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Wide-azimuth angle gathers
for anisotropic wave-equation migration
Paul Sava 1 and Tariq Alkhalifah 2
1Center for Wave Phenomena, Colorado School of Mines
2King Abdullah University of Science and Technology
From the net
Q: What is the di�erence between a Ph.D. in
mathematics and a large pizza?
A: A large pizza can feed a family of four...
From the net
Q: What is the di�erence between a Ph.D. in
mathematics and a large pizza?
A: A large pizza can feed a family of four...
SEAM Consortium
SEAM Consortium
wide-azimuth angle gathers
�
�
accurate
wave�eld
imaging
e�cient
angle
decomposition
wide-azimuth angle gathers
�
�
accurate
wave�eld
imaging
e�cient
angle
decomposition
wide-azimuth angle gathers
�
�
accurate
wave�eld
imaging
e�cient
angle
decomposition
accurate wave�eld imaging
wave�eld reconstruction
L [Ws (x; t)] = Ds (xs ;+t)
L [Wr (x; t)] = Dr (xr ;�t)
conventional imaging condition
R (x) =X
shots
X
t
Ws (x; t)Wr (x; t)
accurate wave�eld imaging
wave�eld reconstruction
L [Ws (x; t)] = Ds (xs ;+t)
L [Wr (x; t)] = Dr (xr ;�t)
conventional imaging condition
R (x) =X
shots
X
t
Ws (x; t)Wr (x; t)
accurate wave�eld imaging
wave�eld reconstruction
L [Ws (x; t)] = Ds (xs ;+t)
L [Wr (x; t)] = Dr (xr ;�t)
extended imaging condition
R (x;�; �) =X
shots
X
t
Ws (x� �; t � �)Wr (x+ �; t + �)
wave�eld-domain
decomposition
loop over shotsfbuild Ws (x; t),Wr (x; t)
decompose Ws (x; t),Wr (x; t)
select main wave paths
apply imaging conditiongdo nothing
image-domain
decomposition
loop over shotsfbuild Ws (x; t),Wr (x; t)
do nothing
do nothing
apply imaging conditiongdecompose R (x;�; �)
wave�eld-domain
decomposition
loop over shotsfbuild Ws (x; t),Wr (x; t)
decompose Ws (x; t),Wr (x; t)
select main wave paths
apply imaging conditiongdo nothing
image-domain
decomposition
loop over shotsfbuild Ws (x; t),Wr (x; t)
do nothing
do nothing
apply imaging conditiongdecompose R (x;�; �)
e�cient angle decomposition
1. use extended images
2. use common-image-point gathers
3. use re ector geometry
R (x;�; �)
common-image gathers: wasteful, biased
R (c;�; �)
common-image-point gathers: e�cient, un-biased
R (c;�; �)
low velocity
high velocity
e�cient angle decomposition
1. use extended images
2. use common-image-point gathers
3. use re ector geometry
conventional IC interpretation
q
nr
ns
n
y
z
a
x
v
extended IC interpretation
q
nr
ns
λ
n
y
λ
z
a
x
v
extended IC interpretation
q
nr
ns
λ
n
y
λ
z
a
x
v
ISO: re ection geometry
n
s
n
n
r
2�
TTI: re ection geometry
s
n
n
rn
2�
(�)
ISO: (�)
q
nr
n
ns
xy
z
0 20 40 60 80−30
−20
−10
0
10
20
30
θ(°)
ψ(°
)
vp = 3km=s
TTI: (�)
q
nr
t
n
ns
xy
z
0 20 40 60 80−30
−20
−10
0
10
20
30
θ(°)
ψ(°
)
vp = 3km=s; � = +0:45; � = �0:29; �a = 35�; �a = 90�
anisotropic decomposition
R (�; �) (�);vs(�; );vr (�; )�����������! R (�; �)
(q̂ � �) sin (2�) = [vs cos (� + ) + vr cos (� � )] �
(n̂ � �) = 0
anisotropic decomposition
R (�; �) (�);vs(�; );vr (�; )�����������! R (�; �)
(q̂ � �) sin (2�) = [vs cos (� + ) + vr cos (� � )] �
(n̂ � �) = 0
e�cient angle decomposition
1. use extended images
2. use common-image-point gathers
3. use re ector geometry
vp = 3km=s
ISO
vp = 3km=s; � = +0:45; � = �0:29; �a = 35�; �a = 90�
TTI
ISO
TTI
ISO
TTI
ISO
TTI
Potential applications
1. Velocity and anisotropy estimation in WAZ 3D
2. Azimuthal anisotrpy estimation
3. AVA
4. Illumination analysis
Potential applications
1. Velocity and anisotropy estimation in WAZ 3D
2. Azimuthal anisotrpy estimation
3. AVA
4. Illumination analysis
Potential applications
1. Velocity and anisotropy estimation in WAZ 3D
2. Azimuthal anisotrpy estimation
3. AVA
4. Illumination analysis
Potential applications
1. Velocity and anisotropy estimation in WAZ 3D
2. Azimuthal anisotrpy estimation
3. AVA
4. Illumination analysis
wide-azimuth angle gathers
accurate
wave�eld
imaging
anisotropic RTM
e�cient
angle
decomposition
extended CIPs
