Transcript Extended Diffraction-Slice Theorem for Wavepath Traveltime

Progress Report:
Interpolation of 3D SSP Data
Using Interferometry
Sherif Hanafy
February 2009
Outline
• Problem: Missing and sparse traces
• Theory: Interferometric interpolation and
extrapolation
• Numerical results:
– 3D layered velocity model
– SEG/EAGE model
• Conclusions and future work
Outline
• Problem: Missing and sparse traces
• Theory: Interferometric interpolation and
extrapolation
• Numerical results:
– 3D layered velocity model
– SEG/EAGE model
• Conclusions and future work
Problem
In marine surveys, receiver
interval could be large
(especially in cross line
direction)
Solution: Use interferometric
interpolation
Water
Water
Outline
• Problem: Missing and sparse traces
• Theory: Interferometric interpolation and
extrapolation
• Numerical results:
– 3D layered velocity model
– SEG/EAGE model
• Conclusions and future work
Theory
SSP
SSP
SSP
Virtual source
Virtual receiver
Ocean
Surface
A
B
Ocean
Surface
Ocean
Surface
x
A
Sea bed
B
x
A
Sea bed
B
x
Sea bed
Reflectors
Reflectors
G(x|B)
G(x|A)
G(B|A)
Model based data
Natural Green’s
function
Interpolated data
SSP
SSP
SSP
SSP











 
G ( B | A)  2ik  G ( x | A) Go ( x | B)* dx 2  Go ( A | B)*
SS



G ( B | A)  2ik 
SSP
SSP
SSP






 
*
2
G ( x | A) Go ( x | B) dx  Go ( A | B)*
SSP
Workflow
SS
Input Data
0
Input Field Data
G(x|B)
G(x|A)
Ocean Surface
Interpolate/Extrapolate
Missing Data
Sea bed
Unfiltered Virtual
0
3.0
0
X (km)
Get Virtual CSG
x
4.5
Time (s)
Generate GF for
Water Multiples
Time (s)
Water Layer Thickness
Filtered Virtual
0
G(B|A)
N
3.0
Max. Itr (MF)
0
X (km)
Time (s)
Matching Filter
4.5
Y
N
Max Iter
Intr/Extr
Y
Final CSG
3.0
0
X (km)
4.5
Outline
• Problem: Missing and sparse traces
• Theory: Interferometric interpolation and
extrapolation
• Numerical results:
– 3D layered velocity model
– SEG/EAGE model
• Future work
Numerical Results
Source
1.4 km
3 km
• 3D velocity model is used to
test the interpolation approach
• 3000 x 3000 x 1400 m3 in x, y,
and z directions
• Source is at (10,10,30) (x,y,z)
• 300 by 300 receiver points are
used with dx=dy=10 m
• Sea bottom is flat @ depth of
750 m
Velocity Model
Sea bed
Reflector # 1
Reflector # 2
1500
Velocity (m/s)
2400
2D Example
Input
Goal
• 60 Traces
• 300 Traces
Source
• Trace interval = 50 m
Sparse geometry
Line # 1
• Trace interval = 10 m
Dense geometry
2D Test
Source Line # 1
0
0
Sparse CSG, 60 trace, dx
= 50 m
Keep every 4th trace
Time (s)
Time (s)
Original CSG, 300 trace,
dx = 10 m
5
5
0
X (m)
3000
0
X (m)
3000
2D Test
Source Line # 1
0
0
Virtual CSG before
matching filter, 300
trace, dx = 10 m
0
Time (s)
Time (s)
Time (s)
Original CSG, 300
trace, dx = 10 m
5
5
5
0
X (m)
3000 0
X (m)
3000 0
Virtual CSG after
matching filter, 300
trace, dx = 10 m
X (m)
3000
3D Example
Input
Goal
• 60 crossline
• 300 crossline
• Crossline interval = 50 m
• Crossline interval = 10m
• 100 traces/line
• 300 traces/line
• Trace interval = 30 m
• Trace interval = 10 m
• Total number of traces = 6000
• Total number of traces = 90,000
Sparse geometry
Dense geometry
Line # 180
SSP Data Line # 180
0
0
Sparse CSG, 60 trace, dx = 50 m
Time (s)
Time (s)
Original CSG, 300 trace, dx = 10 m
5
5
0
X (m)
3000
0
X (m)
3000
Line # 180
SSP Virtual Data
0
Iterations: 1 interpolation
and 8 MF
0
Original CSG, 300 trace, dx = 10 m
Time (s)
Time (s)
Virtual CSG, 300 trace, dx = 10 m
5
5
0
X (m)
3000
0
X (m)
3000
Line # 180
SSP Virtual Data
0
Iterations: 3 interpolation
and 8 MF/interpolation
0
Original CSG, 300 trace, dx = 10 m
Time (s)
Time (s)
Original CSG, 300 trace, dx = 10 m
5
5
0
X (m)
3000
0
X (m)
3000
Outline
• Problem: Missing and sparse traces
• Theory: Interferometric interpolation and
extrapolation
• Numerical results:
– 3D layered velocity model
– SEG/EAGE model
• Conclusions and future work
SEG/EAGE Velocity Model
1500
Velocity (m/s)
4500
Acquisition Parameters
• Input
• Goal
–
–
–
–
–
–
–
–
–
–
8 Streamers
Crossline offset is 30 m
Inline offset is 12 m
170 receivers/streamer
Total number of receivers 1360
Sparse geometry
22 Streamers
Crossline offset is 10 m
Inline offset is 4 m
508 receivers/streamer
Total number of receivers 11176
Dense geometry
SEG/EAGE Model – Input Data
Time (s)
0
1
2
8
1
Streamer
2
Scale
0
2 km
SEG/EAGE Model – Virtual Data
Time (s)
0
8
1
1’
Streamer
2’
2
1
2
1’ 2’
Scale
0
2 km
SEG/EAGE Model – Real Data
Time (s)
0
8
1
2
Streamer
3
4
Scale
0
2 km
Outline
• Problem: Missing and sparse traces
• Theory: Interferometric interpolation and
extrapolation
• Numerical results:
– 3D layered velocity model
– SEG/EAGE model
• Conclusions and future work
Conclusions
• 3D marine SSP data can be interpolated
with interferometry.
• Proposed approach is successfully tested on
two synthetic models.
• Number of receivers can be increased 8 to
10 times by interferometry.
Future Work
• Extrapolation of the data
• Test on field data, we need field data to
complete this part
Acknowledgement
We would like to thank the UTAM
2008 sponsors for their support.
Thank You