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Least Squares Migration ofLeast Squares Migration of JAPEX JAPEX Data and PEMEX DataData and PEMEX Data
Naoshi AokiNaoshi Aoki
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OutlineOutline
1. Theory2. LSM resiliency to artifacts from poor acquisition
geometry3. LSM image sensitivity to wavelet estimation errors4. Multi-scale LSM applied to poststack JAPEX data5. Target-oriented LSM applied to poststack PEMEX
data6. Conclusions
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TheoryTheoryPoststack 2D Syncline Model
Ricker wavelet (15 Hz)
Kirchhoff Migration
LSM
Forward modeling
Inversion
Steepest descent algorithm
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OutlineOutline
1. Theory2. LSM resiliency to artifacts from poor acquisition
geometry3. LSM image sensitivity to wavelet estimation errors4. Multi-scale LSM applied to poststack JAPEX data5. Target-oriented LSM applied to poststack PEMEX
data6. Conclusions
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LSM Resiliency to Artifacts fromLSM Resiliency to Artifacts from Poor Acquisition Geometry Poor Acquisition Geometry
3D U Model Model Description• Model size:
– 1.8 x 1.8 x 1.8 km • U shape reflectivity anomaly
• Cross-spread geometry– Source : 16 shots, 100 m int.– Receiver : 16 receivers , 100 m int.
Depth (m) Reflectivity
250 1
500 -1
750 1
1000 -1
1250 1
● Source● Receiver
U model is designed for testing Prestack 3D LSM with arbitrary 3D survey geometry.
CSG0
5
TW
T (
s)
0 1.8X (m)
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Kirchhoff Migration vs. LSMKirchhoff Migration vs. LSMApplied to the 3D Applied to the 3D UU Model Model
(c) Z = 250 m (e) Z = 750 m (g) Z=1250m(a) Actual Reflectivity
Kirchhoff Migration Images
(b) Test geometry(d) Z=250m
LSM Images after 30 Iterations(f) Z=750m (h) Z=1250m
● Source● Receiver
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Comparison of ImagesComparison of Images from the Cross-spread Data from the Cross-spread Data
Actual Reflectivity Imageof Y = 500 m
Kirchhoff Migration Image
0
1.8
Z (
km)
0 1.8X (km)
0
1.80 1.8
X (km)
LSM Image
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LSM Resiliency to ArtifactsLSM Resiliency to Artifacts
• Test Summary– LSM showed a significant resiliency to artifacts
from poor acquisition geometry.
– LSM has an ability to reduce data acquisition expense.
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OutlineOutline
1. Theory2. LSM resiliency to artifacts from poor acquisition
geometry3. LSM image sensitivity to wavelet estimation errors4. Multi-scale LSM applied to poststack JAPEX data5. Target-oriented LSM applied to poststack PEMEX
data6. Conclusions
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LSM Image Sensitivity to LSM Image Sensitivity to Wavelet Estimation ErrorsWavelet Estimation Errors
• LSM algorithm requires a source wavelet.
• I tested LSM image sensitivity to wavelet estimation errors in the following 2 cases :1. LSM with correct wavelet,2. LSM with a Ricker wavelet (15 Hz).
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LSM Image with Correct Source WaveletLSM Image with Correct Source Wavelet
0
2D
epth
(km
)0 2
X (km)
0
2
TW
T (
s)
0 2X (m)
Data LSM ImageActual Model
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LSM Image with a Ricker Wavelet (15 Hz)LSM Image with a Ricker Wavelet (15 Hz)
Actual Model 0
2D
epth
(km
)0 2
X (km)
LSM ImageKirchhoff Migration
Image
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LSM Image Sensitivity to Errors in the Source LSM Image Sensitivity to Errors in the Source WaveletWavelet
• Test Summary– An accurate estimate of the source wavelet is
important to obtain an accurate LSM image.
– However, LSM images are usually better than the standard migration image.
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OutlineOutline
1. Theory2. LSM resiliency to artifacts from poor acquisition
geometry3. LSM image sensitivity to wavelet estimation errors4. Multi-scale LSM applied to poststack JAPEX data5. Target-oriented 3D LSM applied to poststack
PEMEX data6. Conclusions
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Multi-scale LSMMulti-scale LSM
• Starts by estimating a low wavenumber reflectivity model in order to avoid getting trapped in a local minimum.
• Band-pass filters, where the frequency bandwidth increases with the number of iterations, were iteratively applied to the input data.
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Multi-scale LSM Applied to JAPEX DataMulti-scale LSM Applied to JAPEX Data
Multi-scale (MS) LSM vs. Standard LSM Convergence Curves
25
3032
34 36 3840
MS LSM Image
0.7
1.9
Dep
th (
km)
2.4 4.9X (km)
Standard LSM Image
0.7
1.92.4 4.9
X (km)
X10 5
3.0
0.5R
esid
ual
0 40Iteration
Multi-scale LSM
Standard LSM20
Hz
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LSM vs. Kirchhoff MigrationLSM vs. Kirchhoff Migration
LSM Image0.7
1.9
Dep
th (
km)
2.4 4.9X (km)
0.7
1.9
Dep
th (
km)
2.4 4.9X (km)
Kirchhoff Migration Image
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Resolution comparisonResolution comparison
LSM vs. Standard Migration Magnitude Spectrum of Migration Image
1
0
Mag
nitu
de
0 0.04Wavenumber (1/m)
0.7
1.2
Dep
th (
km)
3.7 4.3X (km)
0.7
1.2
Dep
th (
km)
3.7 4.3X (km)
LSM Image Kirchhoff Migration Image
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OutlineOutline
1. Theory2. LSM resiliency to artifacts from poor acquisition
geometry3. LSM image sensitivity to wavelet estimation errors4. Multi-scale LSM applied to poststack JAPEX data5. Target-oriented LSM applied to poststack PEMEX
data6. Conclusions
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PEMEX 3D OBC Data from GOMPEMEX 3D OBC Data from GOM
0
4
TW
T (
s)
1 1001XL Number
IL3100 Stacked Section
Acquired in1990s.Since acquisition geometry is sparse, noise is dominant in the shallow part.
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Subset of PEMEX DataSubset of PEMEX Data
0
3
TW
T (
s)
3036 3150IL Number
0
3
TW
T (
s)
501 700XL Number
3036
3150
IL N
um
ber
501 700XL Number
Targeted area size:# IL = 115 lines#XL = 201 lines
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LSM Image0.7
1.9
Dep
th (
m)
2.4 4.9X (m)
LSM vs. Kirchhoff MigrationLSM vs. Kirchhoff Migration from PEMEX Data IL3100 from PEMEX Data IL3100
0.7
1.9
Dep
th (
m)
2.4 4.9X (m)
Kirchhoff Migration Image
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Resolution comparisonResolution comparison
LSM vs. Standard Migration Magnitude Spectrum of Migration Image
1
0
Ma
gn
itude
0 0.04Wavenumber (1/m)
LSM Image
1
2.2
Dep
th (
km)
551 650XL Number 551 650
XL Number
Kirchhoff Migration Image
LSM
Kirchhoff Migration
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TO LSM Applied for 3D DataTO LSM Applied for 3D Data
Preliminary Result of LSM Image after 4 iterations
Kirchhoff Migration Image
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ConclusionsConclusions• Numerical results show:
– LSM has a significant resilience to artifacts from poor acquisition geometries .
– an accurate wavelet estimate provides an accurate LSM image.
• Results from JAPEX and PEMEX data show:– faster convergence rate is provided by a multi-scale migration
scheme.– 2D LSM is a practical means for improving quality image.– Encouraging results for TO LSM are obtained from the 3D data
subset.
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Future workFuture work
• GOAL: 3D LSM in less than 10 iterations.– Further improvement in efficiency will be
investigated.
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AcknowledgementsAcknowledgements
• We thank PEMEX Exploration and Production for permission to use and publish its Gulf of Mexico data.
• I would like to thank JOGMEC and JAPEX for supporting my study at the University of Utah.
• We also thank the UTAM consortium members for supporting my work.