (km)
0
4
Salt Model (VTI)
5
  0
0
X (km)
Depth (km)
0
4
Iso-mig
5
0
X (km)
Depth (km)
0
4
VTI Aniso-mig
5
Inaccurate Thomsen’s Parameters (VTI)
0
X (km)
1.5 0
X (km)
1.5 0
X (km)
1.5
Depth (km)
0
4
Anisotropy Error 10 %
Anisotropy Error 20 %
Anisotropy Error 40 %
Inaccurate Thomsen’s Parameters
5
X (km)
10
5
X (km)
10 5
X (km)
10
Depth (km)
3
4
Anisotropy Error 10 %
Anisotropy Error 20 %
Anisotropy Error 40 %
Contents
Motivation
Anisotropy Wave-Equation Migration
Numerical Examples:
Cusp model
2-D SEG/EAGE VTI model
3-D SEG/EAGE VTI model
Conclusions
X (km)
X (km)
5 0
 0  0.045
 0  0.1   0
5
  0
Depth (km)
0
0
4
Iso (y=1.5 km)
VTI Aniso (y=1.5 km)
0
Y (km)
5 0
Y (km)
Depth (km)
0
4
Iso (x=1.5 km)
VTI Aniso (x=1.5 km)
5
0
Y (km)
5 0
Y (km)
Depth (km)
0
4
Iso (x=3 km)
VTI Aniso (x=3 km)
5
0
Y (km)
0
5
X (km)
Iso (z=0.5 km)
5 0
X (km)
VTI Aniso (z=0.5 km)
5
0
Y (km)
0
5
X (km)
Iso (z=2.5 km)
5 0
X (km)
VTI Aniso (z=2.5 km)
5
Contents
Motivation
Anisotropy Wave-Equation Migration
Numerical Examples:
Cusp model
2-D SEG/EAGE model
3-D SEG/EAGE model
Conclusions
Conclusions
o
New > 78 Anisotropic wave propagator:
Works for 2-D and 3-D media
Valid for VTI and TI
Improves spatial resolution
o
78 Propagator Cost = Cost of
Standard 45^o propagator
Thanks To
2003 UTAM Sponsors
CHPC