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
OutlineOutline
1. Wavefield extrapolation.
2. Topographic phase-shift method.
3. Application to migration.
4. Application to multiple prediction.
5. Summary.
OutlineOutline
1. Wavefield extrapolation.
2. Topographic phase-shift method.
3. Application to migration
4. Application to multiple prediction.
5. Summary.
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.
Reshef’s Approach for TopographyReshef’s Approach for Topography
Geophone lineDatum lines
Issues with Reshef’s ApproachIssues with Reshef’s Approach
Non-uniform geophone spacing problem
OutlineOutline
1. Wavefield extrapolation.
2. Topographic phase-shift method.
3. Application to migration.
4. Application to multiple prediction.
5. Summary.
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;,(
Synthetic TestSynthetic Test
z = 0
z = Z(x)
A Part of SMAART DATAA Part of SMAART DATA
Extrapolation to Water BottomExtrapolation to Water Bottom
ReconstructionReconstruction
Waveform ComparisonWaveform Comparison
OutlineOutline
1. Wavefield extrapolation.
2. Topographic phase-shift method.
3. Application to migration.
4. Application to multiple prediction.
5. Summary.
Mapleton Land Seismic DataMapleton Land Seismic Data
Acquisition GeometryAcquisition Geometry
dtdxexZxtPzKP xZKxKtix
zx ))((~
))(;,()0;,(
20 m
78 m
Topographic Phase-shift MigrationTopographic Phase-shift Migration
F2
F3 F4 F5 f6
Waveform Tomography Waveform Tomography (Sheng and Buddensiek, 2004)(Sheng and Buddensiek, 2004)
OutlineOutline
1. Wavefield extrapolation.
2. Topographic phase-shift method.
3. Application to migration.
4. Application to multiple prediction.
5. Summary.
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).
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.
Unocal Data COG (177m)Unocal Data COG (177m)
Predicted WLMPredicted WLM
Waveform ComparisonWaveform Comparison
At a geophone above non-flat water bottom
At a geophone above flat water bottom
WLM AttenuationWLM Attenuation
A Shot GatherA Shot Gather
WLM Prediction in The Shot GatherWLM Prediction in The Shot Gather
WLM Suppression in Shot GatherWLM Suppression in Shot Gather
A NMO PanelA NMO Panel
A NMO PanelA NMO Panelafter Demultipleafter Demultiple
Stack before DemultipleStack before Demultiple
Offset (m)
Tim
e (S)
Stack after DemultipleStack after Demultiple
Tim
e (S)
Offset (m)
Poststack Migration Poststack Migration before Demultiplebefore Demultiple
Poststack Migration Poststack Migration after Demultipleafter Demultiple
3D Synthetic Experiment3D Synthetic Experiment128
11
Sea Floor
Reflector
dy= 50 m
dx= 25 m
3D Synthetic Data3D Synthetic Data
WLM PredictionWLM Prediction
WLM SuppressionWLM Suppression
OutlineOutline
1. Wavefield extrapolation.
2. Topographic phase-shift method.
3. Application to migration
4. Application to multiple prediction.
5. Summary.
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.