ru-shan wu and ling chen modeling and imaging laboratory/igpp university of california, santa cruz
DESCRIPTION
Prestack depth migration in angle-domain using beamlet decomposition: Local image matrix and local AVA. Ru-Shan Wu and Ling Chen Modeling and Imaging Laboratory/IGPP University of California, Santa Cruz ------------------------------------------------------- - PowerPoint PPT PresentationTRANSCRIPT
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Ru-Shan Wu and Ling Chen
Modeling and Imaging Laboratory/IGPPUniversity of California, Santa Cruz
-------------------------------------------------------†Presently at Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China
Prestack depth migration Prestack depth migration in angle-domain in angle-domain
using beamlet decomposition: using beamlet decomposition: Local image matrix and local AVALocal image matrix and local AVA
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Beamlet decomposition: Wave field in angle-domain
Local image matrix and local scattering matrix
Effect of acquisition aperture Local AVA: Preliminary tests Conclusion
Outline
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True-reflection imaging in angle-domain
Preserving the relative amplitudes of scattered waves w.r.t. incident waves.
Benefits:• Improve image (total strength image) quality,
especially for steep reflectors. • Reduce artifacts (angle-domain filtering).• Provide basis for local AVA and local
inversion
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True-amplitude imaging in angle-domain
Amplitude corrections (for ray theory see Hubral et al., Bleistein et al., Xu et al., Audebert et al., ……):
• Transmission loss (boundary reflection and scattering)
• Geometric spreading (for ray method)• Nonuniform information distribution:
Jacobian (Beylkin determinant)• Acquisition aperture effects (hit-count for ray
method)• Intrinsic attenuation (Anelasticity)
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True-reflection imaging in angle-domain
for wave-equation based methods
Preserving the relative amplitudes of scattered waves w.r.t. incident waves:
• Nonuniform information distribution: Jacobian
• Acquisition aperture effects (in angle-domain) (including the geometric spreading and hit-count for ray method)
• Transmission and anelastic losses are less important, especially for small-angle reflections
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B e am l e t d eco m p o s i ti o n o f th e w a v efi e l d :
n mmnmnz
mnn m
mnz
zxbxu
zxbbuxuzxu
,,
,,,~
w h e r e ),(~
zxb mn - - - - - d e c o m p o s i t i o n v e c t o r s ( a t o m s ) ,
),( zxb mn - - - - - r e c o n s t r u c t i o n v e c t o r s ( a t o m s ) ,
mnz xu , - - - - - c o e f f i c i e n t s o f t h e d e c o m p o s i t i o n a t o m s ,
xn nx - - - - - w i n d o w l o c a t i o n ,
mm - - - - - l o c a l w a v e n u m b e r .
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G-D frame atoms
Windowed plane wavesWindowed plane waves
nxi
mn xxgexg m
is a Windowed Plane wave (each beamlet is a windowed plane wave)
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Local plane wavesLocal plane waves
Local plane wave: a superposition of windowed plane waves of the same local wavenumber from all neighboring windows:Partial reconstruction of wavefield (mixed domain wavefield: local phase–space):
The corresponding propagating angle:
l
jlzlxi
j xuxxgezxu j ,,,,,
xvjj 1cos
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Target area
Source Receiver
in
sc
Local Image Matrix(includes aperture and propagation effects)
High-velocity body
**
),( scinL
Local Scattering Matrix
),( scinS
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Point scatterer Planar reflector
shallow
deep
Local image matrix in homogeneous medium(total 201 shots with 176 left-hand receivers )
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Local image matrixLocal image matrix: image condition in beamlet domain and mixed domain
Forward-propagated source field:
Backward-propagated scattered field:
j l
jljlSz
S xgxuzxu ,,,,
p q
pqpqRz
R xgxuzxu SS ,,,,
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S R
Ra
Sa
a
S
S zxWzxW
kzxL
,,,,,,
coscos,,,,
scin
scin20scin
scin20 coscos k
Local image matrix:
Where Serves as the Jacobian
Ws and WRs are the wave fields in angle-domain by beamlet decomposition
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,,,,Re
,,,
scinsinsin
scin
scin, zxLed
zxI
axi zxv
Stacking over frequency to get the final imageIn the local angle-domain:
in sc
,,,, scin zxIzxIThe final image in space domain:
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Local Reflection Local Reflection Analysis (AVA):Analysis (AVA):
For planar reflectors: the local image matrix can be represented as:
with
2
2
scinr
scinn
zxI ,,, rn
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CDAI (common dip-angle CDAI (common dip-angle image) gathersimage) gathers
Sum up all reflections for a common dip-angle: CDAICDAI gather
r
zxIzxI rnn ,,,,,
Obtain the dip-angle of the local reflectors from CDAI.
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CRAI (common reflection-angle CRAI (common reflection-angle image) gathersimage) gathers
Sum up reflected energy for a common reflection-angle for all possible dip-angles: CRAI.CRAI.
Performing local AVA from CRAI gathers.The calculation of local reflection coefficients:
n
zxIN
zxR rnr ,,,1
,,
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Local AVA for an oblique interface in homogeneous background
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Local image matrices at a point on the middle of dipping interface 14° obtained from 80 shots with a two-side receiver array (513 receivers).
The dotted line corresponds to the theoretical prediction without aperture effect.
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Obtain the dip-angle of local reflectors from the CDAI gathers
CDAI gathers for a local reflector at its central location
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. Angle-dependent reflection coefficients at the interface using 256 shots with 513 two-side detectors for the horizontal layered model
with different velocity contrasts: (a) 10%; (b) 25%; (c) 50%; (d)150%
Calculated reflection coefficients from CRAI gathers
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Dotted: synthetic; Red: 513 points two-sidesBlue: 257 points one-side; Green: 129 points two-sides
Angle-dependent reflection coefficients at the interface obtained from LIM
in case of 10% velocity contrast for the horizontal layered model
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Local image matrix and the local scattering matrix
The local image matrix has the acquisition-aperture and propagation effects included. The purpose of the imaging/inversion is to recover the real local scattering matrix and obtain the local reflection coefficients. To achieve the true-reflection imaging, we need to estimate the acquisition-aperture effect and apply the correction.
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Acquisition-Aperture Efficacy(Effect of the source-receiver configuration)
• Acquisition-Aperture Efficacy (AAE) Matrix
• Acquisition-Aperture Dip-response function
• Aperture corrections
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Target area
Source Receiver
in
sc
Acquisition-Aperture Efficacy:
(includes propagation effects)
Overburdenstructures
**
),( scinE
Assume scatteringCoefficients as 1
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With unit impulses at both source and receivers, the local acquisition-aperture efficacy matrix is obtained as:
Acquisition-aperture efficacy matrixAcquisition-aperture efficacy matrix
Where G’s are the Green’s functions in beamlet domain
2
12
*
2
,,,ˆ
,,,ˆ,,,
S
SR q
qRpqz
S llSjlzpjz
xxgxxG
xxgxxGxE
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Acquisition-apertureAcquisition-aperture dip-response functiondip-response function
Acquisition-aperture dip-response as a function of dip-angle of local interface (reflector), which reduce the AAE matrix into a vector:
r
xExE rnznz
,,,,,
with
2
2
scinr
scinn
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Acquisition-Aperture Dip-Response(Acquisition Configuration Response)
**
*S2
S3
S1
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Acquisition-Dip-Response (horizontal reflector) from all the 325 shots
Acquisition-Dip-Response (45 down from horizontal) from all the 325 shots
image by common-shot prestack G-D migration
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G-D beamlet prestackmigration image
Acquisition-DipResponse for 45o
reflectors
Improved image afterDirectional illumination
correction
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Conclusion• Local image matrix can be obtained from
the local incident and scattered plane waves based on beamlet decomposition
• The goal of true-reflection imaging in angle-domain is to remove the acquisition aperture effect and propagation effect through directional illumination analysis and the corresponding corrections
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Conclusion (continued)
• CDAI and CRAI gathers can be deduced from local image matrices (after corrections)
• CDAI gathers can be used to determine the dip-angles of local reflectors
• CRAI gathers can be used for local AVA analysis (and further for local inversion)
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Acknowlegement
We thank the support from WTOPI Research Consortium at UCSC
We thank the support from DOE Project at UCSC
___________________________________________Welcome to visit our Consortium booth #2745