Solving Illumination Problems Solving Illumination Problems in Imaging:Efficient RTM & in Imaging:Efficient RTM & Migration Deconvolution Migration Deconvolution J. Yu, J.Hu, M. Zhou, G.T. Schuster & Yi Luo

Efficient RTM Motivation Target Oriented RTM Numerical Tests Summary

* Motivation: Salt Lens g SALT Uneven Illumination under Salt Uneven Illumination under Salt

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

How to Make RTM Efficient Shots at Depths Difference only Along Wavefronts Wavelet Encoding: 5x efficiency

OUTLINE Motivation Target Oriented RTM Numerical Tests Summary

* Target Oriented RT Migration g SALT Perform FD Solves under Salt Perform FD Solves under Salt Perform Kirchhoff Migration Perform Kirchhoff Migration Above Salt

* Compute Kernel by Src at Depth Compute Kernel by Src at Depth r x * r g(s|x) g(x|r) xg(x|r)* g(x|r)g(s|x)*

Efficient RTM Motivation Target Oriented RTM Numerical Tests Summary

High Velocity Anomaly SEG Salt Dome Model km 1.5 km/s 2.2 km/s 1.8 m/s km 0 km 3.0 km

Standard FD km km Wavefront FD Efficiency: FD along Wavefrojnts

FD/ Wavefront FD Cost # Gridpts along side FD/ Wavefront FD Cost

Model km km 0 Wavefront Migration Image 1.5 km/s 2.2 km/s 1.8 km/s

Wavefront Migration Image Reverse Time Migration km km km 1.5 km/s 2.2 km/s 1.8 km/s

High Velocity Anomaly SEG Salt Dome Model km 1.5 km/s 2.2 km/s 1.8 m/s km 0 km 3.0 km

Wavefront FD Modeling X (km) Depth (km) Wavefront Standard Time = 0.4 s

Wavefront FD Modeling X (km) Depth (km) Wavefront (leading donuts) Wavefront (rectangular)

Reverse-time Images X (km) Depth (km) 2.0 Standard RTM Image Wavefront RTM Image (save 20% CPU time)

X (km) Depth (km) WWM image Synthetic Model WWM Images

X (km) Depth (km) Standard RTM image Synthetic Model WWM Images

Phase Encoding 2x4x 6x10x

Summary Efficient RTM Efficient RTM 2. Difference along Wavefront: > 3x 1. Target Oriented RTM: Sources below Salt 3. Phase Encoding: > 3x

Solving Illumination Problems Solving Illumination Problems in Imaging:Efficient RTM & in Imaging:Efficient RTM & Migration Deconvolution Migration Deconvolution J. Yu, J.Hu, M. Zhou, G.T. Schuster & Yi Luo

Migration Deconvolution Motivation Numerical Tests Summary

* Illumination Problems g SALT Gaps in Src & Rec. Shadow Zones. m = (L L ) L d TT

Migration Deconvolution Motivation Numerical Tests Summary

Solutions of MD vs. LSM m = (L L ) L d TT LSM: T m = (L L ) m’ MD: Migrated image Data

Depth (km) LSM vs MD 4.5 MD LSM 19 0 X (km)

Depth (km) LSM vs MD 4.5 MD LSM 19 0 X (km)

Migration Deconvolution Motivation Numerical Tests Summary

Scatterer Model Kirchhoff Migration Depth (km)

MD LSM Iter=15 Depth (km)

Migration Deconvolution Motivation Numerical Tests Summary : 2-D SEG Model

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

Comparison of Migration and MD Images Prestack Prestack COG COG Migration Migration Image Image m m MD Image 0 4 X (km) X (km) Depth (km) Depth (km) X (km) X (km) Depth (km) Depth (km) 0

Comparison of Migration and MD Images Prestack COG Migration Image Prestack COG Migration Image m m Prestack COG MD Image Prestack COG MD Image m m X (km) Depth (km)

KM Depth (km) X (km) LSM 15

KM Depth (km) X (km) MD

Depth (km) X (km) MD LSM 15

MD KM Depth (km) LSM Depth (km) Zoom View

Depth (km) Why does MD perform better than LSM ? 4.5 MD LSM 19 0 X (km)

Migration Deconvolution Motivation Numerical Tests Summary : Dipping Layers

Time (s) CDP 150 X(km) Prestack Migrated COG (45-55) Section Mig + MDMig

MD and AVO Amp.Analytical MD Layer 1 Layer 2 Analytical MD 0 angle (deg) 70

Migration Deconvolution Motivation Numerical Tests Summary : North Sea

Velocity Model 0 25 X (km) 0 4 Time (s) Velocity (m/s)

Time Migration Image 0 25 X (km) 0 4 Time (s) 6

Migration Deconvolution Image 025 X (km) 0 4 Time (s) 6 MDKM

Migration Deconvolution Image 025 X (km) 0 4 Time (s) 6 MDKM

X (km) Stacked Section WELL

Time (s) CDP 150 Offset (km)Velocity (km/s) CDP 150

Offset (km) Shot Number RMS Amp. before and after preprocessing Raw data After preprocessed

Time (s) X (km) Before MD After MD AVO Parameter : P P S S * Reservoir

B A Crossplot of A and B before MD Near Well A Time interval: ms

B A Crossplot of A and B after MD Near Well A Time interval: ms

B A Crossplot of A and B Based on Wellline log from Well A ( from C.-S. Yin, M.L. Batzle, and C. C. Mosher) Depth: m

Migration Deconvolution Motivation Numerical Tests Summary :G of Mexico

Time (s) X (km) Migration Section

Time (s) X (km) MD Section

Time (s) X (km) AVO Parameter: a*b

Time (s) X (km) AVO Parameter: a*b

B A Crossplot of A and B before MD CDP: 4797 Time interval: ms

B A Crossplot of A and B after MD CDP: 4797 Time interval: ms

Migration Deconvolution Motivation Numerical Tests Summary : 3D SEG Salt

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

Comparison of Migration and MD Image Y (km) Depth (km) Migration Crossline Section Y (km) Depth (km) MD Crossline Section

KM Crossline (X,97) Section MD Crossline (X,97) Section 04 2 Depth (km) 118 X (km) 118 X (km) 04 2

Conclusions Efficiency MD >> LSMFunction Performanc e Resolution MD = LSM. Suppressing noise MD > LSM Robustness MD < LSM

Time (s) X (km) Migration Section

Time (s) X (km) MD Result

Time (s) X (km) Comparison of Mig and MD 1812 X (km) Mig+MDMig Reservoir

KM Depth (km) X (km) LSM 10

Efficient RTM Motivation Gen. Diffraction Mig. Stack Theory Numerical Tests Focusing Operator from Data Summary

* Wave EquationCOG Migration Operators IMPLICATION #3 SALT g(r|x)g(x|s)*

Velocity Model 0 km 1.2 km 0 s 1.0 s Offset =.7 km 4.5 km 6 km/s 5 km/s Time (s) Depth (km) X (km)

COG Migration 0 km 4.5 km COG COGMigrationOperator 0 km 1.2 km Z=.4 km 0 s 1.0 s 0 s 1.0 s MigrationImage Offset =.7 km

Time (s) X(km) Close-up of One CRG Mig + MDMig

* Compute Kernel by Src at Depth Compute Kernel by Src at Depth r x * r g(s|x) g(x|r) xg(x|r)* g(x|r)g(s|x)*

X (km) Depth (km) Standard RTM Image Synthetic Model Reverse-time Images

X (km) Depth (km) Standard RTM migration WWM image WWM Images

m = (L L ) L d TT Least Squares Migration Reflectivity Modeling operator Seismic data Migration operator

Time (s) CDP 150 X(km) Closeup of COG (45-55) Section Mig+ MDMig

Frequency (Hz) CDP 150 Trace No. Spectrums of Mig and MD Images Mig + MDMig