Wavepath Migration versus Kirchhoff Migration: 3-D Prestack Examples H. Sun and G. T. Schuster University of Utah

Outline Problems in Kirchhoff Migration Problems in Kirchhoff Migration Wavepath Migration Wavepath Migration Implementation of WM Implementation of WM Numerical Results Numerical Results Conclusions Conclusions

Forward Modeling ( Xg, 0 ) ( Xs, 0 ) Specular Ray

3D Kirchhoff Migration ( Xg, 0 ) ( Xs, 0 ) 3D Fat Ellipsoid

3-D KM of a Single Trace RS A A B B C C

Problems in Kirchhoff Migration Traveltime Information Where Was Wave Reflected ? The Whole Fat Ellipsoid ! Problem 1 Strong Far-Field Migration Artifact Problem 2 Slow for 3-D Iterative Velocity Analysis

Outline Problems in Kirchhoff Migration Problems in Kirchhoff Migration Wavepath Migration Wavepath Migration Implementation of WM Implementation of WM Numerical Results Numerical Results Conclusions Conclusions

3D Wavepath Migration ( Xg, 0 ) Fat Ray FatEllipsoid KM : Fat Ellipsoid, O(N ) WM: Hatching Area, O(N ) 31.5

3-D WM of a Single Trace RS A B C A B C

Traveltime + Ray Direction True Reflection point Small Migration Aperture FewerArtifactsLessExpensive Wavepath Migration

To Achieve Higher CPU Efficiency To Achieve Higher CPU Efficiency Compared to 3-D KM Compared to 3-D KM To Generate Comparable or Better To Generate Comparable or Better Image Quality than 3-D KM Image Quality than 3-D KM Key Goals of 3-D WM

Related References Time-Map Migration Time-Map Migration Sherrif & Geldhart (1985) Sherrif & Geldhart (1985) Wave Equation Tomography Wave Equation Tomography Woodward & Rocca (1988) Woodward & Rocca (1988) Gaussian Beam Migration Gaussian Beam Migration Ross Hill (1990) Ross Hill (1990) Kirchhoff Beam Migration Kirchhoff Beam Migration Yonghe Sun et al., (1999) Yonghe Sun et al., (1999)

Outline Problems in Kirchhoff Migration Problems in Kirchhoff Migration Wavepath Migration Wavepath Migration Implementation of WM Implementation of WM Numerical Results Numerical Results Conclusions Conclusions

Key Steps in WM Raypath RSRaypath Fresnel Zone Migration Quasi-ellipsoidQuasi-ellipsoid

Outline Problems in Kirchhoff Migration Problems in Kirchhoff Migration Wavepath Migration Wavepath Migration Implementation of WM Implementation of WM Numerical Results Numerical Results 3-D Prestack Point Scatterer Data 3-D Prestack Point Scatterer Data 3-D Prestack SEG/EAGE Salt Data 3-D Prestack SEG/EAGE Salt Data 3-D Prestack West Texas Field Data 3-D Prestack West Texas Field Data Conclusions Conclusions

3-D Prestack KM Point Scatterer Response Reflectivity Y Offset (km) X Offset (km) Reflectivity Y Offset (km) X Offset (km) Reflectivity Y Offset (km) X Offset (km) Reflectivity Y Offset (km) X Offset (km) Z0 Z0-1 Z0-9 Z0+8

Reflectivity Y Offset (km) X Offset (km) Reflectivity Y Offset (km) X Offset (km) Reflectivity Y Offset (km) X Offset (km) Reflectivity Y Offset (km) X Offset (km) D Prestack WM Point Scatterer Response Z0 Z0-1 Z0-9 Z0+8

Outline Problems in Kirchhoff Migration Problems in Kirchhoff Migration Wavepath Migration Wavepath Migration Implementation of WM Implementation of WM Numerical Results Numerical Results 3-D Prestack Point Scatterer Data 3-D Prestack Point Scatterer Data 3-D Prestack SEG/EAGE Salt Data 3-D Prestack SEG/EAGE Salt Data 3-D Prestack West Texas Field Data 3-D Prestack West Texas Field Data Conclusions Conclusions

A Common Shot Gather Trace Number 1390 Time (sec) 0 5.0

Inline Velocity Model Offset (km) 09.2 Depth (km) SALT

Inline KM (CPU=1) Inline WM (CPU=1/33) Offset (km) Depth (km) Offset (km) 09.2

Inline KM (CPU=1) Inline WM (CPU=1/170) Offset (km) Depth (km) Offset (km) 09.2 (subsample)

Zoom Views of Inline Sections Offset: 3~6.5 km, Depth: 0.3~1.8 km WM Model KM SubWM

Offset: 1.8~4 km, Depth: 0.6~2.1 km WM Model KM SubWM Zoom Views of Crossline Sections

Inline: 1.8~7.2 km, Crossline: 0~4 km WM Model KM SubWM Horizontal Slices (Depth=1.4 km)

Outline Problems in Kirchhoff Migration Problems in Kirchhoff Migration Wavepath Migration Wavepath Migration Implementation of WM Implementation of WM Numerical Results Numerical Results 3-D Prestack Point Scatterer Data 3-D Prestack Point Scatterer Data 3-D Prestack SEG/EAGE Salt Data 3-D Prestack SEG/EAGE Salt Data 3-D Prestack West Texas Field Data 3-D Prestack West Texas Field Data Conclusions Conclusions

A Common Shot Gather Trace Number Time (sec) 0 3.4

Inline KM (CPU=1) Inline WM (CPU=1/14) Offset (km) Depth (km) Offset (km)

Inline KM (CPU=1) Inline WM (CPU=1/50) Offset (km) Depth (km) Offset (km) (subsample)

Crossline KM (CPU=1) Crossline WM (CPU=1/14) Offset (km) Depth (km) Offset (km)

Crossline KM (CPU=1) Crossline WM (CPU=1/50) (subsample) Offset (km) Depth (km) Offset (km)

Inline: 0~4.6 km, Crossline: 0~3.8 KM (CPU=1) Horizontal Slices (Depth=2.5 km) WM (CPU=1/14) WM (Sub, CPU=1/50)

Outline Problems in Kirchhoff Migration Problems in Kirchhoff Migration Wavepath Migration Wavepath Migration Implementation of WM Implementation of WM Numerical Results Numerical Results Conclusions Conclusions

Conclusions SEG/EAGE Salt Data SEG/EAGE Salt Data Fewer Migration Artifacts Fewer Migration Artifacts Better for Complex Salt Boundary Better for Complex Salt Boundary Higher Computational Efficiency Higher Computational Efficiency CPU CPU KM: 1 WM: 1/33 KM: 1 WM: 1/33 Subsampled WM: 1/170 Subsampled WM: 1/170

Conclusions West Texas Field Data West Texas Field Data Fewer Migration Artifacts Fewer Migration Artifacts Similar Image Quality Similar Image Quality Higher Computational Efficiency Higher Computational Efficiency CPU CPU KM: 1 WM: 1/14 KM: 1 WM: 1/14 Subsampled WM: 1/50 Subsampled WM: 1/50

Acknowledgements Acknowledgements We thank UTAM sponsors for their financial support