Transcript d(M|s) - University of Utah`s Tomography and Modeling/Migration

Seeing the Invisible with Seismic
Interferometry: Datuming and
Migration
Gerard T. Schuster, Jianhua Yu,
Xiao Xiang and Jianming Sheng
University of Utah
Outline
Seismic Interferometry
Interferometric Datuming
Interferometric Tomography
Interferometric Migration
Conclusions
Constructive Interference
Wave 1
=
Wave 2
Destructive Interference
Wave 1
=
Wave 2
iwt1
e
iwt1
e
+ eiwt 2
= 2
e
-iwt 2
=
e
iw(t - t )
1
- 2cos(w(t1 - t ))
2
Interferometry uses interference patterns or time differences
2
Pattern
IsInterference
the Lens Broken?
Optical
Optical Lens
Lens
LASER
t
Buried sources redatumed to target
LASER
Interferogram only sensitive to lens geometry
Pattern
IsInterference
the Lens Broken?
Optical
Optical Lens
Lens
LASER
t
Buried sources redatumed to target
LASER
Interferogram only sensitive to lens geometry
Outline
Seismic Interferometry
Interferometric Datuming
Interferometric Tomography
Interferometric Migration
Conclusions
Time
ToGoal:
Remove
Transform
Kinematics
Ghost
of Traveling
Reflections
ininto
Uninteresting
Primary
Medium Time
Reflection
Shift Traces
Traveltimes
by Direct Times
Ghost
Direct
TM
{
BASIN
Direct
Ghost
LASER
Uninteresting Part
of Medium
Time
ToGoal:
Remove
Greens
Transform
Thm:
Kinematics
Every
Ghost
of
Point
Traveling
Reflections
on Surface
ininto
Uninteresting
acts
Primary
as a
Medium Time
Reflection
Secondary
Shift Traces
Traveltimes
Source
by Direct Times
Direct
Ghost
Direct
Ghost
Uninteresting Part
of Medium
Time
ToGoal:
Remove
Greens
Transform
Thm:
Kinematics
Every
Ghost
of
Point
Traveling
Reflections
on Surface
ininto
Uninteresting
acts
Primary
as a
Medium Time
Reflection
Secondary
Shift Traces
Traveltimes
Source
by Direct Times
Direct
Ghost
Direct
Source Moved to Surface. Statics Eliminated
Uninteresting Part
of Medium
Replace Time Shifting by Crosscorrelation
Time
d(M|s)
M
s
d(g|s)
g
Uninteresting Part
of Medium
Replace Time Shifting by Crosscorrelation
Time
d(M|s)
M
s
d(g|s)
g
Uninteresting Part
of Medium
Replace Time Shifting by Crosscorrelation
Time
d(M|s)
M
s
d(g|s)
g
Uninteresting Part
of Medium
Replace Time Shifting by Crosscorrelation
Time
d(M|s)
M
s
d(g|s)
g
Uninteresting Part
of Medium
Replace Time Shifting by Crosscorrelation
(g,M,s
,s)= d(M|s)* d(g|s)
Time
s
d(M|s)
M
d(g|s)
g
Every VSP source at different S reflects off M
And recorded at g
s
Uninteresting Part
of Medium
Replace Time Shifting by Crosscorrelation
(g,M,s
,s)= d(M|s)* d(g|s)
Time
s
d(M|s)
M
d(g|s)
g
Every VSP source at different S reflects off M
And recorded at g
s
Uninteresting Part
of Medium
Time
Replace Time Shifting by Crosscorrelation
(g,M,s
,s)= d(M|s)* d(g|s)
s
d(M|s)
M
d(g|s)
g
Every VSP source at different S reflects off M
And recorded at g
We accidentally found specular ray for given (M,g),
& stationary phase says this is dominant
contribution.
Uninteresting
Part
of Medium
s
Time
Replace Time Shifting by Crosscorrelation
(g,M,s
,s)= d(M|s)* d(g|s)
s
d(M|s)
M
d(g|s)
g
Every VSP source at different S reflects off M
And recorded at g
Above Datuming Formula = CSG
Uninteresting
for source atPart
M and
receiver at g of Medium
s
Interferometric VSP Datuming


Eliminates well statics and
uninteresting parts of the medium.
Raise buried src to surface.
(g,M,s
,s)=
d(M|s)* d(g|s)
s
Interferometric
VSP Datuming
Extrapolation Deconvolution
by LeastED
Squares
Data with source at surface
T
Data with source at depth
d0 = E d z
T
-1 T
d0 = [E E] E dz
Natural extrapolation operator
(g,M,s
,s)=
d(M|s)* d(g|s)
s
Interferometric Deviated VSP
Datuming


Eliminates well statics and
uninteresting parts of the medium.
Lower surface src to well.
(g,M,s
,s)=
d(M|s)* d(g|s)
s
Interferometric CDP Datuming


Eliminates src/rec statics and
uninteresting parts of the medium.
Lower buried src to reference inter.
(g,M,s
,s)=
d(M|s)* d(g|s)
s
reference
reflector
reference
reflector
Outline
Seismic Interferometry
Interferometric Datuming
Interferometric Tomography
Interferometric Migration
Conclusions
Outline
Seismic Interferometry
Interferometric Datuming
Interferometric Tomography
Interferometric Migration
Conclusions
Time
Replace Time Shifting by Crosscorrelation
(g,M,s
,s)= d(M|s)* d(g|s)
s
d(M|s)
Shot gather for source
at M and geophone
d(g|s)at g
M
g
Every surface
Above pt
Formula
at different
= CSG
M for
acts
Uninteresting
source
as secondary
at M Part
and
source
To contribute
receiver attog’gof Medium
s
m(x)=
g
Time
M
(g, M, t gx+ t Mx )
M
g
X = trial image pt.
Above pt
Formula
= CSG
Uninteresting
source
at M Part
and
Every surface
at different
M for
acts
as secondary
source
receiver attog’gof Medium
To contribute
s
Outline
Seismic Interferometry
Interferometric Datuming
Interferometric Tomography
Interferometric Migration: Exxon VSP
Conclusions
30
Time (s)
0
0.3
Depth (ft)
900
Raw Data(CRG15)
30
Time (s)
0
0.3
Depth (ft)
900
Ghosts
Depth (ft)
200
1300
0
X (ft)
400
Standard mig
0
X (ft)
400
Xcorr. mig
Outline
Seismic Interferometry
Interferometric Datuming
Interferometric Tomography
Interferometric Migration: CDP
Conclusions
X (km)
3
Shots: 280
Shot interval: 10 m
Receivers: 300
Receiver interval: 10 m
Temporal interval:1ms
Depth (km)
0
0
1.8
Salt model
X (km)
Time (s)
0
0
3
CSG 100
3
X (km)
3
Depth (km)
0
0
1.8
Velocity model with inaccurate salt boundary,
oceam bottom, and overburden
X (km)
Depth (km)
0
0
1.8
Kirmig with inaccurate salt boundary, ocean
bottom, and overburden
3
X (km)
Depth (km)
0
0
1.8
RT mig with inaccurate salt boundary, ocean
bottom, and overburden
3
X (km)
3 0
X (km)
3 0
X (km)
Depth (km)
0
0
1.8
Standard mig
Standard mig
Correct velocity
Incorrect velocity
RT mig
3
Summary
Seismic Interferometry
d(g)
d(g’)*
d(g) d(g’)*
Summary
Seismic Interferometry
Time Shift = Remove Uninteresting
Kinematics+Statics
d(g)
d(g’)*
d(g) d(g’)*
Datuming
Migration
Tomography
Issues
1. VSP Natural Home for Interferometry
Eliminates statics+overburden. Widens coverage
2. CDP Interferometry
Effective if Guide Star/Reference Interface Known
Less Effective if Reference not Known
3. Interferometric Datuming
Naturally Datumed Data can be Filtered
ID vs ED
Outline
Seismic Interferometry
Interferometric Datuming
Interferometric Tomography
Interferometric Migration: CDP
Conclusions
Salt Flank Imaging PS Waves
Goal: Image Interface by PS Transmitted Waves
Time
d(M|s)
M
PS
Uninteresting Part
of Medium
P
d(g|s)
g
PP
(g,M) = d(M|s) d(g|s)*
iwt+iwt
=e
PS
i w (t – t)
s
=e
e
-i w t - i w t
PP
Goal: Image Interface by PS Transmitted Waves
Time
d(M|s)
M
PS
Uninteresting Part
of Medium
P
s
d(g|s)
g
PP
d(M|s) d(g|s)*
(g,M) =
s
Goal: Image Interface by PS Transmitted Waves
Time
d(M|s)
M
PS
Uninteresting Part
of Medium
P
s
d(g|s)
g
PP
d(M|s) d(g|s)*
(g,M) =
s
Goal: Image Interface by PS Transmitted Waves
Time
d(M|s)
d(g|s)
g
M
PP
PS
Uninteresting Part
of Medium
P
x
Datuming
Unique Specular Point Snell’s Law OK
s
(g,M) e
m(x) =
s
d(M|s) d(g|s)*
(g,M) =
Migration
g,M
–
i w (t – t)
x x
Interferometric PS Datuming


Eliminates src/rec statics and
uninteresting parts of the medium.
Raise buried src to interesting inter.
(g,M) e
m(x) =
g,M
–
i w (t – t)
x x