V 2 Wavepath Migration Overview Kirchhoff migration smears

V. 2 Wavepath Migration Overview Kirchhoff migration smears a reflection along a fat ellipsoid, so that most of the reflection energy is placed in regions far from the actual specular reflection point. This is both inefficient and artifact-prone. To place the reflection energy at or near its specular reflection point we first perform a local slant stack on the trace, and propagate it along its associated wavepath cosnistent with the incident angle of the arrival. The reflection is now smeared along the portion of the wavepath centered about the specular reflection point. Thus wavepath migration smears the reflection energy along a small portion of a wavepath, which reduces both cost and aliasing artifacts. The drawback is the sensitivity of the incidence angle calculation due to noise or inaccurate migration velocities.

Outline • Problem & Motivation • Theory • Synthetic Numerical Examples • Field Data Numerical Examples • Conclusions

Accuracy Migration Accuracy vs $$$ Full-Wave Target RTM No Approx. Ray-Beam Phase-Shift Kirchhoff Expense Multiple Arriv Anti-aliasing

Problem B R C A S A B C 3 -D KM of a Single Trace

Problem & Solution Problem: Kirchhoff Migration Expensive; O(N 3 ) per Trace Reflection Energy Smeared All Along Ellipse Solution: Wavepath Migration. Smear Energy along Wavepaths not 1. 5 Ellipses; O(N )per Trace

Smear Reflection along Wavepath Inc. Angle by Slant Stack S R Image Point Fresnel Zone

MVA Objectives • Can WMVA effectively improve the migration velocity? • Whether the WMVA updated velocity differs much from the KMVA updated velocity? • Can WMVA be much faster than KMVA?

Solution B R C A S A B C 3 -D WM of a Single Trace

Problem & Solution Problem: Kirchhoff Migration Expensive; O(N 3 ) per Trace Reflection Energy Smeared All Along Ellipse Solution: Wavepath Migration. Smear Energy along Wavepaths not 1. 5 Ellipses; O(N )per Trace

Numerical Tests • 3 -D Pt. Scatterer Model

3 -D Prestack KM Point Scatterer Response Reflectivity Z 0 -9 0. 4 Reflectivity 0. 1 -0. 05 -0. 2 1 1 1 Y Offset (km) 0 1 Y Offset (km) X Offset (km) 0. 02 Reflectivity 1 Z 0 -1 -0. 5 Z 0+8 -0. 01 1 1 Y Offset (km) 0 X Offset (km)

3 -D Prestack WM Point Scatterer Response Reflectivity Z 0 -9 0. 4 Reflectivity 0. 1 -0. 05 -0. 2 1 1 1 Y Offset (km) 0 1 Y Offset (km) X Offset (km) 0. 02 Reflectivity 1 Z 0 -1 -0. 5 Z 0+8 -0. 01 1 1 Y Offset (km) 0 X Offset (km)

Numerical Tests • 3 -D Pt. Scatterer Model • 2 -D SEG/EAGE overthrust model

Velocity Model 0 Depth (m) 3000 4500 5 km 10 km 15 km 6000 Velocity (m/sec) 1500 0 km 2500

Wavepath vs Kirchhoff Migration WM Image (CPU: 0. 088) (Slant Stack) 4 Depth (km) 0. 5 2. 5 Offset (km) 10 KM Image (CPU: 1. 0) Structure 4 Offset (km) 10

Numerical Tests • 3 -D Pt. Scatterer Model • 2 -D SEG/EAGE overthrust model • 2 -D Canadian Land Data

A Raw CSG of Husky Field Data 1 Time (sec) 0 3. 0 Trace Number 300

Husky Field Data Results KM (CPU: 1. 0) 0 0 WM (CPU: 2. 23) Offset (km) 14 Depth (km) A 14 A B 7 Offset (km) 0 B

Husky Field Data Results KM Image (Box A) 5. 5 2. 5 Depth (km) Offset (km) Depth (km) 2. 5 WM Image (Box A) 5. 0 Offset (km) 5. 5

Husky Field Data Results KM (CPU: 1. 0) 0 0 WM (Slant Stack, CPU: 0. 24) Offset (km) 14 Depth (km) A Offset (km) 14 A B 7 0 B

Numerical Tests • 3 -D Pt. Scatterer Model • 2 -D SEG/EAGE overthrust model • 2 -D Canadian Land Data • 3 -D SEG/EAGE Salt Model

Receiver Distribution Crossline (m) 1920 2320 1920 Inline (m) 4480

Inline Velocity Model 0 Offset (km) 9. 2 Depth (km) 0 3. 8 SALT

Inline KM (CPU=1) 0 Depth (km) 0 3. 8 Offset (km) Inline WM (CPU=1/33) 9. 2 0 Offset (km) 9. 2

Zoom Views of Inline Sections Kirchhoff WM Sub WM Model Offset: 3~6. 5 km, Depth: 0. 3~1. 8 km

Migration of SEG Salt Data (Crossline Sections) KM WM Model Sub WM Offset: 1. 8~4 km, Depth: 0. 6~2. 1 km

Migration of SEG Salt Data (Horizontal Slices) KM WM Model Sub WM Inline: 1. 8~7. 2 km, Crossline: 0~4 km

Numerical Tests • 3 -D Pt. Scatterer Model • 2 -D SEG/EAGE Overthrust model • 2 -D Canadian Land Data • 3 -D SEG/EAGE Salt Model • 3 -D W. Texas Data

A Common Shot Gather Time (sec) 0 3. 4 54 Trace Number 193

Receiver Distribution Crossline (km) 3. 5 1. 2 1. 5 Inline (km) 4. 5

Receiver Distribution Crossline (km) 3. 5 1. 2 1. 5 Inline (km) 4. 5

Inline KM (CPU=1) 0. 4 Depth (km) 0. 8 3. 8 Offset (km) Inline WM (CPU=1/14) 4. 5 0. 4 Offset (km) 4. 5

Inline KM (CPU=1) 0. 4 Depth (km) 0. 8 3. 8 Offset (km) Inline WM (CPU=1/50) (subsample) 4. 5 0. 4 Offset (km) 4. 5

Crossline KM (CPU=1) Crossline WM (CPU=1/14) 0. 3 Depth (km) 0. 8 3. 3 Offset (km) 3. 5 0. 3 Offset (km) 3. 5

Crossline KM (CPU=1) Crossline WM (CPU=1/50) (subsample) 0. 3 Depth (km) 0. 8 3. 3 Offset (km) 3. 5 0. 3 Offset (km) 3. 5

Horizontal Slices (Depth=2. 5 km) KM (CPU=1) WM (CPU=1/14) Inline: 0~4. 6 km, WM (Sub, CPU=1/50) Crossline: 0~3. 8

Numerical Tests • 3 -D Pt. Scatterer Model • 2 -D SEG/EAGE Overthrust model • 2 -D Canadian Land Data • 3 -D SEG/EAGE Salt Model • 3 -D W. Texas Data • MVA

Initial Migration Velocity 0 Horizontal Distance (km) 18 2. 1 (km /s) Depth (km) 0 1. 5

0 KM Image with Initial Velocity 18 km Depth (km) 0 1. 5 KMVA Velocity Changes in the 1 st Iteration 0 (m /s) Depth (km) 50 0 1. 5

2 km KM Image with Initial Velocity Depth (m) 1070 1260 KM Image with Updated Velocity Depth (m) 1070 1260 9 km

KMVA CIGs with Initial Velocity Depth (km) 0 1. 5 KMVA CIGs with Updated Velocity

0 KMVA Velocity Changes in the 1 st Iteration (CPU=6) 18 km 0 (m /s) Depth (km) 50 0 1. 5 50 (m /s) Depth (km) 0 WMVA Velocity Changes in the 1 st Iteration (CPU=1) 0

2 km WM Image with Initial Velocity Depth (m) 1070 1260 WM Image with Updated Velocity Depth (m) 1070 1260 9 km

WMVA CIGs with Initial Velocity WMVA CIGs with Updated Velocity Depth (km) 0 1. 5

2 km KM Image with Initial Velocity Depth (m) 1070 1260 KM Image with KMVA Updated Velocity Depth (m) 1070 1260 KM Image with WMVA Updated Velocity Depth (m) 1070 1260 9 km

Numerical Tests • 3 -D Pt. Scatterer Model • 2 -D SEG/EAGE Overthrust model • 2 -D Canadian Land Data • 3 -D SEG/EAGE Salt Model • Crosswell Data

Crosswell Imaging of Synthetic Fault Data Model Depth (m) 0 KM 210 0 90 WM

Conclusions • Typically WM has fewer artifacts than KM • Typically WM 2 -50 times faster than KM • Tradeoff between quality and speed • Conflicting dip arrivals still an issue • Slant stack traces essential for efficiency • Fast velocity analysis tool

Conclusions Works on synthetic and field poststack time migration data, improve resolution, mitigate some migration artifacts Subdivision method is able to account for lateral-velocity variations and attenuate some far-field artifacts A post-migration processing: Cost 2 X

Accuracy Migration Accuracy vs $$$ Full-Wave Target RTM No Approx. Ray-Beam Phase-Shift Kirchhoff Expense Multiple Arriv Anti-aliasing