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.