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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
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.
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;,(
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.
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.
Waveform ComparisonWaveform Comparison
At a geophone above non-flat water bottom
At a geophone above flat water bottom
OutlineOutline
1. Wavefield extrapolation.
2. Topographic phase-shift method.
3. Application to migration
4. Application to multiple prediction.
5. Summary.