Enhancing Migration Image Quality by 3-D Prestack Migration Deconvolution Gerard Schuster Jianhua Yu, Jianxing Hu University of Utah andGXT

Blurring Problems in Migration Outline Migration Deconvolution Examples Conclusions

Outline Migration Deconvolution Examples Conclusions Blurring Problems in Migration

Migration noise and artifacts Migration Noise Problems Depth (km) Weak illumination Footprint

m = L d T Migration = Blurred r but d = L  Migrated Section DataModeling

m = L T but d = L  Migrated Section L L L L  Migration Image m = True Reflectivity Model  Migration = Blurred r

Outline Migration Deconvolution Examples Conclusions Blurring Problems in Migration

Migration Deconvolution m  LLT Migration imageReflectivity  Migration Green’s function

m  LLT  LL T][ LL T][ 1 1 Migration Deconvolution

m   LL T][ 1

Assume Local v(z) Approximation m   LL T][ 1 Migration Deconvolution

m   LL T ][ r r 0  r,r  0 0 r ith column=ith pt scatterer Response to migration r 0 Migration Deconvolution r r 0 Pt. scatterer location Trial image pt. sgsoogsg rdrdrrGrrGrrGrrG)()()()( **  ][ Migration Green’s function (Schuster and Hu, 2000)

m   LL T ][ sgsoogsg rdrdrrGrrGrrGrrG)()()()( **  ][ Migration Green’s function (Schuster and Hu, 2000)  r,r  0 0 r r 0 Migration Deconvolution r r 0 r r 0 Special Case: r=r o e  gx e  sx e  gx e  sx |g-x| 2 |s-x| 2  |g-x| 2 |s-x| 2 xx = LL T ][ Preconditioner for LSM Pt. scatterer location Trial image pt.

MD Implementation Steps: Step 1: Prepare traveltime table Velocity cube Acquisition geometry information or Use migration timetable

Calculate the migration Green’s function MD Implementation Steps: Step 2: Y (km) Depth (km) m  r L L T ][ * N ithdepth L  r,r  0 r r r0

N Calculate the migration Green’s function for pts along vertical line MD Implementation Steps: Step 2: Y (km) L M  R ][ithdepth  r,r  0 r r r0

Calculate the migration Green’s function for pts along vertical line MD Implementation Steps: Step 2: Y (km) Depth (km) M  R ][ithdepth  r,r  0 r r 0

Calculate the migration Green’s function for pts along vertical line MD Implementation Steps: Step 2: Y (km) M  R ][ithdepth  r,r  0 r r 0

Calculate the migration Green’s function for pts along vertical line MD Implementation Steps: Step 2: Y (km) M  R ][ithdepth  r,r  0 r r 0

Step 3: FFT in x and y   ),0,0|,,( 0 zzyyxx oomig oooooo dzdzdydydxdxzyx R( ),,( Model Space ooomig rdrRrrrm)()()(   Model Space x-y shift invariance

Step 3: FFT in x and y   ),0,0|,,( 0 zzyyxx oomig oooooo dzdzdydydxdxzyx R ),,( Model Space FFT in x and y FFT in x and y ooomig rdrRrrrm)()()(   Model Space   ),0,0|,,( ~ ),,( ~ 0 zzkkzkk m yxyx ooyx dzdzzkkR),,( ~

Discrete MD Equation FFT of Migrateddata True Reflectivity Invert Blocks of 15x15 matrices for each k

Step 4: Invert MD image at the depth Z i by solving linear equations MD Implementation Steps: Step 5: Repeat Steps 2-4 until the maximum depth is finished M  R ][  (k, k, z  xy

Outline Migration Deconvolution Examples : Synthetic data Conclusions Blurring Problems in Migration

0 3 km 0 3-D Point Scatterer Model 3 km 11 X 11 Receivers 11 X 11 Receivers dxg=dyg=0.3 km Imaging: dx=dy=50 m dz=100 m 3X3 Sources; dxshot=dyshot=1.5 km 10 km

0 3 X (km) 0 3 Y (km) 0 3 X (km) 0 3 Y (km) 0 3 X (km) 0 3 Y (km) 0 3 X (km) 0 3 Y (km) 0 3 X (km) 0 3 Y (km) 0 3 X (km) 0 3 Y (km) MIG MD Z=1 km Z=3 km Z=5 km Depth Slices

0 3 X (km) 0 3 Y (km) 0 3 X (km) 0 3 Y (km) 0 3 X (km) 0 3 Y (km) 0 3 X (km) 0 3 Y (km) 0 3 X (km) 0 3 Y (km) 0 3 X (km) 0 3 Y (km) MIG MD Z=7 km Z=9 km Z=10 km Depth Slices

0 2.5 km 0 Meandering Stream Model 2.5 km 5 X 1 Sources; 11 X 7 Receivers 3.5 km

Mig MD Model 0 Y (km) X (km) Z=3.5 KM

Meandering River Model X (m) Y (m)

Kirchhoff Migration Image X (m) Y (m)

MD Image X (m) Y (m)

km 0 3-D SEG/EAGE Salt Model 12.2 km 9 X5 Sources; dxshot=dyshot=1 km 201 X 201 Receivers Imaging: dx=dy=20 m

3-D SEG/EAGE Salt Model X (km)Y (km) Y=7.12 km

Mig and MD ( z=1.4 km, negative polarity) X (km) 3 10 Y (km) X (km) MDMig

3-D SEG/EAGE Salt Model X (km)Y (km) Y=7.12 km

MD (z=1.2 km)Mig (z=1.2 km) X (km) 3 10 Y (km) X (km)

MD (z=1.2 km)Mig (z=1.2 km)

X (km) Depth (km) SIGSBEE2B Model

X (km) Depth (km) Wave Equation Migration Before MD

X (km) Depth (km) Wave Equation Migration after MD

Outline Migration Deconvolution Examples: 2-D field data Conclusions Blurring Problems in Migration

PSTM Image 0 6 X (km) 0 8 Time (s) MD PSTM Image

PSTM Image 0 6 X (km) 0 8 Time (s) MD PSTM Image

Outline Migration Deconvolution Examples: 3-D field data Conclusions Blurring Problems in Migration

3-D Land Field Data : Receivers : Sources

Unocal Alaska 3D Data 8 km 0 km 5 km

Kirchhoff Migration MD

Unocal Alaska 3D Data 8 km 0 km 5 km

Inline Number Depth (kft) 90Inline Number1 Kirchhoff MigrationMD (Crossline=50)

Unocal Alaska 3D Data 8 km 0 km 5 km

(crossline 200) Depth (kft) Kirchhoff MigrationMD

2.0 s MDStandard MD 1.2 s

Depth (kft) Crossline Number (Inline =50) Mig ( Unocal ) MD

Unocal Alaska 3D Data 8 km 0 km 5 km

Kirchhoff Migration MD Inline Number Crossline Number Inline Number 3 km

(3.08 kft) Inline Number Crossline Number Inline Number Mig (Courtesy of Unocal) MD

(3.6 kft) Inline Number Crossline Number Inline Number Mig (Courtesy of Unocal) MD

Outline Migration Deconvolution Examples Conclusions Blurring Problems in Migration

Conclusions MD = Least Squares Migration MD Improve resolution, suppresses mig. artifacts, balances illumination 2 km; km Sensitive to choice of filter parameters MD $$ = 1 Migration MD Problems MD effectiveness diminishes with depth Local V(z) Approximation

Gaussian Beam MD, WE MD MD Future Conjugate Gradient MD

10 Depth (km) After MD No AGC Before MD

5 10 Depth (km) Before MD After MD

0 6 X (km) 0 8 Time (s) MD

0 6 X (km) 0 8 Time (s) MD PSTM(courtesy of Unocal) PSTMD

0 6 X (km) 3 8 Time (s) MD

MD Time (s) Mig (courtesy of Aramco)

Time (s) Mig (Courtesy of Aramco)MD

Mig MD Mig MD

Fault

Purpose of MD Processing: Enhancing illumination Suppressing migration noise and artifacts Improving spatial resolution

Acknowledgements Aramco, Unocal, and Chevron- TexacoAramco, Unocal, and Chevron- Texaco UTAM sponsorsUTAM sponsors Bob Estill and George Yao (Unocal), Alan Leeds (ChevronTexaco)Bob Estill and George Yao (Unocal), Alan Leeds (ChevronTexaco)

Mig MD Model 0 Y (km) X (km) Z=3.5 KM

1.6 s Inline Crossline 3D PSTM (courtesy of Unocal) MD