Transcript No Slide Title

Reverse-Time Migration =
Generalized Diffraction
Stack Migration
G.T. Schuster
Geology and Geophysics Department
University of Utah
OUTLINE
Motivation
Gen. Diffraction Stack Mig. Theory
Implications
Summary
Migration Accuracy vs $$$
Full-Wave
Wavefront
No Approx.
Ray-Beam
Kirchhoff
Phase-Shift
Expense
Multiple Arrival
Anti-aliasing
OUTLINE
Motivation
Gen. Diffraction Stack Mig. Theory
Implications
Summary
Born Forward Modeling
s
r
x
Forward Modeling Kernel
G(s|x)m(x)G(x|r) =d(r)
Reverse Time Migration
Forward Modeling Kernel*
*
*
*
[G(s|x) G(x|r) ] d(r)=
w Forward Modeling Kernel
w
traces
G(s|x)*[G(x|r) * d(r) ] =
Direct wave
Backpropagated
T=0
traces
w
w
*
m(x)
m(x)
Gen. Diffraction. Stack Migration
Forward Modeling Kernel
*
*
[G(s|x) G(x|r) ] d(r)=
w Forward Modeling Kernel
traces
w
*
m(x)
Gen. Diffraction. Stack Migration
Forward
Forward Modeling
Modeling Kernel
Kernel
*
*
*
[G(s|x)* G(x|r)
[g(s|x)
g(x|r) ]] d(r)=
d(r) = m(x)
m(x)
w Forward Modeling Kernel dot-product
w
traces Data
T=0
s
r
x
Gen. Diffraction. Stack Migration
Forward
Focusing
Modeling
KernelKernel
*
*
*
[G(s|x)* G(x|r)
[g(s|x)
g(x|r) ]] d(r)=
d(r) = m(x)
m(x)
w Forward Focusing
w
Modeling Kernel dot-product
traces Data
T=0
s
r
x
1. Compute Kernel by Src at Recs
g(s|x) * g(x|r)
r*
x
*
r
s
g(s|x) * x
g(x|r)
g(r|x)
2. Compute Kernel by Src at Depth
g(s|x) * g(x|r)
r*
x
g(x|r)
g(s|x) * g(x|r)
x
*
r
OUTLINE
Motivation
Gen. Diffraction Stack Mig. Theory
Implications
1. Target Oriented RTM
Summary
IMPLICATION #1
Target Oriented RT Migration
*
g
Perform Kirchhoff Migration
Above Salt
SALT
Perform FD Solves under Salt
Velocity Model
0 km
Depth (km)
6 km/s
Offset = .7 km
5 km/s
1.2 km
CSG
Time (s)
0s
1.0 s
0 km
X (km)
4.5 km
GDS Migration
0s
CSG
w/o Direct
1.0 s
0s
CSG
Migration
Operator
Z=.4 km
1.0 s
0 km
Migration
Image
1.2 km
g(s|x)* g(r|x)
0 km
4.5 km
GDS Migration
0s
CSG
w/o Direct
1.0 s
0s
CSG
Migration
Operator
Z=.4 km
1.0 s
0 km
Migration
Image
1.2 km
0 km
4.5 km
g(s|x)* g(r|x)
GDS Migration
0s
CSG
CSG
w/o Direct
1.0 s
0s
CSG
Migration
Operator
Z=.4 km
1.0 s
0 km
Migration
Image
1.2 km
0 km
4.5 km
GDS Migration
0s
CSG
CSG
w/o Direct
1.0 s
0s
CSG
Migration
Operator
Z=.4 km
1.0 s
0 km
Migration
Image
1.2 km
0 km
4.5 km
OUTLINE
Motivation
Gen. Diffraction Stack Mig. Theory
Implications
2. Focusing Operator from Data
Summary
IMPLICATION #2
Exact Migration Operators from VSP
*
SALT
g(s|x)
IMPLICATION #2
Exact Migration Operators from VSP
*
g(r|x) g(s|x)
*
SALT
Exxon RVSP Data
0s
Direct
Reflections
Multiples
Z = .18 km
0.5 s
0 km
Focusing
Operator
g(s|x)
*
g(x|r)
X
0.2 km
Exxon RVSP Data
0s
Direct
Reflections
Multiples
Z = .18 km
0.5 s
0 km
X
0.2 km
0s
Focusing
Kirchhoff
summation curve
Operator
g(s|x)
*
g(x|r)
0 km
Multiple summation
0.5 s curve
X
0.2 km
Exxon RVSP Data
Prim Refl. Kirchhoff
Focusing Operator
0.2 s
0.28 s
0 km
X
Interbed
InterbedMultiple
MultipleRefl.
Refl. Kirchhoff
FocusingOperator
Operator
0.2 km
0.31 s
0.37 s
0 km
X
0.2 km
What about focusing away from well?
?
Prim Refl. Kirchhoff
Focusing
Operator
Prim Refl. Kirchhoff
Focusing
Operator
0 km
0 km
OUTLINE
Motivation
Gen. Diffraction Stack Mig. Theory
Implications
3. COG RTM operator
Summary
IMPLICATION #3
Wave Equation COG Migration Operators
g(r|x) g(x|s)
*
*
SALT
Velocity Model
0 km
Depth (km)
6 km/s
Offset = .7 km
5 km/s
1.2 km
Time (s)
0s
1.0 s
0 km
X (km)
4.5 km
COG Migration
Offset = .7 km
0s
COG
1.0 s
0s
COG
Migration
Operator
Z=.4 km
1.0 s
0 km
Migration
Image
1.2 km
0 km
4.5 km
COG Migration
Offset = .7 km
0s
COG
1.0 s
0s
COG
Migration
Operator
Z=.4 km
1.0 s
0 km
Migration
Image
1.2 km
0 km
4.5 km
OUTLINE
Motivation
Gen. Diffraction Stack Mig. Theory
Implications
4. Efficient Wavefront Migration
Summary
IMPLICATION #4
Efficient RT Migration Operators
*
SALT
FD only in
expanding box
IMPLICATION #4
Standard FD
0
1.5 km
0
4.5 km
Wavefront FD
FD/ Wavefront FD Cost
FD/ Wavefront FD Cost
45
5
500
3000
# Gridpts along side
Model
0
2.2 km/s
1.5 km/s
1.8 km/s
1.5 km
Wavefront Migration Image
0
1.5 km
0
4.5 km
Reverse Time Migration
0
2.2 km/s
1.5 km/s
1.8 km/s
1.5 km
Wavefront Migration Image
0
1.5 km
0
4.5 km
OUTLINE
Motivation
Gen. Diffraction Stack Mig. Theory
Implications
5. Filtering RTM operator
Summary
IMPLICATION #5
Filtering of Wave Equation
Migration Operators
Truncation: anti-aliasing
SALT
IMPLICATION #5
Filtering of Wave Equation
Migration Operators
Slant stack
SALT
Filtering of Wave Equation Migration Operators
COG Mig. Op.
Filtered COG Mig. Op.
0s
Z=70 m
Time (s)
1.0 s
0 s0
km
X (km)
4.5 km
0 km
X (km)
4.5 km
Z=270 m
1.0 s
0s
Z=1190 m
1.0 s
0 km
X (km)
4.5 km
0 km
X (km)
4.5 km
Filtering of Wave Equation Migration Operators
COG Mig. Op.
Filtered COG Mig. Op.
0s
Z=70 m
Time (s)
1.0 s
0s
Z=270 m
1.0 s
0 s0
km
X (km)
4.5 km
0 km
X (km)
4.5 km
Z=1190 m
1.0 s
0 km
X (km)
4.5 km
0 km
X (km)
4.5 km
Filtering of Wave Equation Migration Operators
COG Mig. Op.
Filtered COG Mig. Op.
0s
Z=70 m
Time (s)
1.0 s
0s
Z=270 m
1.0 s
0s
Z=1190 m
1.0 s
0 km
X (km)
4.5 km
0 km
X (km)
4.5 km
Summary
• RTM = Gen. Diffraction Stack Migration
• Wave Equation Migration of COG/CAG
• Filtering of Focusing Kernels
• Wavefront Migration
• Any Modeling Method can be Used
• Target RTM
• Data-Driven Focusing Operators