3D fast reflectorless tomographic

1
3-D fast reflectorless tomographic migration
velocity analysis
Weihong Fei and George A. McMechan
3/3/2005
2
Outline

• Introduction

• Algorithm

• Synthetic example

• Conclusions

• Acknowledgment

3
Introduction

• An accurate interval velocity model is crucial
• for depth imaging
• Conventional migration velocity analysis is
  very
• time-consuming for 3-D data and needs
  extensive
• event picking

• In the proposed algorithm

• Picking is limited to only one common-offset or
  zero-offset section
• Computation time for each iteration is fast
• Convergence is fast

4
Algorithm

• Incident angle estimation and parsimonious
  migration

• Ray-tracing to define the CRP gathers

• Velocity update estimation for each CRP gather

• Composite velocity model update

5

• Step 1 Incident angle estimation and
• parsimonious migration

• 1. Selecting reference common-offset or stacked
  section
• 2. Positions of the salient reflections are
  picked automatically
• on the selected section
• 3. Estimate p values for the picked events

6
P-value estimation for reference section
or
Zero-offset section
Common-offset section
Within each shot Px in streamer line
direction Py in receiver direction
Px in inline direction Py in crossline direction
3-D parsimonious poststack migration
3-D parsimonious prestack migration
Spatial locations and orientations of reflection
points
7

• Step2 Common-Reflection Point Gather
• Extraction

• Two rays that have the same angle with respect
  to the
• zero-offset ray, and with azimuth that
  satisfies Snells
• law, are shot to the surface

• On the basis of the surface intersections of the
  two rays,
• extract the corresponding CRP trace

• Change the azimuth and angle to repeat the
  process
• to provide a complete CRP gather

8
y
r
s
x
z
9
CRP gather extraction
T
Tcal
10

• Step3 Velocity perturbation for each CRP gather

1) TnewTcal2?lsin(?)/v0
Offset
2) T?Tnewv1/v0
Time
Position
sn
rn
T
Tcal
?
Depth
11

• Step4 Composite velocity model update

a) The estimated velocity updates for each CRP
gather are back projected along the ray
paths associated with the CRP gather
b) Averaging of all the predicted updates in each
pixel gives the update for that pixel for
the current iteration
12
The same tomographic constraint strategy is used
in 3-D as in 2-D
Position (km)
Time (s)
13
Synthetic example
Velocity model size X 14 km Y 4 km Z 3
km
14
0.0
Time (s)
1.0
2.0
4.0
3.0
14.0
12.0
2.0
10.0
8.0
Zero-offset sections
X position (km)
1.0
6.0
Y position (km)
4.0
2.0
0.0
0.0
0.0
0.5
Time (s)
1.0
1.5
14.0
2.0
12.0
4.0
10.0
3.0
8.0
6.0
2.0
X position (km)
Y position (km)
4.0
1.0
2.0
0.0
0.0
15
Position (km)
Missing reflection
Traveltime (s)
16
Position (km)
Depth (km)
17
Modeling Geometry

• Sources are on 20 lines with 200 meter spacing.
• Each shot line has 72 shots with interval 200
  meters.

3.2 km

• 11 streamers with interval 40 meters

• Each streamer has 81 receivers with
• interval 40 meters

Shot position
Total traces 1,283,040
18
One common-shot gather
0.0
0.5
Time (s)
1.0
1.5
2.0
0.4
0.3
3.0
0.2
2.0
Y position (km)
0.1
1.0
Offset (km)
0.0
0.0
19
correct velocity model
0.0
1.0
Depth (km)
12.0
2.0
Slice positions X 2.5 km Y 0.5 km Z 0.7 km
11.0
10.0
3.0
9.0
8.0
4.0
7.0
3.0
6.0
X position (km)
2.0
5.0
4.0
1.0
3.0
Y position (km)
0.0
2.0
estimated velocity model
0.0
Problem?
1.0
Depth (km)
12.0
2.0
11.0
10.0
3.0
9.0
8.0
4.0
7.0
3.0
6.0
X position (km)
2.0
5.0
4.0
1.0
3.0
Y position (km)
0.0
2.0
20
correct velocity model
0.0
1.0
Depth (km)
2.0
12.0
Slice positions X 5.5 km Y 1.2 km Z 2.7 km
11.0
10.0
3.0
9.0
8.0
4.0
7.0
3.0
6.0
X position (km)
2.0
5.0
1.0
4.0
Y position (km)
0.0
3.0
2.0
estimated velocity model
0.0
1.0
Depth (km)
12.0
2.0
11.0
10.0
3.0
9.0
8.0
4.0
7.0
3.0
6.0
X position (km)
2.0
5.0
1.0
4.0
3.0
Y position (km)
0.0
2.0
21
correct velocity model
0.0
1.0
Depth (km)
12.0
2.0
11.0
Slice positions X 9.0 km Y 3.3 km Z 2.2 km
10.0
3.0
9.0
8.0
4.0
7.0
3.0
6.0
X position (km)
2.0
5.0
4.0
1.0
3.0
Y position (km)
0.0
2.0
estimated velocity model
0.0
1.0
Depth (km)
12.0
2.0
11.0
10.0
9.0
3.0
8.0
4.0
7.0
3.0
6.0
X position (km)
5.0
2.0
4.0
1.0
3.0
Y position (km)
0.0
2.0
22
correct velocity model
Slice positions X 8.0 km Y 2.0 km Z 1.5 km
estimated velocity model
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Y1.0 km
Offset (km)
0.0
3.2
0.0
1.0
Depth (km)
2.0
3.0
0.0
1.0
Depth (km)
2.0
3.0
24
Y1.8 km
Offset (km)
0.0
3.2
0.0
1.0
Depth (km)
2.0
3.0
0.0
1.0
Depth (km)
2.0
3.0
25
Y3.0 km
Offset (km)
0.0
3.2
0.0
1.0
Depth (km)
2.0
3.0
0.0
1.0
Depth (km)
2.0
3.0
26
Y3.4 km
Offset (km)
0.0
3.2
0.0
1.0
Depth (km)
2.0
3.0
0.0
1.0
Depth (km)
2.0
3.0
27
Offset (km)
Offset (km)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0.0
0.4
0.8
Time (s)
1.2
1.6
2.0
Iteration 1
Iteration 5
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Offset (km)
Offset (km)
0.0
0.4
0.8
Time (s)
1.2
1.6
2.0
Iteration 10
Iteration 15
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Unit m/s
5495
4698
3901
2307
Position (km)
Position (km)
Depth (km)
Iteration 1
Iteration 3
Position (km)
Position (km)
Depth (km)
Iteration 5
Iteration 7
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Unit m/s
5495
4698
3901
2307
Position (km)
Position (km)
Depth (km)
Iteration 9
Iteration 13
Position (km)
Position (km)
Depth (km)
Iteration 15
Correct velocity
31
0.0
1.0
Depth (km)
2.0
12.0
11.0
10.0
3.0
9.0
4.0
8.0
7.0
3.0
6.0
2.0
X position (km)
5.0
1.0
4.0
Y position (km)
3.0
0.0
2.0
0.0
1.0
Depth (km)
12.0
2.0
11.0
10.0
3.0
9.0
4.0
8.0
7.0
3.0
6.0
2.0
X position (km)
5.0
1.0
4.0
Y position (km)
3.0
0.0
2.0
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0.0
1.0
Depth (km)
2.0
12.0
11.0
10.0
3.0
9.0
8.0
4.0
7.0
3.0
6.0
X position (km)
2.0
5.0
4.0
1.0
Y position (km)
3.0
0.0
2.0
0.0
1.0
Depth (km)
2.0
12.0
11.0
10.0
3.0
9.0
4.0
8.0
7.0
3.0
6.0
X position (km)
2.0
5.0
4.0
1.0
Y position (km)
3.0
0.0
2.0
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Average time residual per ray (s)
Iteration number
34
Computation time

• Using 10 AMD Opterons, one iteration needs
• about 1.8 hours for 1.28 million traces

• Could be faster if do not do I/O of rays and
• CRP gathers, but no QC will be available

35
Conclusions

• Event picking is greatly reduced and needs to be
  done only once
• Fast convergence
• Fast computation time
• Provides accurate velocity models and hence
  better migrations

36
Acknowledgments

• UT Dallas Consortium sponsors
• SEG/EAGE for the velocity model