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Topographic Phase Shift Topographic Phase Shift with Applications to Migration with Applications to Migration
and Multiple Predictionand Multiple Prediction
Ruiqing He
University of Utah
Feb. 2005
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OutlineOutline
1. Wavefield extrapolation.
2. Topographic phase-shift method.
3. Application to migration.
4. Application to multiple prediction.
5. Summary.
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OutlineOutline
1. Wavefield extrapolation.
2. Topographic phase-shift method.
3. Application to migration
4. Application to multiple prediction.
5. Summary.
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Wavefield ExtrapolationWavefield Extrapolation
• One-way wave-equation.- Phase-shift method (Gazdag, 1984).
• Iterative (depth-by-depth) implementation.
• Horizontal velocity variation:- PSPI, Split-step, Fourier-FD, etc.
• Irregular surfaces.
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Reshef’s Approach for TopographyReshef’s Approach for Topography
Geophone lineDatum lines
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Issues with Reshef’s ApproachIssues with Reshef’s Approach
Non-uniform geophone spacing problem
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OutlineOutline
1. Wavefield extrapolation.
2. Topographic phase-shift method.
3. Application to migration.
4. Application to multiple prediction.
5. Summary.
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Topographic Phase-shift MethodTopographic Phase-shift Method
22
2
))((~
)0;,(2
1))(;,(
xz
xxZKxKti
x
Kc
K
ddkezKPxZxtP zx
z = 0
z = Z(x)
.))(;,( inducecan that )0;,( find To xZzxtPzxtP
dtdxexZxtPzKP xZKxKtix
zx ))((~
))(;,()0;,(
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Synthetic TestSynthetic Test
z = 0
z = Z(x)
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A Part of SMAART DATAA Part of SMAART DATA
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Extrapolation to Water BottomExtrapolation to Water Bottom
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ReconstructionReconstruction
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Waveform ComparisonWaveform Comparison
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OutlineOutline
1. Wavefield extrapolation.
2. Topographic phase-shift method.
3. Application to migration.
4. Application to multiple prediction.
5. Summary.
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Mapleton Land Seismic DataMapleton Land Seismic Data
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Acquisition GeometryAcquisition Geometry
dtdxexZxtPzKP xZKxKtix
zx ))((~
))(;,()0;,(
20 m
78 m
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Topographic Phase-shift MigrationTopographic Phase-shift Migration
F2
F3 F4 F5 f6
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Waveform Tomography Waveform Tomography (Sheng and Buddensiek, 2004)(Sheng and Buddensiek, 2004)
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OutlineOutline
1. Wavefield extrapolation.
2. Topographic phase-shift method.
3. Application to migration.
4. Application to multiple prediction.
5. Summary.
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Water-layer Multiple (WLM)Water-layer Multiple (WLM)
• Major free-surface multiples in marine data.• Can be very precisely predicted. • Very few acquisition requirements.
(even in a single shot gather).
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Finite-difference ExperimentsFinite-difference Experiments
• Only one type WLM can be predicted.
• Unpredictable WLM resemble their predictable counterparts.
• Improvement can be made by using the receiver-side ghost rather than the data in the prediction.
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Unocal Data COG (177m)Unocal Data COG (177m)
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Predicted WLMPredicted WLM
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Waveform ComparisonWaveform Comparison
At a geophone above non-flat water bottom
At a geophone above flat water bottom
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WLM AttenuationWLM Attenuation
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A Shot GatherA Shot Gather
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WLM Prediction in The Shot GatherWLM Prediction in The Shot Gather
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WLM Suppression in Shot GatherWLM Suppression in Shot Gather
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A NMO PanelA NMO Panel
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A NMO PanelA NMO Panelafter Demultipleafter Demultiple
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Stack before DemultipleStack before Demultiple
Offset (m)
Tim
e (S)
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Stack after DemultipleStack after Demultiple
Tim
e (S)
Offset (m)
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Poststack Migration Poststack Migration before Demultiplebefore Demultiple
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Poststack Migration Poststack Migration after Demultipleafter Demultiple
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3D Synthetic Experiment3D Synthetic Experiment128
11
Sea Floor
Reflector
dy= 50 m
dx= 25 m
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3D Synthetic Data3D Synthetic Data
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WLM PredictionWLM Prediction
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WLM SuppressionWLM Suppression
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OutlineOutline
1. Wavefield extrapolation.
2. Topographic phase-shift method.
3. Application to migration
4. Application to multiple prediction.
5. Summary.
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SummarySummary
• Topographic phase shift is efficient for wavefield extrapolation from irregular surfaces.
• It is useful for migration and multiple prediction, especially for large and 3D data sets.