migration velocity analysis
DESCRIPTION
Migration Velocity Analysis. 01. Outline. Motivation. Estimate a more accurate velocity model for migration. Theory. Tomographic migration velocity analysis. Numerical Results. Conclusions. 02. Motivation. Forward modeling. d = L m. Kirchhoff Migration. m mig = L T d. - PowerPoint PPT PresentationTRANSCRIPT
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Migration Velocity AnalysisMigration Velocity Analysis
01
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OutlineOutline
MotivationMotivationEstimate a more accurate velocity model for migrationEstimate a more accurate velocity model for migration
Tomographic migration velocity analysis Tomographic migration velocity analysis
02
TheoryTheory
Numerical ResultsNumerical Results
ConclusionsConclusions
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Motivation
03
d = L m
mmig = LT d
Forward modeling
Kirchhoff Migration
Function of velocity: LT (s)
Inaccurate velocity model
mmig = LT d
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Motivation
04
True velocity model
True velocity model
Kirchhoff Migration Image
Inaccurate velocity model
Inaccurate velocity model
Kirchhoff Migration Image
Goal of MVA:To get a more accurate velocity model
Structure error
Position error
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OutlineOutline
MotivationMotivationEstimate a more accurate velocity model for migrationEstimate a more accurate velocity model for migration
Tomographic Migration Velocity AnalysisTomographic Migration Velocity Analysis
05
TheoryTheory
Numerical ResultsNumerical Results
ConclusionsConclusions
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Theory
06
The fundamental principle underlying MVA is that the migration image of the same reflector should be the same for different source, when using the correct velocity, so pre-stack common image gather (CIG) provides the information of whether the migration velocity is correct and how far away it is from the true velocity.
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Theory
07
Common Image Gather ( CIG)
different CSGs
CSG #1
CSG #2
CSG #3
Point scatterer
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Theory
08
Common Image Gather ( CIG)
Prestack migration
s
KM of CSG #1
x
z
x0
x
z
KM of CSG #2
x0
x
z
KM of CSG #3
x0
CIG
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Theory
09
Tomographic MVAxx0
z
xx0
z
s
z
CIG
Flat
xx0
z
Correct Velocity
x
z
2000 m/s
x0
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Theory
10
Tomographic MVA
Curved
Incorrect Velocity
1500 m/s
x
z
x0
xx0
z
s
z
CIG
xx0
z z
xx0
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Theory
11
Offset (km) 1
CIG
-1
CIG
Offset (km) 1-1
Tomographic MVA
Hyperbolic approximation
Zh2 = Z0
2 + A h2
picking depth,
Zh
Zh
Z0
zero-offset depth,Z0
Depth residual reference depth
Usually choose Z0 as Zref
ΔZ = Zh - Zref Zref
x0
h
offset, h
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Theory
12
Tomographic MVA
Convert depth residual to time residual
x0xs xgFind the source-receiver pair by ray tracing to obey Snell’s lawθ1 θ2
x0xs xg
R reflector with reference depth Zref
R’ reflector with picked depth Zh t’ = LSR’ s + LRG st = LSR s + LRG s
Δt = t’ - t
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Theory
13
For a small slowness perturbation
traveltime, raypath operator, background slowness.
t = L st L s
Δs
Δt = t’-t0 = LΔs = L(s’-s0)Parameterize the model as a grid of cells
traveltime residual for the raypath , slowness purturbation in grid cell
Δti = Σ Δsj Δlij
n
j=1Δti i Δsj
j
Update the slowness with a steepest descent method
Back project along the raypaths to get
Δti Δsj
sj(k+1) = sj
(k+1) – α Δsj(k+1)
Tomographic MVAUpdate the slowness
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Theory
14
Misfit function
Iteration will stop when all curved events in CIG are flatten.
picked depth residual for offset in CIG of the iteration
Tomographic MVA
Fmisfit = Σ Σ (Δzij )2 i=1 j=1
m n(k) (k)
Δzij j i k(k)
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15
Migration velocity model s0
TheoryTheory
Predict travel time by eikonal solver
Pre-stack KM , form CIGs
Pick the reference depth residual (usually zero-offset)
Find ray paths connecting the reflector to both S and R positions
Convert depth residual to travel time residual
Update velocity model by back projecting the traveltime residuals along the raypaths.
Work Flow:
Migration velocity model sk
Pick the depth residual automatically
Observed data
All events are flattened?
Y
MVA finished !
N
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OutlineOutline
MotivationMotivationEstimate a more accurate velocity model for migrationEstimate a more accurate velocity model for migration
Tomographic migration velocity analysis Tomographic migration velocity analysis
16
TheoryTheory
Numerical ResultsNumerical Results
ConclusionsConclusions
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Numerical Results
17
2D Synthetic Model
KM image CIGTrue velocity model
H. Sun. 1999
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Numerical Results
18
2D Synthetic Model
H. Sun. 1999
Homogeneous velocity model KM image CIG
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Numerical Results
19
2D Synthetic Model
H. Sun. 1999
Final updated velocity model KM image CIG
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Initial Migration VelocityInitial Migration Velocity
0000
1818
1.51.5
Horizontal Distance (km)Horizontal Distance (km)
Dep
th (
km)
Dep
th (
km) 2.12.1
1.51.5
(km
/s)
(km
/s)
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KM Image with Initial VelocityKM Image with Initial Velocity0000
18 km18 km
1.51.5
Dep
th (
km)
Dep
th (
km)
00
1.51.5
Dep
th (
km)
Dep
th (
km)
KMVA Velocity Changes in the 1st IterationKMVA Velocity Changes in the 1st Iteration
5050
00
(m
/s)
(m /s
)
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KM Image with Initial VelocityKM Image with Initial Velocity
KM Image with Updated VelocityKM Image with Updated Velocity
9 km9 km
12601260
De
pth
(m
)D
ep
th (
m)
2 km2 km
10701070
12601260
De
pth
(m
)D
ep
th (
m)
10701070
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KMVA CIGs with Initial VelocityKMVA CIGs with Initial Velocity
00
1.51.5
Dep
th (
km)
Dep
th (
km)
KMVA CIGs with Updated VelocityKMVA CIGs with Updated Velocity
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0000
18 km18 km
1.51.5
Dep
th (
km)
Dep
th (
km)
00
1.51.5
Dep
th (
km)
Dep
th (
km)
KMVA Velocity Changes in the 1st Iteration (CPU=6)KMVA Velocity Changes in the 1st Iteration (CPU=6)
5050
00
(m
/s)
(m /s
)
WMVA Velocity Changes in the 1st Iteration (CPU=1)WMVA Velocity Changes in the 1st Iteration (CPU=1)
5050
00
(m
/s)
(m /s
)
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WM Image with Initial VelocityWM Image with Initial Velocity
WM Image with Updated VelocityWM Image with Updated Velocity
9 km9 km
12601260
De
pth
(m
)D
ep
th (
m)
2 km2 km
10701070
12601260
De
pth
(m
)D
ep
th (
m)
10701070
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WMVA CIGs with Initial VelocityWMVA CIGs with Initial Velocity
00
1.51.5
Dep
th (
km)
Dep
th (
km)
WMVA CIGs with Updated VelocityWMVA CIGs with Updated Velocity
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KM Image with Initial VelocityKM Image with Initial Velocity 9 km9 km
12601260
De
pth
(m
)D
ep
th (
m)
2 km2 km
10701070
KM Image with KMVA Updated VelocityKM Image with KMVA Updated Velocity
12601260
De
pth
(m
)D
ep
th (
m)
10701070
KM Image with WMVA Updated VelocityKM Image with WMVA Updated Velocity
12601260
De
pth
(m
)D
ep
th (
m)
10701070
![Page 28: Migration Velocity Analysis](https://reader035.vdocuments.us/reader035/viewer/2022062410/568159aa550346895dc70d25/html5/thumbnails/28.jpg)
OutlineOutline
MotivationMotivationEstimate a more accurate velocity model for migrationEstimate a more accurate velocity model for migration
Tomographic migration velocity analysis Tomographic migration velocity analysis
26
TheoryTheory
Numerical ResultsNumerical Results
ConclusionsConclusions
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27
• Pre-stack migration with inaccurate velocity can bring curved events in CIGs, which provides the opportunity for migration velocity analysis.
• Iterative tomographic MVA can estimate better migration velocity and improve the migration image.
ConclusionsConclusions
• Question: what are the advantages and disadvantages of migration velocity analysis compared to velocity estimation in data domain ?
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Numerical Results
20
2D Field Data
H. Sun. 1999
00
00
18181.51.5
Initial migration velocity from NMOInitial migration velocity from NMO
Dep
th (
km
)D
epth
(k
m)
2.12.1
1.51.5
(k
m /s
)(k
m /s
)
Horizontal distance (km)Horizontal distance (km)
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Numerical Results
21
2D Field Data
H. Sun. 1999
00
00
18181.51.5
KM image with the initial velocityKM image with the initial velocity
Dep
th (
km
)D
epth
(k
m)
Horizontal distance (km)Horizontal distance (km)
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Numerical Results
22
2D Field Data
H. Sun. 1999
00
1.51.5
KM CIGs with the initial velocityKM CIGs with the initial velocityD
epth
(k
m)
Dep
th (
km
)
1.21.2
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Numerical Results
23
KM Image with Initial VelocityKM Image with Initial Velocity
00
00
1.51.5
Dep
th (
km)
Dep
th (
km)
00
1.51.5
Dep
th (
km)
Dep
th (
km)
KM Image with Updated VelocityKM Image with Updated Velocity 1818
![Page 34: Migration Velocity Analysis](https://reader035.vdocuments.us/reader035/viewer/2022062410/568159aa550346895dc70d25/html5/thumbnails/34.jpg)
Numerical Results
24
KM Image with Initial VelocityKM Image with Initial Velocity
KM Image with Updated VelocityKM Image with Updated Velocity
9 km9 km
12601260
Dep
th (
m)
Dep
th (
m)
2 km2 km
10701070
12601260
Dep
th (
m)
Dep
th (
m)
10701070
![Page 35: Migration Velocity Analysis](https://reader035.vdocuments.us/reader035/viewer/2022062410/568159aa550346895dc70d25/html5/thumbnails/35.jpg)
Numerical Results
25
KMVA CIGs with Initial VelocityKMVA CIGs with Initial Velocity
00
1.51.5
Dep
th (
km
)D
epth
(k
m)
KMVA CIGs with Updated VelocityKMVA CIGs with Updated Velocity