Amplitude-preserving wave
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Transcript Amplitude-preserving wave
Amplitude-preserving
wave-equation migration
Paul Sava*
Biondo Biondi
Stanford University
Stanford University
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The problem
Recover reliable migration amplitudes:
i.e. reflectivity as a function of incidence angle
Reflectivity
description
Migration
algorithm
Illumination
balance
Describe reflectivity
as a function of
incidence angle
Apply amplitude
corrections to the
migration operator
Restore amplitudes in
shadow zones
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Agenda
Angle-domain common
image gathers
Definitions
Methods
Imaging effects
Amplitude corrections
Propagation effects
Acquisition effects
Applications
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Common image gathers
Kirchhoff
Wave-equation
h
h
Offset
domain
flat events
focused events
z
z
g
g
Angle
domain
flat events
flat events
z
z
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Angle-Domain Common Image Gathers
Source
Receiver
V(x,y,z)
g g
2h
g g
kh
tan g
kz
kh
ph
a
v
S-G migration
Prucha et al., 1999
Sava et al., 2001
Shot-profile migration
de Bruin et al., 1990
Rickett & Sava, 2001
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ADCIG: S-G migration
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Agenda
Angle-domain common
image gathers
Definitions
Methods
Imaging effects
Amplitude corrections
Propagation effects
Acquisition effects
Applications
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Modeling operator
modeling
migration
d Lm0
*
mLd
m L Lm 0
*
2
W m0
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Jacobian weighting: arbitrary geometry
1
1
s
Wk
h
cos(g a ) cos(g a )
1
2h
2
g g
image space
a
s
data space
2
p
1
1
2
h
s
W ph
4s
cos(g a ) cos(g a )
1
1
cos(g a ) cos(g a )
k m ph
4s
1
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Jacobian weighting: flat reflectors
1
Wk cos g
h
2s
2
2h
g
g
image space
data space
s
1 1
Wp
h
2s cos g
2
(Wapenaar et al., 1999)
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Jacobian weighting
Ideal
offset-gather
Ideal
angle-gather
Reflection
angle
Offset
ray parameter
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Jacobian weighting
Ideal
offset-gather
Ideal
angle-gather
Reflection
angle
Offset
ray parameter
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Agenda
Angle-domain common
image gathers
Definitions
Methods
Imaging effects
Amplitude corrections
Propagation effects
Acquisition effects
Applications
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WKBJ & scattering operators
d Lm
d LAG r
k zs k zr
A
0
0
k zs k zr
Clayton & Stolt (1981)
is
G
4k zs k zr
2
Clayton & Stolt (1981)
Stolt & Benson (1986)
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Agenda
Angle-domain common
image gathers
Definitions
Methods
Imaging effects
Amplitude corrections
Propagation effects
Acquisition effects
Applications
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Stationary-phase operator
d LSAG r
2-D
S
z
0
i sgn d 2 k zCA
dk 2 4
2
hy
e
2 CA
d kz
d
dk h2y
Bleistein & Handelsman (1975)
CAM
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Agenda
Angle-domain common
image gathers
Definitions
Methods
Imaging effects
Amplitude corrections
Propagation effects
Acquisition effects
Applications
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Applications
LLW
*
2
Pseudo-unitary migration
L u LW
-1
L Lu I
*
u
d LSAG r
True-amplitude migration
L SAG W L
1
*
t
2 *
Ldr
*
t
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Example: vertical section
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Example: vertical section
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Example: horizontal section
uncorrected
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Example: horizontal section
corrected
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Summary
• Amplitude-preserving transformation to the
angle domain
• Amplitude corrections
– imaging effects
– propagation effects
– acquisition effects
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