Imaging and Velocity Analysis with

1
Imaging and Velocity Analysis with Stationary
Phase Migration
Jing Chen University of Utah
2
Outline

• Resolution Analysis
• Specular Ray Parameters
• Stationary Phase Migration
• Tomographic Velocity Analysis
• Conclusions

3
Outline

• Resolution Analysis
• Specular Ray Parameters
• Stationary Phase Migration
• Tomographic Velocity Analysis
• Conclusions

4
Objective

• What are 2-D 3-D Horizontal
  Resolution Limits of Migration Images?
• What are Dynamic Ranges of 2-D 3-D Migration
  Images?

5
Assumptions

• Kirchhoff Migration
• A Point Scatterer Buried in a Homogeneous Media
• Far-Field Approximation

6
2-D Poststack Geometry
L
g
Z
Image Point
Point Scatterer
7
2-D Prestack Geometry
Image Point
Point Scatterer
8
3-D Poststack Geometry
9
3-D Prestack Fixed Geometry
10
3-D Prestack Moving Geometry
Receiver Matrix
Source Matrix
11
3-D Prestack Moving Geometry
Receiver Matrix
Source Matrix
12
Definitions
Dynamic Range
Main Lobe
Side Lobe
Horizontal Resolution
13
2-D Poststack Migration

• 2-D Zero-Offset Data

• 2-D Poststack Migration Operator

14
2-D Poststack Migration

• Point Scatterer Response

• Far-Field Formula

15
Definitions
Dynamic Range
Main Lobe
Side Lobe
Horizontal Resolution
16
2-D Poststack Migration

• Horizontal Resolution

17
2-D Prestack Migration

• Point Scatterer Response

• Far-Field Formula

18
2-D Prestack Migration

• Horizontal Resolution

19
Comparison of 2-D Migrations
Prestack
Poststack
20
3-D Poststack Migration

• Far-Field Formula

21
3-D Poststack Migration

• Horizontal Resolution

22
3-D Prestack Migrationwith Fixed Geometry

• Far-Field Formula

23
3-D Prestack Migrationwith Fixed Geometry

• Horizontal Resolution

24
3-D Migrations
Poststack
Prestack (Fixed Geometry)
25
3-D Prestack Migrationwith Moving Geometry

• Far-Field Formula

26
3-D Prestack Migrationwith Moving Geometry

• Horizontal Resolution

27
3-D Prestack Moving Geometry
28
Outline

• Resolution Analysis
• Specular Ray Parameters
• Stationary Phase Migration
• Tomographic Velocity Analysis
• Conclusions

29
Parameter Extraction
Extract specular-ray related parameters from
prestack migration
S
G
R
30
Why Specular-Ray Parameters Needed ?

• Prestack Depth Migration
• Traveltime Inversion
• Tomographic MVA
• AVO
• Etc...

31
Prestack Migration Operator
Image
Data
Aperture
Weight
32
Stationary Phase Approximation
33
Weighted Prestack Migration Operator
Image
Weight
Data
Aperture
Parameter
34
Stationary Phase Approximation
35
Specular-Ray Parameters
36
Specular-Ray Parameters
Source
Receiver
Midpoint
Traveltime
Reflector Normal
Departure Angle
Emergence Angle
Incidence Angle
37
Kirchhoff Migration of a COG
38
Weighted Kirchhoff Migration of a COG
Extra Weight
39
Division of Two COG Images

40
COG Incidence Angles
Distance (km)
16
8
0
0
20
(Degrees)
Depth (km)
10
2
4
0
41
COG Incidence Angles
Distance (km)
16
8
0
0
20
(Degrees)
Depth (km)
10
2
4
0
After Median Filtering
42
COG Traveltimes
Distance (km)
16
8
0
3.5
0
(Seconds)
Depth (km)
1.75
2
4
0
43
COG Traveltimes
Distance (km)
16
8
0
3.5
0
(Seconds)
Depth (km)
1.75
2
4
0
After Median Filtering
44
COG S-R Midpoint Coordinates
Distance (km)
16
8
0
20
0
Depth (km)
(km)
10
2
4
0
45
COG S-R Midpoint Coordinates
Distance (km)
16
8
0
20
0
Depth (km)
(km)
10
2
4
0
After Median Filtering
46
Verification of Extracted Parameters
47
COG S-R Midpoint Coordinates
Distance (km)
16
8
0
20
0
Depth (km)
(km)
10
2
4
0
48
COG Traveltimes
Distance (km)
16
8
0
3.5
0
(Seconds)
Depth (km)
1.75
2
4
0
49
Verification of Extracted Parameters
Trace Midpoint Coordinates
15
13
11
1
Time (sec)
Trvaeltimes Extracted
2
50
Outline

• Resolution Analysis
• Specular Ray Parameters
• Stationary Phase Migration
• Tomographic Velocity Analysis
• Conclusions

51
Stationary Phase Migration
SPM uses specular-ray parameters to

• Migrate traces within Fresnel zone
• Reject traces out of Fresnel zone
• Suppress alias artifacts

52
Stationary Phase Migration

• Algorithm
• Synthetic Data Example
• Field Data Example

53
Stationary Phase Migration Operator
Schleicher et al. (1997)
Fresnel zone width
Minimum Aperture
Fresnel Zone
Stationary phase point
54
Stationary Phase Migration

• Algorithm
• Synthetic Data Example
• Field Data Example

55
Kirchhoff Migration of a COG
Distance (km)
16
8
0
4
12
0
1
Depth (km)
2
3
4
56
Stationary Phase Mig. of a COG
Distance (km)
16
8
0
4
12
0
1
2
Depth (km)
3
4
57
Migration Operator
Trace Contributions
58
Kirchhoff Migration of a COG
Distance (km)
16
8
0
4
12
0
1
Depth (km)
2
3
4
59
Trace Contributions KM
Trace Number
300
150
0
0
Depth (km)
2
4
60
Trace Contributions SPM
Trace Number
300
150
0
0
Depth (km)
2
4
61
Kirchhoff Migration of a COG
Distance (km)
16
8
0
4
12
0
1
Depth (km)
2
3
4
62
Trace Contributions KM
Trace Number
300
150
0
0
Depth (km)
2
4
63
Trace Contributions SPM
Trace Number
300
150
0
0
Depth (km)
2
4
64
Kirchhoff Migration of a COG
Distance (km)
16
8
0
4
12
0
1
Depth (km)
2
3
4
65
Trace Contributions KM
Trace Number
300
150
0
0
Depth (km)
2
4
66
Trace Contributions SPM
Trace Number
300
150
0
0
Depth (km)
2
4
67
Incidence Angle
CIG
Offset (km)
Offset (km)
0
3
3
0
70
0
0
Depth (km)
Depth (km)
35
2
2
4
0
4
(Deg)
68
Incidence Angle
CIG
Offset (km)
Offset (km)
0
3
3
0
70
0
0
Depth (km)
Depth (km)
35
2
2
4
0
4
(Deg)
69
Stacked SPM Image After Muting
Distance (km)
16
8
0
4
12
0
1
2
Depth (km)
3
4
70
Stacked SPM Image Without Muting
Distance (km)
16
8
0
4
12
0
1
2
Depth (km)
3
4
71
Stationary Phase Migration

• Algorithm
• Synthetic Data Example
• Field Data Example

72
Kirchhoff Migration of a COG
Distance (km)
14
6
0
2
12
4
8
10
0
2
Depth (km)
4
6
73
Stationary Phase Mig. of a COG
Distance (km)
14
6
0
2
12
4
8
10
0
2
Depth (km)
4
6
74
Stacked KM Image
Distance (km)
14
6
0
2
12
4
8
10
0
2
Depth (km)
4
6
75
Stacked SPM Image
Distance (km)
14
6
0
2
12
4
8
10
0
2
Depth (km)
4
6
76
Outline

• Resolution Analysis
• Specular Ray Parameters
• Stationary Phase Migration
• Tomographic Velocity Analysis
• Conclusions

77
Steps in Tomographic MVA

• Build Initial Migration Velocity
• Migrate Seismic Data
• Obtain S R Coordinates with SPM
• Find Specular-Ray Paths
• Pick Depth Residual Moveouts
• Pick Reflector Positions
• Update Velocities
• Migrate Seismic Data With
• Updated Velocities
• Repeat Above Steps

78
Preparing Input For Velocity Update
Seismic Data
Initial Migration Velocities
Stationary-Phase Migration
CIGs
Source Xs(Xi,h)
Receiver Xr(Xi,h)
ZO Image
Auto Scan
Residual Moveouts DZ(Xi,h)
Reflector Positions Xi
Xi DZ(Xi,h) Xs(Xi,0) Xr(Xi,0) Xs(Xi,h) Xr(Xi,h)
79
Velocity Updating Scheme
Xi DZ(Xi,h) Xs(Xi,0) Xr(Xi,0) Xs(Xi,h) Xr(Xi,h)
Initial Mig. Velocity
DZ --gt DT
2 Pt. Ray Tracing
Adjust Reflector Depths
Back Projection SIRT DT --gt DS
New DZ
Reflector Adjustment Iteration
New Slowness SSDS
SIRT Iteration
DZ --gt DT
New DT
Yes
Misfit Func. Decrease?
Yes
No
Misfit Func. Decrease?
No
STOP
80
Initial Migration Velocity
Distance (km)
15
10
0
5
10000
0
1
Depth (km)
7450
2
3
4900
(ft/sec)
81
Image With Initial Velocity
Distance (km)
15
10
0
5
0.3
1.0
Depth (km)
2.0
82
Peak-Amplitude Positions
Distance (km)
15
10
0
5
0.3
1.0
Depth (km)
2.0
83
Reflectors Picked
Distance (km)
15
10
0
5
0.3
1.0
Depth (km)
2.0
84
Reflectors Picked
Distance (km)
15
10
0
5
0.3
1.0
Depth (km)
2.0
85
Depth Residuals Picked
Depth Residual Moveouts (m)
Horizontal Coordinates Along Reflector (km)
86
Depth Residuals Picked
After Median Filtering and Muting
Depth Residual Moveouts (m)
Horizontal Coordinates Along Reflector (km)
87
Raypaths
Distance (km)
15
10
0
5
0.3
1.0
Depth (km)
2.0
88
Raypaths
Distance (km)
15
10
0
5
0.3
1.0
Depth (km)
2.0
89
Misfit Function vs Iteration No.
Reflector Adjustment Iterations
Misfit Function
SIRT Iterations
Iteration Number
90
Velocity Increment
Distance (km)
15
10
0
5
150
0
1
Depth (km)
50
2
3
-50
(ft/sec)
91
Image With Updated Velocity
Distance (km)
15
10
0
5
0.3
1.0
Depth (km)
2.0
92
Image With Initial Velocity
Distance (km)
15
10
0
5
0.3
1.0
Depth (km)
2.0
93
Common Image Gathers
With Initial Velocity
0.5
1.2
Depth (km)
2.0
94
Common Image Gathers
With Updated Velocity
0.5
1.2
Depth (km)
2.0
95
Outline

• Resolution Analysis
• Specular Ray Parameters
• Stationary Phase Migration
• Tomographic Velocity Analysis
• Conclusions

96
Conclusions

• Horizon resolutions are proportional to
  wavelength, scatterer depth and inversely
  proportional to aperture size
• 2-D prestack migration has the same resolution
  as the 2-D poststack migration, but higher
  dynamic range.

97
Conclusions

• 3-D fixed geometry prestack migration has lower
  resolution than 3-D postatck migration, but 3-D
  moving geometry presatck migration has the same
  resolution as 3-D poststack migration. Both 3-D
  prestack migrations have higher dynamic ranges
  than 3-D poststack migration.

98
Conclusions

• Specular-ray related parameters can be
  estimated from presatck migration
• SPM produces fewer alias artifacts and improves
  horizon continuity
• Automatic tomographic velocity analysis is able
  to obtain better migration velocity

99
Acknowledgements

• I thank the committee members for supervising
  my studies and researches in the past years.
• I thank Fuhao Qin and J.C. Wan of Hess for
  supervising my summer works in Hess.
• I thank the UTAM sponsors for their supports.
• I thank UTAM members for their helps.