Local Reverse Time Migration with VSP Green’s Functions
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Local Reverse Time Migration with VSP Green’s Functions
Xiang Xiao
UTAM, Univ. of Utah
May 1, 2008
PhD Defense
99 pages
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2
Outline
• Introduction and overview• SSP VSP SWP interferometric
transform• Local reverse time migration: horizontal
reflector imaging• Local reverse time migration: salt flank
imaging with transmitted P-to-S waves• Summary
Overview SSPVSP Local RTM Local RTM PS Summary
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3
Outline
Overview SSPVSP Local RTM Local RTM PS Summary
• Introduction and overview• SSP VSP SWP interferometric
transform• Local reverse time migration: horizontal
reflector imaging• Local reverse time migration: salt flank
imaging with transmitted P-to-S waves• Summary
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Data
Tim
e
Offset
ModelD
epth
Offset
r(x) D(g|s)Forward modelling
InverseMigration
m(x)
Migration Image
Low subsalt resolution,Defocusing!
Overview SSPVSP Local RTM Local RTM PS Summary
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Subsalt Imaging
s
x
G(x|g) g
G(x|s)
m(x) ~
~ G(x|s)
Model- based
G(x|g)*
Model-based
gsds
*
D(g|s)
D(g|s)dg
Overview SSPVSP Local RTM Local RTM PS Summary
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6
Subsalt Imaging
s
x
G(x|g) g
G(x|s)
m(x) ~
~ G(x|s)
Forwarddirect
sds
*
D(g|s)
G(x|g)*
Backward reflection
g
D(g|s)dg
Errors in the overburden
and salt body velocity model
Defocusing
Overview SSPVSP Local RTM Local RTM PS Summary
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7
Interferometric Imaging
s
x
G(x|g) G(x|s)
g
m(x) ~ s
~ ds G(x|s)
Data-based
G(x|g)* D(g|s)dg
Model-based
g
*
Overview SSPVSP Local RTM Local RTM PS Summary
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Local Reverse Time Migration
s
x
G(x|g) g
G(x|s)
g’
G(x|s)= G(x|g’)* D(g’|s)dg’
Backward Direct wave
g’ Local VSP Green’s function
Overview SSPVSP Local RTM Local RTM PS Summary
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Local Reverse Time Migration
s
x
G(x|g) g
G(x|s)
g’
Overview SSPVSP Local RTM Local RTM PS Summary
s
m(x) ~
~ G(x|s)
Backwardapprox
sds
* G(x|g)*
Backward reflection
g
D(g|s)dg
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10
Outline
Overview SSPVSP Local RTM Local RTM PS Summary
• Introduction and overview• SSP VSP SWP interferometric
transform• Local reverse time migration: horizontal
reflector imaging• Local reverse time migration: salt flank
imaging by transmitted P-to-S waves• Summary
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11
Outline
Overview SSPVSP Local RTM Local RTM PS Summary
• SSP VSP SWP interferometric transform
– Motivation– Theory – Numerical Tests
• SEG/EAGE salt model• Double datuming
– Conclusions
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I. Why we need more VSP?
Surface related statics
SSP VSP
•Twice OnceSeabedSeabed
SaltSalt
TargetTarget
Overburden velocity error
•Twice OnceRaypath
•Longer Shorter Attenuation
•More LessFrequency
Resolution
•Lower Higher
•Lower Higher
SSPVSP Motivation Theory Numerical Tests Conclusions
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How to get more VSP?
dxG(B|A) ~
RVSP VSP
G(A|x)* G(B|x)
SSP
S2
~
S2
A
Bx
S1
RVSP
S2
A
Bx
S1
VSP
S2
A
Bx
S1
SSP
SSPVSP Motivation Theory Numerical Tests Conclusions
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3D Application
3D VSP3D SSP
Naturally datuming !
3D RVSP
SSP + VSP RVSP !
Low fold
High fold !
SSPVSP Motivation Theory Numerical Tests Conclusions
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X
SS
SeabedSeabed
TargetTarget
SaltSalt
SSP/RVSP apertureSSP/RVSP aperture
ggVSP apertureVSP aperture
Shot coverageShot coverageReceiver coverageReceiver coverage
SSPVSP Motivation Theory Numerical Tests Conclusions
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Use it, or lost it…
3D RVSP
SSP + VSP RVSP !
High folds !
SaltSalt
Better image under the salt !
SSP, VSPWell log
Better Geologic interpretation !
SSPVSP Motivation Theory Numerical Tests Conclusions
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What is the benefit ?
– Higher fold virtual RVSP data are obtained;– Sources are closer to the target;
SSP + VSP RVSP
SaltSalt
– No velocity model is needed;– Multi-arrival are considered;
SSPVSP Motivation Theory Numerical Tests Conclusions
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How to skip overburden?
dxG(g|g’) ~
SWP VSP
G(g’|s)* G(g|s)
VSP
S~
gg’
s
VSP
gg’
s
VSP
gg’
s
Virtual Source Gather
No velocity model is needed !
SSPVSP Motivation Theory Numerical Tests Conclusions
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Application of VSPSWP transform:
gg’
s
Virtual Source Gather
Salt flank imaging
P and S wave checkshot
Sediment imaging
Multiple/teleseismic imaging
4D Reservoir monitoring
Shear wave splitting and crack orientation
Seismic while drilling
……
Application
SSPVSP Motivation Theory Numerical Tests Conclusions
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Outline
Overview SSPVSP Local RTM Local RTM PS Summary
• SSP VSP SWP interferometric transform
– Motivation– Theory – Numerical Tests
• SEG/EAGE model• Double datuming
– Conclusions
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P-wave velocity model0
Dep
th (
m)
-7850 7850Offset (m)
Velocity (m/s)4500
15003600
SEG/EAGE Salt Model
SSPVSP Motivation Theory Numerical Tests Conclusions
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P-wave velocity model0
Dep
th (
m)
-7850 7850Offset (m)
Velocity (m/s)4500
15003600
SSP Data Geometry…SSP
SSPVSP Motivation Theory Numerical Tests Conclusions
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Data
Synthetic SSP CSG
Tim
e (s
)
0
6
Offset (m)-2000 2000
SSPVSP Motivation Theory Numerical Tests Conclusions
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P-wave velocity model0
Dep
th (
m)
-7850 7850Offset (m)
Velocity (m/s)4500
15003600
VSP Geometry…
SSPVSP Motivation Theory Numerical Tests Conclusions
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Data
Tim
e (s
)
Synthetic VSP CRG0
6
Offset (m)-7850 7850
Synthetic SSP CSG
Tim
e (s
)
0
6
Offset (m)-7850 7850
SSPVSP Motivation Theory Numerical Tests Conclusions
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Traces comparisons
Am
pli
tud
e
Time (s)2 6
Synthetic RVSP CSG
Tim
e (s
)
0
6
Redatumed RVSP
Tim
e (s
)
0
6Offset (m)-7850 7850
1.4 kmComparison
Zoom area
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Zoom View of TracesN
orm
aliz
ed A
mp
litu
de
Time (s) 5.53
Redatumed RVSP trace
Direct waves are cut
poor data folds
SSPVSP Motivation Theory Numerical Tests Conclusions
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P-wave velocity model0
Dep
th (
m)
-7850 7850Offset (m)
Velocity (m/s)4500
15003600
Another Datuming Results
SSPVSP Motivation Theory Numerical Tests Conclusions
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Synthetic RVSP CSGT
ime
(s)
0
6
Redatumed RVSP
Tim
e (s
)
0
6Offset (m)-2000 2000
Traces comparisons
Am
pli
tud
e
Time (s)2 6
2.4 kmComparison
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No
rmal
ized
Am
pli
tud
e
Time (s)2.5 6
Zoom viewDirect waves are cut
poor data foldsRedatumed RVSP trace
SSPVSP Motivation Theory Numerical Tests Conclusions
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P-wave velocity model0
Dep
th (
m)
-7850 7850Offset (m)
Velocity (m/s)4500
15003600
SEG/EAGE Salt Model
SSPVSP Motivation Theory Numerical Tests Conclusions
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Shot 320 SSP primary WEM 20 Hz1.5
3.5
Dep
th (
km)
-4 4Offset (km)
Shot 320 RVSP WEM 20 Hz
Dep
th (
km)
1.5
3.5
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33 shots SSP WEM 20 Hz
33shots VSP WEM 20 Hz
Dep
th (
km)
0
3.6Offset (km)-4 4
33 RVSP+VSP WEM 20 Hz
Offset (km)-4 4
SEG/EAGE salt model0
3.6
Dep
th (
km)
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ss gg
s’s’
ss
s’s’
gg
s’s’
gg
s’s’ g’g’
gg
g’g’ s’s’ g’g’
SSPVSPSWP Transform
SSPVSP Motivation Theory Numerical Tests Conclusions
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1% error in migration model
2% error in migration model
Dep
th (
km)
0
3.6Offset (km)-8 8
3% error in migration model
Offset (km)-8 8
645 shots SSP WEM0
3.6
Dep
th (
km)
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1% error in migration model
2% error in migration model
Dep
th (
km)
0
3.6Offset (km)-8 8
3% error in migration model
Offset (km)-8 8
33 shots VSP WEM0
3.6
Dep
th (
km)
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645 shots SSP primary WEM 20 Hz0
3.5
Dep
th (
km)
-8 8Offset (km)
Shot 320 BSSP WEM 20 Hz
Dep
th (
km)
1.5
3.5
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645 shots SSP primary WEM 20 Hz0
3.5
Dep
th (
km)
-8 8Offset (km)
Shot 320 BSSP WEM 20 Hz
Dep
th (
km)
1.5
3.5
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Conclusions
• Natural datuming, no velocity model is needed !
• Higher fold virtual VSP data are obtained !
• Source are closer to the target, less approximation.• Better resolution.
SSPVSP Motivation Theory Numerical Tests Conclusions
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Outline
Overview SSPVSP Local RTM Local RTM PS Summary
• Introduction and overview• SSP VSP SWP interferometric
transform• Local reverse time migration: horizontal
reflector imaging• Local reverse time migration: salt flank
imaging with transmitted P-to-S waves• Summary
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42
Outline
Motivation Theory Numerical Tests ConclusionsLocal RTM
• Local reverse time migration: horizontal reflector imaging
– Motivation– Theory – Numerical Tests
• Sigsbee VSP Data Set• GOM VSP Data Set
– Conclusions
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VSP Forward Modeling
s
x
g
D(g|s)
VSP data
Motivation Theory Numerical Tests ConclusionsLocal RTM
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Reverse Time Migration
s
x
g
D(g|s)
VSP data
Motivation Theory Numerical Tests ConclusionsLocal RTM
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Reverse Time Migration
s
x
G(x|g) g
G(x|s)
BackwardD(g|s)
Forwarddirect
m(x) ~ s
~ ds G(x|s)
Forward direct
G(x|g)* D(g|s)dg
Backward data
g
*
Motivation Theory Numerical Tests ConclusionsLocal RTM
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Reverse Time Migration (RTM)
s
x
G(x|g) g
G(x|s)
BackwardD(g,s)
Forwarddirect
Forward direct:1) Salt velocity model is required, but hard to
build.2) Errors due to imperfect velocity models.
3) Need to estimate statics, anisotropy, etc.
Motivation Theory Numerical Tests ConclusionsLocal RTM
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s
g
g’
x
VSPSWP Interferometry
Migrate virtual source gather D(g|g’) Limitations
1) s and x are at different sides of the well2) Image near vertical structures
Motivation Theory Numerical Tests ConclusionsLocal RTM
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Outline
Motivation Theory Numerical Tests ConclusionsLocal RTM
• Local reverse time migration: horizontal reflector imaging
– Motivation– Theory – Numerical Tests
• Sigsbee VSP Data Set• GOM VSP Data Set
– Conclusions
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Key Idea of Local RTM
(a) VSP data: P(g|s)=T(g|s)+R(g|s)
Transmission T(g|s)
s
g
Reflection R(g|s)
x
Motivation Theory Numerical Tests ConclusionsLocal RTM
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(a) VSP data: P(g|s)=T(g|s)+R(g|s)
T(g|s)
s
gR(g|s)
x
s
(b) Backward reflection
R(g|s)g
x
R(x|s)= G(x|g)*R(g|s)g
(c) Backward transmission
T(g|s)
s
g
x
T(x|s)= G(x|g)*T(g|s)
g
(d) Crosscorrelation
m(x)= R(x|s)*T(x|s)s
Local VSP Green’s function
R(g|s)g
x
Key Idea of Local RTM
Motivation Theory Numerical Tests ConclusionsLocal RTM
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(d1) Crosscorrelation imaging condition
m(x)= R(x|s)*T(x|s)s
R(g|s)g
x
Deconvolution Imaging Condition
Motivation Theory Numerical Tests ConclusionsLocal RTM
(d2) Deconvolution imaging condition
m(x)= R(x|s)*T(x|s)s
s
T(x|s)*T(x|s)
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Benefits
• Target oriented!– Only a local velocity model near the well is
needed.– Salt and overburden is avoided.
– Fast and easy to perform.
• Source statics are automatically accounted for.
• Immune to salt-related interbed cross-talk.
Motivation Theory Numerical Tests SummaryLocal RTM
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Outline
Motivation Theory Numerical Tests ConclusionsLocal RTM
• Local reverse time migration: horizontal reflector imaging
– Motivation– Theory – Numerical Tests
• Sigsbee VSP Data Set• GOM VSP Data Set
– Conclusions
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Sigsbee P-wave Velocity Model0
Dep
th (
km)
9.2
4500
1500
m/s
-12.5 12.5Offset (km)
279 shots
150 receivers
Motivation Theory Numerical Tests ConclusionsLocal RTM
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Local Reverse Time Migration Results
4.6
9.2
Dep
th (
km)
-3 3Offset (km)
True modelMigration image
f = fault
f
d
d
(1)
(2)
(3)
(1) specular zone (2) diffraction zone(3) unreliable zone
d = diffractor
Motivation Theory Numerical Tests ConclusionsLocal RTM
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56
Outline
Motivation Theory Numerical Tests ConclusionsLocal RTM
• Local reverse time migration: horizontal reflector imaging
– Motivation– Theory – Numerical Tests
• Sigsbee VSP Data Set• GOM VSP Data Set
– Conclusions
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57
Dep
th
(m)
Offset (m)4878
0 1829
0
GOM VSP Well and Source LocationSource @150 m offset
2800 m
3200 m
Salt
82 receivers
Motivation Theory Numerical Tests ConclusionsLocal RTM
@600 m offset @1500 m offset
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58
P-to-S ratio = 2.7
Velocity ProfileS WaveP Wave
Dep
th
(m)
0
45000 5000 0 5000
2800 m
3200 m
Salt
Incorrect velocity model
P-to-S ratio = 1.6
Velocity (m/s) Velocity (m/s)
Motivation Theory Numerical Tests ConclusionsLocal RTM
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59
Z-Component VSP DataD
epth
(m
)
Traveltime (s)
2652
3887
1.2 3.0
Salt
Direct P
Reflected P
Reverberations
Motivation Theory Numerical Tests ConclusionsLocal RTM
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60
X-Component VSP DataD
epth
(m
)
Traveltime (s)
2652
3887
1.2 3.0
Salt
Direct P
Reflected P
Reverberations Direct S
Motivation Theory Numerical Tests ConclusionsLocal RTM
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61
Local Reverse Time Migration Result
(1)
(2)
(3)
(1) specular zone, (2) diffraction zone, (3) unreliable zone
3.3
Dep
th (
km)
3.9
0 100Offset (m)
39receivers
reflectivity
Motivation Theory Numerical Tests ConclusionsLocal RTM
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62
150 m offset
3.3
3.9
0 100
Motivation Theory Numerical Tests ConclusionsLocal RTM
Dep
th (
km)
Offset (m) 0 100Offset (m)
Without deconvolution
With deconvolution
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63
600 m offset
3.3
4.4
0 600
Motivation Theory Numerical Tests ConclusionsLocal RTM
Dep
th (
km)
Offset (m) 0 600Offset (m)
Without deconvolution
With deconvolution
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64
1500 m offset
3.3
4.4
0 600
Motivation Theory Numerical Tests ConclusionsLocal RTM
Dep
th (
km)
Offset (m) 0 600Offset (m)
Without deconvolution
With deconvolution
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65
Conclusions• Subsalt reflectors are accurately imaged
near the well with subsalt velocity model only.
• Diffractors are also imaged.
• GOM local RTM image agrees with the well reflectivity.
• Deconvolution imaging condition helps.
• Illuminates horizontal subsalt reflectors around a vertical well.
Motivation Theory Numerical Tests ConclusionsLocal RTM
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66
Outline
Overview SSPVSP Local RTM Local RTM PS Summary
• Introduction and overview• SSP VSP SWP interferometric
transform• Local reverse time migration: horizontal
reflector imaging• Local reverse time migration: salt flank
imaging with transmitted P-to-S waves• Summary
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67
Outline
Local RTM PS Motivation Theory Numerical Tests Summary
• Local reverse time migration: salt flank imaging by transmitted P-to-S waves
– Motivation– Theory – Numerical Tests
• Schlumberger VSP Data Set• GOM VSP Data Set
– Conclusions
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68
Standard P-to-S Migration
x
s
m(x) ~ s
~ ds G(x|s)
Forward source P
P
S
g’
G(x|g’)*D(g’|s)dg’
Backward data S
g’
*
Converted wave VSP
D(g|s)
Local RTM PS Motivation Theory Numerical Tests Summary
Salt and overburdenvelocity model is needed
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69
Interferometric P-to-S Migration
x
s
P
P
S
D(g|g’) ~
s
~ ds*
g’
g
D(g’|s) D(g|s)
m(x) ~ g’
~ dg’dgg
D(g|g’)G(x|g) G(x|g’)* *
Virtual source gather
Local RTM PS Motivation Theory Numerical Tests Summary
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70
Kirchhoff P-to-S Migration
x
s
m(x) ~ s
~ ds
P
S
g’
e-itxg’ D(g’|s)dg’g’
Converted wave VSP
D(g|s)
Local RTM PS Motivation Theory Numerical Tests Summary
e-itsx
Pg
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71
Reduce Time Migration
~( ~( tt + + tt )- )- ( ( tt + + tt ) )sxsx xxgg
pickpickpickpick
sxsx xxgg
errorerrortt sxsx xxg’g’=( =( tt + + tt )- )- ( ( tt + + tt ) )pickpickpickpick
sxsx xxg’g’
x
s
P
S
g
Converted wave VSP
D(g|s)
Local RTM PS Motivation Theory Numerical Tests
m(x) ~ s
~ ds e-itxg’ D(g’|s)dg’g’
e-i(tsx+terror)
Summary
Pg
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72
Outline
Local RTM PS Motivation Theory Numerical Tests Summary
• Local reverse time migration: salt flank imaging by transmitted P-to-S waves
– Motivation– Theory – Numerical Tests
• Schlumberger VSP Data Set• GOM VSP Data Set
– Conclusions
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73
x
s
P
P
S
m(x) ~ s
~ dsg’
G(x|g’)* D(g’,s) dg’
Backward P
G(x|g)* D(g,s)dg
Backward S
g
g’
g
*
Local Reverse Time Migration Theory
Local RTM PS Motivation Theory Numerical Tests Summary
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74
Outline
Local RTM PS Motivation Theory Numerical Tests Summary
• Local reverse time migration: salt flank imaging by transmitted P-to-S waves
– Motivation– Theory – Numerical Tests
• Schlumberger VSP Data Set• GOM VSP Data Set
– Conclusions
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75
Dep
th
(km
)
Offset (km)
10-12 12
0
Schlumberger 2D Isotropic Elastic Model
0
291 shots
287 receivers
Local RTM PS Motivation Theory Numerical Tests Summary
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76
Dep
th
(km
)
10
0
Offset (km)-12 120
(a) Ray tracing direct P
(c) PPS events (d) Pp events
(b) PSS events
Dep
th
(km
)
10
0
Offset (km)-12 120
Aperture by Ray Tracing
Local RTM PS Motivation Theory Numerical Tests Summary
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77
Direct P
PPS
PSS
Dep
th
(km
)
Time (s)
8
0 8
VSP CSG X-component
VSP CSG Z-component4
Dep
th
(km
)
8
4
Two-component VSP Synthetic Data Set
Local RTM PS Motivation Theory Numerical Tests Summary
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78
4.5
2.0
km/s(a) P-wave submodelD
epth
(k
m)
8.7
6.0 2.5
1.0
km/s(b) S-wave submodel
4.5
2.0
km/s(c) P background model
Dep
th
(km
)
8.7
6.0
Offset (km)0 1.8
2.5
1.0
km/s(d) S background model
Offset (km)0 1.8
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79
Dep
th
(km
)
8.7
6
Offset (km)0 1.8
(a) Standard Kirchhoff
(c) Interferometric migration (IM) (d) Local RTM
(b) Reduced-time migration (RM)
Dep
th
(km
)
8.7
6
Offset (km) 1.80
Comparison with Migration Methods
Local RTM PS Motivation Theory Numerical Tests Summary
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80Offset (km)0 1.8
Local RTM without wavefield separationD
epth
(k
m)
8.7
6
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81Offset (km)0 1.8
Local RTM with wavefield separationD
epth
(k
m)
8.7
6
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82Offset (km)0 1.8
Local RTM using Z component onlyD
epth
(k
m)
8.7
6
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83
Outline
Motivation Theory Numerical Tests
Schlumberger VSP Data Set GOM VSP Data Set
Conclusions
Local RTM PS Motivation Theory Numerical Tests Summary
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84
Dep
th
(m)
Offset (m)4878
0 1829
0
GOM VSP Well and Source LocationSource @150 m offset
2800 m
3200 m
Salt
82 receivers
Local RTM PS Motivation Theory Numerical Tests Summary
@600 m offset @1500 m offset
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85
P-to-S ratio = 2.7
Velocity ProfileS WaveP Wave
Dep
th
(m)
0
45000 5000 0 5000
2800 m
3200 m
Salt
Incorrect velocity model
P-to-S ratio = 1.6
Velocity (m/s) Velocity (m/s)
Local RTM PS Motivation Theory Numerical Tests Summary
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86
Z-Component VSP DataD
epth
(m
)
Traveltime (s)
2652
3887
1.2 3.0
Salt
Direct P
Reflected P
Reverberations
Local RTM PS Motivation Theory Numerical Tests Summary
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87
X-Component VSP DataD
epth
(m
)
Traveltime (s)
2652
3887
1.2 3.0
Salt
Direct P
Reflected P
Reverberations Direct S
Local RTM PS Motivation Theory Numerical Tests Summary
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88
Processing WorkflowOriginal Data
Rotate components
Pick desired events
Median filtering
Migration (KM, RM, IM, RTM)
Local RTM PS Motivation Theory Numerical Tests Summary
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89
Raypath Coverage
2000
4200
0 200
Dep
th
(m)
Migration of PPS
Salt
Offset (m)
39receivers
Local RTM PS Motivation Theory Numerical Tests Summary
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90
Migration of PPS
Salt
RM IM
0 200 0 200
KM
2000
4200
0 200
Dep
th
(m)
Offset (m)Offset (m) Offset (m)
Local RTM PS Motivation Theory Numerical Tests Summary
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91
Migration of PPS
Salt
IM, sediment flood Local RTM
0 200 0 200
RM
2000
4200
0 200
Dep
th
(m)
Offset (m)Offset (m) Offset (m)
Local RTM PS Motivation Theory Numerical Tests Summary
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92
Dep
th
(km
)
3.9
2.9
Offset (m)0 100
(a) Without deconvolution (b) With deconvolution
Offset (m)0 100
150 m Offset LRM Image
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93
600 m Offset LRM Image
Dep
th
(km
)
4.4
2.9
Offset (m)0 600
(a) Without deconvolution (b) With deconvolution
Offset (m)0 600
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94
Dep
th
(km
)
4.4
2.9
Offset (m)0 600
(a) Without deconvolution (b) With deconvolution
Offset (m)0 600
1500 m Offset LRM Image
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95
a) Synthetic b) 150 m offsetReduce time migration
c) 600 m offsetReduce time migration
Reduce Time Migration Image
Salt
2800 m
3200 m
Dep
th
(km
)
4.5
2.4
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96
Summary
• Target oriented!– Only a local velocity model near the well is
needed.– Salt and overburden is avoided.
– Fast and easy to perform.
• Source statics are automatically accounted for.
• Immune to salt-related interbed cross-talk.
Local RTM PS Motivation Theory Numerical Tests Summary
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97
Summary
• Introduction and overview• SSP VSP SWP interferometric
transform• Local reverse time migration: horizontal
reflector imaging• Local reverse time migration: salt flank
imaging with transmitted P-to-S waves• Summary
Overview SSPVSP Local RTM Local RTM PS Summary
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98
Acknowledgements
• Dr. Gerard Schuster and my committee members: Dr. Michael Zhdanov, Dr. Robert smith, Dr. Cari Johnson, Dr. Jianming Sheng for their advice and constructive criticism;
• Scott Leaney and Hornby Brian for their help on modeling;
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99
Acknowledgements
• UTAM friends:– Jianhua Yu and Yonghe Sun on the research;– Jianming Sheng and Min Zhou for their experiences
on interferometric imaging;– Zhiyong Jiang and Ruiqing He for their help on
classes;– Travis Crosby and all UTAM students for their
cheerful attitude; All UTAM sponsors for their support;• Family
– My parents, brother and sister;
• Friends– Liyun Ma, Min Zhou, Jun Wang, Shuqian Dong,
Chaoxiong Ma, who encouraged me to continue on with my research.
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100
Questions?