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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. - PowerPoint PPT Presentation
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Wave-Equation Migration in Wave-Equation Migration in Anisotropic MediaAnisotropic Media
Jianhua YuJianhua Yu
University of UtahUniversity of Utah
Contents Contents
Motivation
Anisotropic Wave-Equation Migration
Numerical Examples:
Cusp model
Conclusions
2-D SEG/EAGE model
3-D SEG/EAGE model
Contents Contents
Motivation
Anisotropic Wave-Equation Migration
Numerical Examples:
Cusp model
Conclusions
2-D SEG/EAGE model
3-D SEG/EAGE model
What Blurs Seismic Images? What Blurs Seismic Images?
Irregular acquisition geometry
Bandwidth source wavelet
Velocity errors
Higher order phenomenon: Anisotropy
Anisotropic ImagingAnisotropic Imaging
Ray-based anisotropic migration: Anisotropic velocity model
Anisotropic wave-equation migration:
---Ristow et al, 1998
---Han et al. 2003
Objective: Objective:
High efficiency
Improve image accuracy
Develop 3-D anisotropic wave-equation migration method in orthorhombic model
>78 wave propagatoro
Contents Contents
Motivation
Anisotropy Wave-Equation Migration
Numerical Examples:
Cusp model
Conclusions
2-D SEG/EAGE model
3-D SEG/EAGE model
General Wave EquationGeneral Wave EquationWave equation in displacement
il
kijkl
j
i Fx
uC
xt
u
)(2
2
Ui : displacement component
Cijkl : 4th-order stiffness tensor
3 3
3,2,1,,k l
jiklijklij ec
Eigensystem EquationEigensystem Equation
0
3
2
1
2333231
232
2221
13122
11
U
U
U
V
V
V
Polarization components of P-P, SV, and SH waves
Orthorhombic AnisotropicOrthorhombic Anisotropic2355
2266
211111 ncncncΓ
21661112 n)nc(cΓ
31551313 n)nc(cΓ
2344
2222
216622 ncncncΓ
2333
2244
215533 ncncncΓ
Orthorhombic AnisotropicOrthorhombic Anisotropic
21662121 n)nc(cΓ
32442323 n)nc(cΓ
31553131 n)nc(cΓ
32443232 n)nc(cΓ
Decoupled P plane Wave Motion Decoupled P plane Wave Motion Equations in (x,z) and (y,z) planesEquations in (x,z) and (y,z) planes
0)(
)(
2
1
2233
2555513
551322
552
11
U
U
KcKcKKcc
KKccKcKc
zxzx
zxzx
0)(
)(
3
2
2233
2444423
442322
442
22
U
U
KcKcKKcc
KKccKcKc
zxzx
zxzx
and
Decoupled P plane Wave Motion Decoupled P plane Wave Motion Equations in (x,z) and (y,z) planesEquations in (x,z) and (y,z) planes
0)(
)(
2
1
2233
2555513
551322
552
11
U
U
KcKcKKcc
KKccKcKc
zxzx
zxzx
0)(
)(
3
2
2233
2444423
442322
442
22
U
U
KcKcKKcc
KKccKcKc
zxzx
zxzx
and
det
det
Dispersion EquationsDispersion Equations
24)1()1(22
2)1(2242
)(2
)1(
x
xz K
KK
(x,z) plane
24)2()2(22
2)2(2242
)(2
)1(
y
yz K
KK
(y,z) plane
Thomsen’s Parameters
33c
33
3322)1(
2c
cc
)(2
)()(
443333
24433
24423)1(
ccc
cccc
Thomsen’s Parameters
33
3311)2(
2c
cc
)(2
)()(
553333
25533
25513)2(
ccc
cccc
VTI:
)2()1(
)2()1(
5544 cc
20
20
2
0 )](1[
)(
x
xm
A
KBB
KA
24000
20
2
200
242
)(2
)21(
x
xz K
KK
)11
(0
FFD algorithm
FFD Anisotropy Migration
)21( )1(00 aA
)21( )1(aA
)1(0
)1(00 )(2)2(2 bababB
)1()1( )(2)2(2 bababB
How to Set Velocity and Anisotropy Parameters
a & b : Optimization coefficients of Pade approximation for FD
d 0Velocity:
Anisotropy:
)1()1(0
)1( d
)1()1(0
)1( d
0
5
Err
or %
0 90
Pade Approximation Comparison
Angle
0
0.05
Error %
0 78
Pade Approximation Comparison
Angle
Beyond 78 within 0.02 %
Contents Contents
Motivation
Anisotropy Wave-Equation Migration
Numerical Examples:
Cusp model
Conclusions
2-D SEG/EAGE model
3-D SEG/EAGE model
0.6
0
Kz
Kx -0.3 0.3 Kx -0.3 0.3
Weak Anisotropy Strong Anisotropy
Exact Exact
** Approximation ** Approximation
2.01.0 00 4.05.0
00 00 0015.005.0
0.3
0
Kz
Kx -0.3 0.3
Dispersion Equation Approximation
Strong anisotropy
0
2.0
Dep
th (
km
)
V/V0=3
V/V0=3
iso
iso
New
Sta
nd
ard
0
2.0
Dep
th (
km
)
V/V0=3
V/V0=3
Weak Aniso
Strong Aniso
2.01.0 00 4.05.0
00 00 0015.005.0
Contents Contents
Motivation
Anisotropy Wave-Equation Migration
Numerical Examples:
Cusp model
Conclusions
2-D SEG/EAGE model
3-D SEG/EAGE model
00
1
Dep
th (
km
)1.5X (km)
Velocity (2.0-3.0 km/s)Velocity (2.0-3.0 km/s)
00
1
Tim
e (s
)
1.5X (km)
Velocity (2.0-3.0 km/s)
0 1.5
Anisotropic data (SUSYNLVFTI)
0
1.2
Tim
e (s
)
X (km)
Isotropic data (SUSYNLY)
1.004.0 00 00
00
1
Dep
th (
km
)
1.5
X (km)
Isotropic data Isotropic mig (su)
0 1.5
Anisotropic data Isotropic mig
0 1.5
Anisotropic data Anisotropic mig
Contents Contents
Motivation
Anisotropy Wave-Equation Migration
Numerical Examples:
Cusp model
Conclusions
2-D SEG/EAGE model
3-D SEG/EAGE model
00
4
Dep
th (
km
)5X (km)
Salt Model (VTI)
1.0045.0 00 00
00
4
Dep
th (
km
)5X (km)
Iso-mig
00
4
Dep
th (
km
)5X (km)
VTI Aniso-mig
0 1.5
Anisotropy Error 40 %
X (km)
0
4
Dep
th (
km
)
0 1.5
Anisotropy Error 10 %
X (km)0 1.5
Anisotropy Error 20 %
X (km)
Inaccurate Thomsen’s Parameters (VTI)
5 10
Anisotropy Error 40 %
X (km)
3
4
Dep
th (
km
)
5 10
Anisotropy Error 10 %
X (km)5 10
Anisotropy Error 20 %
X (km)
Inaccurate Thomsen’s Parameters
Contents Contents
Motivation
Anisotropy Wave-Equation Migration
Numerical Examples:
Cusp model
Conclusions
2-D SEG/EAGE VTI model
3-D SEG/EAGE VTI model
0
4
Dep
th (
km
)0 5X (km) 0 5X (km)
VTI Aniso (y=1.5 km)Iso (y=1.5 km)
1.0045.0 00 00
0
4
Dep
th (
km
)0 5Y (km) 0 5Y (km)
VTI Aniso (x=1.5 km)Iso (x=1.5 km)
0
4
Dep
th (
km
)0 5Y (km) 0 5Y (km)
VTI Aniso (x=3 km)Iso (x=3 km)
00
5
Y (
km
)
5X (km) 0 5X (km)
VTI Aniso (z=0.5 km)Iso (z=0.5 km)
00
5
Y (
km
)
5X (km) 0 5X (km)
VTI Aniso (z=2.5 km)Iso (z=2.5 km)
Contents Contents
Motivation
Anisotropy Wave-Equation Migration
Numerical Examples:
Cusp model
Conclusions
2-D SEG/EAGE model
3-D SEG/EAGE model
Conclusions Conclusions
Works for 2-D and 3-D media
New > 78 Anisotropic wave propagator:
Improves spatial resolution
Valid for VTI and TI
o
78 Propagator Cost = Cost of Standard 45^o propagator
o
Thanks To Thanks To
2003 UTAM Sponsors
CHPC