3d super-virtual refraction interferometry kai lu king abdullah university of science and technology
TRANSCRIPT
Outline
• Introduction and Motivation• Theory: conventional SVI with stationary
phase integration• Synthetic data example• Field data example• Conclusion• Acknowledgement
Outline
• Introduction and Motivation• Theory: conventional SVI with stationary
phase integration• Synthetic data example• Field data example• Conclusion• Acknowledgement
B CA3
dt
A2 A1
dt
dt
1.Stacked Refractions: + Stacking
dt
B C
wA
B C
Common Pair Gather (Dong et al., 2006)
Benefit: SNR = N
d d AB AC ~ d BCA
virtual
~
2D Super-virtual Interferometry
2. Dedatum Virtual Refraction to Known Surface Point
B C B CA B CA
=*
=*
+
d d AB AC
~ d BCAsrc
virtual
real super-virtual
d d AB BC
~ d ACBrec
supervirtual
*virtual
Raw trace Virtual trace(Calvert+Bakulin, 2004)
Super-virtual trace
BrecAsrc
Datuming Dedatuming
2D Super-virtual Interferometry
2D Super-virtual Interferometry Theory and workflow:
Are first arrivals at far-offsets
pickable ?
Window around first arrivals and mute near offset
Correlate and stack to generate virtual refractions
Input Data
Output Data
Convolve and stack to generate Super-virtual refractions
N
Ʃ
Ʃ
Raw Data
Super-virtual refraction Data
Windowed Data Iterative
SVI
Difficulties from 2D to 3D• Difficulty to find locations of stationary sources and receivers
S
A1
Unknown Path
Few sources and receiver available
A2
• Limited number of sources and receivers
Solution
• 2D: all traces are stationary
• 3D: stationary phase integrationA
B
Virtual Trace
Virtual Trace
S1 S2 S3 Sn• • •
S*
Outline
• Introduction and Motivation• Theory: conventional SVI with stationary
phase integration• Synthetic data example• Field data example• Conclusion• Acknowledgement
Stationary Phase IntegrationStationary phase analysis (Bleistein, 1984) applied to the line integral:
𝑓 (𝜔 )=∫−∞
∞
𝑔(𝑥)𝑒𝑖𝜔∅ (𝑥)𝑑𝑥 𝛼𝑒𝑖𝜔∅ (𝑥∗)𝑔 (𝑥∗)
∫𝑆1
𝑆𝑛
𝐺 ( 𝐴|𝑆 )𝐺∗ (𝐵|𝑆 ) 𝑑𝑆 𝐺 (𝐴|𝑆∗)𝐺∗ (𝐵|𝑆∗ )
Applied to SVI:
Virtual trace AB
AB
S1 S2 S3 Sn• • •S*
Cross-correlation Type
AB
CRG A CRG B Cross-correlation Results
Ʃ
Correlation of S*A and S*B
Virtual trace AB
Source1 180
Time (s)
0
4Source1 180 Source1 180 Amplitude-1 1
S1 S1Sn SnS* S*
Virtual Trace Stacking over Source Lines
A
B
S1 S2 S3 Sn
lineN
line1
line2
2D: Stacking over sources:
3D: Stacking over source lines:
∑𝑆1
𝑆𝑛
𝐺 ( 𝐴|𝑆 )𝐺∗(𝐵∨𝑆)∑𝑙𝑖𝑛𝑒 1
𝑙𝑖𝑛𝑒𝑛
❑ 𝐺 (𝐵∨𝐴)𝑣𝑖𝑟𝑡
CA1 B CA1 B C B
=
A2 A2A3 A3
Super Virtual Trace – Convolution Type
A
S
B1B2 B3
Bn
lineN
line1
line2
2D: Stacking over receivers:
3D: Stacking over receiver lines:
∑𝐵 1
𝐵𝑛
𝐺 (𝐵|𝑆 )𝐺(𝐵∨𝐴)𝑣𝑖𝑟𝑡∑𝑙𝑖𝑛𝑒 1
𝑙𝑖𝑛𝑒𝑛
❑ 𝐺 (𝐴∨𝑆)𝑠𝑢𝑝𝑒𝑟−𝑣𝑖𝑟𝑡𝑢𝑎𝑙
CA B1 CA B C B1
* =
B2 B2 B3 B3
Workflow of 3D SVI
Window around the targeted refraction
Generate virtual trace AB:
Input Band-pass filtered Data
Output Data
Generate super-virtual trace SA:
Stack generated from different sources
Stack generated from different receiver lines
Iterative SVI
Outline
• Introduction and Motivation• Theory: conventional SVI with stationary
phase integration• Synthetic data example• Field data example• Conclusion• Acknowledgement
Synthetic Test – Undulating Layer Model
••
•
V1=1500m/s
V2=3000m/s
151 receivers, 76 sources on every line
11 survey lines
Line1
Line11Synthetic Result •••
Original data Data with random noise
Super-virtual refraction Iterative Super-virtual RefractionTrace
Time (s)
0
31 151 Trace
Time (s)
0
31 151
Trace
Time (s)
0
31 151 Trace
Time (s)
0
31 151
Outline
• Motivation: from 2D to 3D• Theory: conventional SVI with stationary
phase integration• Synthetic data example• Field data example• Conclusion• Acknowledgement
19
x [km]
y [k
m]
2 14
-2
18
3D OBS Survey Geometry
400 m
50 m50 m
5 m
• Sihil 3D OBS data– 234 OBS stations– 129 source-lines
• Irregular geometry.
Map view
Field Results 1Raw data
Band-pass filtered data Super-virtual resultTrace
Time (s)
0
41 361
Trace
Time (s)
0
41 361 Trace
Time (s)
0
41 361
Zoom View ComparisonZoom view of band-pass filtered data Zoom view of super-virtual data
Trace
Time (s)
1
31 361 Trace
Time (s)
1
31 361
Zoom view of super-virtual data
Unpickable
Field Results 2Raw data
Super-virtual result Iterative Super-virtual resultTrace
Time (s)
0
41 361
Trace
Time (s)
0
41 361 Trace
Time (s)
0
41 361
Zoom View ComparisonRaw data
Super-virtual result Iterative Super-virtual resultTrace
Time (s)
0
41 361
Trace
Time (s)
0
41 361 Trace
Time (s)
0
41 361
Unpickable
Unpickable
Outline
• Introduction and Motivation• Theory: conventional SVI with stationary
phase integration• Synthetic data example• Field data example• Conclusion• Acknowledgement
Conclusion• We apply stationary phase integration method
to achieve super-virtual refraction with enhanced SNR in 3D cases.
• Iterative method is an option to further improve SNR when super-virtual refraction is still noisy.
• Artifacts can be produced because of the limited aperture for integration as well as a coarse spacing of sources or receivers.