V.2 Wavepath Migration Overview 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. 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.

Problem & MotivationProblem & Motivation TheoryTheory Synthetic Numerical ExamplesSynthetic Numerical Examples Field Data Numerical ExamplesField Data Numerical Examples ConclusionsConclusions Outline

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

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

Problem & Solution Problem: Kirchhoff Migration Expensive; Problem: Kirchhoff Migration Expensive; O(N ) per Trace O(N ) per Trace Reflection Energy Smeared All Reflection Energy Smeared All Along Ellipse Along Ellipse Solution: Wavepath Migration. Smear Energy along Wavepaths not Energy along Wavepaths not Ellipses; O(N )per Trace Ellipses; O(N )per Trace 3 1.5

SR ImagePoint Fresnel Zone Smear Reflection along Wavepath Inc. Angle by Slant Stack

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

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

Problem & Solution Problem: Kirchhoff Migration Expensive; Problem: Kirchhoff Migration Expensive; O(N ) per Trace O(N ) per Trace Reflection Energy Smeared All Reflection Energy Smeared All Along Ellipse Along Ellipse Solution: Wavepath Migration. Smear Energy along Wavepaths not Energy along Wavepaths not Ellipses; O(N )per Trace Ellipses; O(N )per Trace 3 1.5

Numerical Tests 3-D Pt. Scatterer Model3-D Pt. Scatterer Model

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

Numerical Tests 3-D Pt. Scatterer Model3-D Pt. Scatterer Model 2-D SEG/EAGE overthrust model2-D SEG/EAGE overthrust model

Velocity Model 0km 0km15km10km5km Depth (m) Velocity (m/sec)

Wavepath vs Kirchhoff Migration Offset (km)410 Depth (km) Offset (km)104Offset (km)10 WM Image (CPU: 0.088)KM Image (CPU: 1.0) Structure (Slant Stack)

Numerical Tests 3-D Pt. Scatterer Model3-D Pt. Scatterer Model 2-D SEG/EAGE overthrust model2-D SEG/EAGE overthrust model 2-D Canadian Land Data2-D Canadian Land Data

A Raw CSG of Husky Field Data Trace Number 1300 Time (sec) 0 3.0

Husky Field Data Results Offset (km) Depth (km) KM (CPU:1.0) A B WM (CPU: 2.23) Offset (km) 0 14 A B

Husky Field Data Results Offset (km) Depth (km) KM Image (Box A) WM Image (Box A) Offset (km) Depth (km) 5.0

Husky Field Data Results Offset (km) Depth (km) KM (CPU:1.0) A B WM (Slant Stack, CPU: 0.24) Offset (km) 014 A B

Numerical Tests 3-D Pt. Scatterer Model3-D Pt. Scatterer Model 2-D SEG/EAGE overthrust model2-D SEG/EAGE overthrust model 3-D SEG/EAGE Salt Model3-D SEG/EAGE Salt Model 2-D Canadian Land Data2-D Canadian Land Data

Receiver Distribution Crossline (m) Inline (m)

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

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

Model Migration of SEG Salt Data (Crossline Sections) Offset: 1.8~4 km, Depth: 0.6~2.1 km WMKM SubWM

Inline: 1.8~7.2 km, Crossline: 0~4 km WM Model KM SubWM Migration of SEG Salt Data (Horizontal Slices)

Numerical Tests 3-D Pt. Scatterer Model3-D Pt. Scatterer Model 2-D SEG/EAGE Overthrust model2-D SEG/EAGE Overthrust model 3-D SEG/EAGE Salt Model3-D SEG/EAGE Salt Model 2-D Canadian Land Data2-D Canadian Land Data 3-D W. Texas Data3-D W. Texas Data

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

Receiver Distribution Crossline (km) Inline (km)

Receiver Distribution Crossline (km) Inline (km)

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)

Numerical Tests 3-D Pt. Scatterer Model3-D Pt. Scatterer Model 2-D SEG/EAGE Overthrust model2-D SEG/EAGE Overthrust model 3-D SEG/EAGE Salt Model3-D SEG/EAGE Salt Model 2-D Canadian Land Data2-D Canadian Land Data 3-D W. Texas Data3-D W. Texas Data MVAMVA

Initial Migration Velocity Horizontal Distance (km) Depth (km) (km /s) (km /s)

KM Image with Initial Velocity km 1.5 Depth (km) KMVA Velocity Changes in the 1st Iteration 50 0 (m /s) (m /s)

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

KMVA CIGs with Initial Velocity Depth (km) KMVA CIGs with Updated Velocity

km 1.5 Depth (km) KMVA Velocity Changes in the 1st Iteration (CPU=6) 50 0 (m /s) (m /s) WMVA Velocity Changes in the 1st Iteration (CPU=1) 50 0 (m /s) (m /s)

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

WMVA CIGs with Initial Velocity Depth (km) WMVA CIGs with Updated Velocity

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

Numerical Tests 3-D Pt. Scatterer Model3-D Pt. Scatterer Model 2-D SEG/EAGE Overthrust model2-D SEG/EAGE Overthrust model 3-D SEG/EAGE Salt Model3-D SEG/EAGE Salt Model 2-D Canadian Land Data2-D Canadian Land Data Crosswell DataCrosswell Data

Model Crosswell Imaging of Synthetic Fault Data WMKM 0210 Depth (m) 0 90

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

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

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